SyncVals · Trajectory

neonatal-drug-exposure-nlme

claude-code claude-opus-4-8 ✗ failed BAD_FAILURE ↑ View task

Solved from the instruction alone, tests/ and solution/ were withheld from the agent's workspace and restored only for grading.

Reward = tests/test.sh exit code (0 → resolved); the classification below is post-hoc and cannot change it.

Classification , post-hoc; cannot change the reward

BAD_FAILUREThe task is at fault, underspecified/contradictory instruction, brittle/flaky tests, or tests demanding undiscoverable behavior.

SubtypeUnderspecified Instruction - Hidden Evaluation Criteria

EvidenceTest execution shows agent produced all required output files with correct schema and statistics (base logL=-505, cl_wt=-479, full=-437 with AIC strictly decreasing; LR p-values 8e-13 and 6e-19 both <1e-6; correlations 0.814 and 0.971 exceeding 0.55 and 0.75 thresholds). However, the task fails on llm_judge.py (tests/llm_judge.py:45-50) which scores plots against an inaccessible rubric (tests/rubric.json). The instruction specifies plots must have 'visible legend, axes labelled with units, descriptive title' but these are vague qualitative criteria. The agent cannot access the rubric (forbidden by FORBIDDEN_ACCESS_PATTERNS in test_outputs.py:60-67) and has no way to know what the LLM judge will accept beyond generic plot best-practices. The grading pipeline (test.sh:38-43) runs pytest (passes per output), then llm_judge (fails per reward=0.0), indicating plot quality issues that the agent couldn't have anticipated without seeing the rubric.

Root causeThe task requires subjective plot quality assessment by an LLM judge using a hidden rubric that is explicitly forbidden from the agent's access (tests/rubric.json is in /tests directory which agents cannot read). The instruction provides only vague plot specifications that leave interpretation to the judge, making it impossible for the agent to implement correctly without seeing the actual rubric.

RecommendationFix by: (1) Include the complete rubric criteria in instruction.md so the agent knows exactly what plots must contain (e.g., specific axis labels, legend placement, color scheme expectations), or (2) Remove the llm_judge step and rely only on pytest structural/statistical checks which the agent can understand and satisfy, or (3) Provide example plots in the instruction showing what passes vs fails the LLM judge assessment."

Trajectory

Tool-by-tool agent trajectory

169 tool calls · 3 tool types · 169 steps

Work only in `/app/analysis.jl`. The bundled inputs are: - `/app/Phenobarb.csv` - `/app/dataset_manifest.json` Do not read from `/tests` or `/solution`. ## Background `Phenobarb.csv` is a real neonatal pharmacokinetics study of preterm infants given intravenous phenobarbital. Each baby contributes a small number of serum concentration measurements interleaved with dose events. A neonatology analytics team wants a population PK fit that estimates clearance and volume of distribution at the population level and per subject, tests whether birth weight and Apgar category shift those parameters, and produces diagnostic plots for the clinical report. Your `analysis.jl` will be executed on a held-out perturbation of `Phenobarb.csv` with a different number of subjects and rows. Derive all counts from the CSV at runtime , do not hardcode subject or row counts. ## Input semantics `Phenobarb.csv` has exactly these columns: - `Subject` , integer subject identifier - `Wt` , birth weight in kg - `Apgar` , Apgar score at 5 minutes, integer 1 through 10 - `ApgarInd` , two-level factor, either `< 5` (asphyxiated) or `>= 5` (normal) - `time` , time in hours since first event for that subject - `dose` , dose in mg at this event row, missing for sample rows - `conc` , serum concentration in mg/L at this event row, missing for dose rows A row is a dose event when `dose` is non-missing; a sample event when `conc` is non-missing. Do not drop dose rows. Use `dataset_manifest.json` as the contract source for required output filenames and exact column order for every output CSV. ## Required modelling Fit a one-compartment open PK model with first-order elimination at the population level. Model clearance and volume on the log scale (`lCl`, `lV`). Each subject has random intercepts on `lCl` and `lV` with a diagonal (no correlation) random-effect covariance structure. Do the covariate build-up in this exact sequence: 1. **Base model** (`base`): `lCl ~ 1`, `lV ~ 1` 2. **cl_wt model** (`cl_wt`): add birth weight as fixed effect on `lCl` 3. **Full model** (`full`): keep weight on `lCl`, add `ApgarInd` on `lCl`, add weight on `lV` Each step must yield a strictly lower AIC than the step before it. The likelihood-ratio p-value for both step 1→2 and step 2→3 must be below 1e-6. ## Required output files All files go into `/app/output/`. Use exact filenames from `dataset_manifest.json`. ### Tables 1. **`model_summary.json`** , JSON for the final (full) model with exactly: - `n_obs` , integer, count of non-missing `conc` rows - `n_subjects` , integer, count of distinct Subject values - `fixed_effects` , array of objects with fields `term`, `estimate`, `std_error`, `t_value`, `df`. Terms in this exact order: `lCl.(Intercept)`, `lCl.Wt`, `lCl.ApgarInd>= 5`, `lV.(Intercept)`, `lV.Wt` - `random_effects_sd` , object with positive numeric fields `lCl`, `lV`, `Residual` - `logLik`, `aic`, `bic` , numeric scalars for the final model 2. **`lrt_chain.csv`** , columns (in order): `step, model_name, n_params, logLik, AIC, BIC, LR_stat, LR_pvalue` - `step`: 1, 2, 3; `model_name`: `base`, `cl_wt`, `full` - `LR_stat` and `LR_pvalue` are empty/missing for step 1 3. **`per_subject_params.csv`** , columns: `Subject, Cl, V` - Empirical-Bayes estimates in native units (not log scale), all positive - Sorted by integer `Subject` ascending 4. **`obs_vs_pred.csv`** , columns: `Subject, time, conc_obs, pred_pop, pred_ind` - One row per non-missing concentration observation - `pred_pop`: population prediction (zero random effects) - `pred_ind`: individual prediction (subject empirical-Bayes estimates) - `cor(conc_obs, pred_ind)` must exceed 0.75; `cor(conc_obs, pred_pop)` must exceed 0.55 - Sorted by Subject then time 5. **`residual_diagnostics.csv`** , columns: `Subject, time, fitted_ind, resid, std_resid` - `resid = conc_obs - fitted_ind` - `std_resid = resid / σ` where `σ` is the estimated residual SD …[truncated]

Let me start by exploring the input files and understanding what's needed.

bash

ls /app/ && echo "---" && cat /app/dataset_manifest.json && echo "---" && head -30 /app/Phenobarb.csv

output

Phenobarb.csv
analysis.jl
dataset_manifest.json
output
---
{
  "dataset_name": "Phenobarb",
  "source": "nlme::Phenobarb (Pinheiro & Bates 2000, Mixed-Effects Models in S and S-PLUS, section 6.4)",
  "columns": {
    "Subject": "integer subject identifier",
    "Wt": "birth weight in kg",
    "Apgar": "Apgar score at 5 minutes, 1 through 10",
    "ApgarInd": "Apgar category factor, '< 5' or '>= 5'",
    "time": "hours since first event",
    "dose": "dose in mg, present on dose rows only",
    "conc": "serum concentration in mg/L, present on sample rows only"
  },
  "required_outputs": {
    "model_summary": "model_summary.json",
    "lrt_chain": "lrt_chain.csv",
    "per_subject_params": "per_subject_params.csv",
    "obs_vs_pred": "obs_vs_pred.csv",
    "residual_diagnostics": "residual_diagnostics.csv",
    "plot_conc_profile": "plot_conc_profile.png",
    "plot_per_subject_fit": "plot_per_subject_fit.png",
    "plot_covariate_effect": "plot_covariate_effect.png",
    "plot_obs_vs_pred": "plot_obs_vs_pred.png",
    "plot_residuals": "plot_residuals.png"
  },
  "column_order": {
    "lrt_chain": ["step", "model_name", "n_params", "logLik", "AIC", "BIC", "LR_stat", "LR_pvalue"],
    "per_subject_params": ["Subject", "Cl", "V"],
    "obs_vs_pred": ["Subject", "time", "conc_obs", "pred_pop", "pred_ind"],
    "residual_diagnostics": ["Subject", "time", "fitted_ind", "resid", "std_resid"]
  },
  "model_chain": {
    "step_1": "base: lCl + lV ~ 1",
    "step_2": "cl_wt: lCl ~ Wt, lV ~ 1",
    "step_3": "full: lCl ~ Wt + ApgarInd, lV ~ Wt"
  }
}
---
"Subject","Wt","Apgar","ApgarInd","time","dose","conc"
1,1.4,7,">= 5",0,25,
1,1.4,7,">= 5",2,,17.3
1,1.4,7,">= 5",12.5,3.5,
1,1.4,7,">= 5",24.5,3.5,
1,1.4,7,">= 5",37,3.5,
1,1.4,7,">= 5",48,3.5,
1,1.4,7,">= 5",60.5,3.5,
1,1.4,7,">= 5",72.5,3.5,
1,1.4,7,">= 5",85.3,3.5,
1,1.4,7,">= 5",96.5,3.5,
1,1.4,7,">= 5",108.5,3.5,
1,1.4,7,">= 5",112.5,,31
2,1.5,9,">= 5",0,15,
2,1.5,9,">= 5",2,,9.7
2,1.5,9,">= 5",4,3.8,
2,1.5,9,">= 5",16,3.8,
2,1.5,9,">= 5",27.8,3.8,
2,1.5,9,">= 5",40,3.8,
2,1.5,9,">= 5",52,3.8,
2,1.5,9,">= 5",63.5,,24.6
2,1.5,9,">= 5",64,3.8,
2,1.5,9,">= 5",76,3.8,
2,1.5,9,">= 5",88,3.8,
2,1.5,9,">= 5",100,3.8,
2,1.5,9,">= 5",112,3.8,
2,1.5,9,">= 5",124,3.8,
2,1.5,9,">= 5",135.5,,33
3,1.5,6,">= 5",0,30,
3,1.5,6,">= 5",1.5,,18

bash

wc -l /app/Phenobarb.csv && awk -F',' 'NR>1 {print $1}' /app/Phenobarb.csv | sort -u | wc -l

output

745 /app/Phenobarb.csv
59

bash

cat /app/analysis.jl 2>/dev/null; echo "---"; ls /app/output/ 2>/dev/null

output

# Work only in this file.
#
# Inputs:
#   /app/Phenobarb.csv          , neonatal phenobarbital PK data
#   /app/dataset_manifest.json  , output filename and column contracts
#
# Outputs: write everything to /app/output/
using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions,
      LinearAlgebra, Optim
data_path()     = get(ENV, "PHENOBARB_DATA_PATH",    "/app/Phenobarb.csv")
manifest_path() = get(ENV, "PHENOBARB_MANIFEST_PATH", "/app/dataset_manifest.json")
output_dir()    = get(ENV, "PHENOBARB_OUTPUT_DIR",   "/app/output")

function main()
    out_dir = output_dir()
    mkpath(out_dir)

    # TODO: implement the full three-step NLME covariate chain on the
    # neonatal phenobarbital dataset, write the five output tables listed
    # in the manifest, and render the five diagnostic plots.
    error("analysis.jl is not implemented yet")
end

main()---

Now I understand the structure. Let me plan a pharmacokinetic (PK) one-compartment model fit via maximum likelihood (approximate, using a Laplace-like approach or direct marginal likelihood via numerical integration). The PK model for one-compartment with first-order elimination and IV bolus dosing: - After each dose, concentration is superposition of previous amounts. - C(t) = sum_over_doses[ D_k / V * exp(-ke * (t - t_k)) ] for t >= t_k where ke = Cl / V. For each subject i: - lCl_i = β_Cl_intercept + β_Cl_wt * Wt_i + β_Cl_apgar * I(ApgarInd_i = ">= 5") + η_Cl_i - lV_i = β_V_intercept + β_V_wt * Wt_i + η_V_i - Cl_i = exp(lCl_i), V_i = exp(lV_i) - η_Cl_i ~ N(0, σ²_Cl), η_V_i ~ N(0, σ²_V) , diagonal - conc_obs_ij = C(t_ij; Cl_i, V_i, doses) + ε_ij, ε_ij ~ N(0, σ²) We fit via FOCE or Laplace approximation. For a cleaner implementation, I'll use Laplace approximation: for fixed fixed-effects and variance components, maximize posterior over η for each subject (EB estimates), use the Laplace approximation to compute marginal likelihood. Outer: minimize -2 * logL_marg over (β, σ_Cl, σ_V, σ) Inner: for each subject i, minimize -(log f(y|η) + log f(η)) Given the sample size (~59 subjects), this is feasible. Let me write this carefully. For Laplace approximation: logL_i ≈ log f(y_i | η̂_i, θ) + log f(η̂_i | θ) - 0.5 * log det(H_i / (2π)) where H_i is the Hessian of -(log f(y|η) + log f(η)) w.r.t. η at η̂_i. For 2 random effects per subject, this is tractable. Let me implement this step by step. Given time constraints, I'll use Optim.jl for both inner and outer optimization. Let me use BFGS for the outer loop and BFGS for the inner. The gradient of inner can be computed with finite differences or ForwardDiff... but ForwardDiff isn't listed as available. I'll use numerical derivatives for Hessian. Actually wait , the required packages don't include ForwardDiff. I'll need to do everything with finite differences. Let me code this up. ```julia struct Subject id::Int Wt::Float64 ApgarInd::String doses::Vector{NamedTuple{(:t, :amt), Tuple{Float64, Float64}}} samples::Vector{NamedTuple{(:t, :y), Tuple{Float64, Float64}}} end function predict_conc(t, Cl, V, doses) ke = Cl / V c = 0.0 for d in doses if d.t <= t c += d.amt / V * exp(-ke * (t - d.t)) end end return c end function neg_inner_loglik(η, subj, fixef, apgar_design, wt_cl_eff, wt_v_eff, σCl, σV, σ) # Given η = (η_Cl, η_V), compute -(log f(y|η) + log f(η)) lCl = fixef.cl_int + wt_cl_eff * subj.Wt + apgar_design * fixef.cl_apgar + η[1] lV = fixef.v_int + wt_v_eff * subj.Wt + η[2] Cl = exp(lCl); V = exp(lV) ll = 0.0 for s in subj.samples p = predict_conc(s.t, Cl, V, subj.doses) ll += -0.5*((s.y - p)/σ)^2 - log(σ) - 0.5*log(2π) end ll += -0.5*(η[1]/σCl)^2 - log(σCl) - 0.5*log(2π) ll += -0.5*(η[2]/σV)^2 - log(σV) - 0.5*log(2π) return -ll end # For the full model, the fixef struct has fields: cl_int, cl_wt, cl_apgar, v_int, v_wt # For simpler models, some fields are zero. ``` For the outer loop, we need to parameterize. Let me have a flexible structure. Actually, to keep things clean, I'll have three model-fitting functions, each with a specific parameter vector layout. Let me think about the Laplace computation more carefully. logL_i (marginal) = log ∫ f(y_i|η) f(η|θ) dη Laplace approximation with mode η̂: = log f(y_i|η̂) + log f(η̂|θ) + 0.5*log(2π)*p - 0.5*log det(H) where p is the dimension of η (= 2 here) and H is the Hessian of the negative log joint. So the marginal logL per subject: = -(neg_inner_loglik(η̂)) + 0.5*p*log(2π) - 0.5*log det(H) where neg_inner_loglik at mode is fixed at the minimum. H is computed via finite differences. Let me code this up. I'll need to be careful with numerical stability. For speed, I'll define a reasonable model design and pre-compute matrices. One more concern: AIC and BIC computation. - k = number …[truncated]

Let me examine the data structure more carefully and then design the analysis.

bash

awk -F',' 'NR>1 {print $1, $2, $4}' /app/Phenobarb.csv | sort -u | head -10
echo "---"
awk -F',' 'NR>1 && $7!="" {n++} END {print "N conc obs:", n}' /app/Phenobarb.csv
awk -F',' 'NR>1 && $6!="" {n++} END {print "N dose rows:", n}' /app/Phenobarb.csv
awk -F',' 'NR>1 {print $4}' /app/Phenobarb.csv | sort | uniq -c

output

1 1.4 ">= 5"
10 1.4 ">= 5"
11 1.2 ">= 5"
12 1.3 ">= 5"
13 1.1 ">= 5"
14 1.1 ">= 5"
15 1.3 ">= 5"
16 1.2 ">= 5"
17 1.1 ">= 5"
18 1 ">= 5"
---
N conc obs: 155
N dose rows: 589
    109 "< 5"
    635 ">= 5"

Great, so: - 59 subjects - 155 concentration observations - 589 dose rows - Two Apgar categories Let me now write the full analysis.

Now let me write the full analysis script:

str_replace_based_edit_tool

command: create
path: /app/analysis.jl
file_text: # Work only in this file.
#
# Inputs:
#   /app/Phenobarb.csv          , neonatal phenobarbital PK data
#   /app/dataset_manifest.json  , output filename and column contracts
#
# Outputs: write everything to /app/output/
using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions,
      LinearAlgebra, Optim

data_path()     = get(ENV, "PHENOBARB_DATA_PATH",    "/app/Phenobarb.csv")
manifest_path() = get(ENV, "PHENOBARB_MANIFEST_PATH", "/app/dataset_manifest.json")
output_dir()    = get(ENV, "PHENOBARB_OUTPUT_DIR",   "/app/output")

# -------- Data structures --------

struct SubjData
    id::Int
    Wt::Float64
    ApgarInd::String
    apgar_hi::Float64          # 1 if ">= 5" else 0
    dose_t::Vector{Float64}
    dose_amt::Vector{Float64}
    samp_t::Vector{Float64}
    samp_y::Vector{Float64}
end

function build_subjects(df::DataFrame)
    subs = SubjData[]
    for sid in sort(unique(df.Subject))
        sdf = df[df.Subject .== sid, :]
        wt = Float64(sdf.Wt[1])
        apg = string(sdf.ApgarInd[1])
        apg_dummy = apg == ">= 5" ? 1.0 : 0.0
        dt = Float64[]; da = Float64[]
        st = Float64[]; sy = Float64[]
        for row in eachrow(sdf)
            if !ismissing(row.dose)
                push!(dt, Float64(row.time)); push!(da, Float64(row.dose))
            end
            if !ismissing(row.conc)
                push!(st, Float64(row.time)); push!(sy, Float64(row.conc))
            end
        end
        push!(subs, SubjData(sid, wt, apg, apg_dummy, dt, da, st, sy))
    end
    return subs
end

# -------- PK prediction --------

@inline function predict_conc(t::Float64, Cl::Float64, V::Float64,
                              dose_t::Vector{Float64}, dose_amt::Vector{Float64})
    ke = Cl / V
    c = 0.0
    @inbounds for i in eachindex(dose_t)
        td = dose_t[i]
        if td <= t
            c += dose_amt[i] / V * exp(-ke * (t - td))
        end
    end
    return c
end

# -------- Parameter unpacking --------

struct PKParams
    cl_int::Float64
    cl_wt::Float64
    cl_apgar::Float64
    v_int::Float64
    v_wt::Float64
    σCl::Float64
    σV::Float64
    σ::Float64
end

function unpack_params(model::Symbol, θ::AbstractVector)
    if model == :base
        return PKParams(θ[1], 0.0, 0.0, θ[2], 0.0,
                        exp(θ[3]), exp(θ[4]), exp(θ[5]))
    elseif model == :cl_wt
        return PKParams(θ[1], θ[2], 0.0, θ[3], 0.0,
                        exp(θ[4]), exp(θ[5]), exp(θ[6]))
    elseif model == :full
        return PKParams(θ[1], θ[2], θ[3], θ[4], θ[5],
                        exp(θ[6]), exp(θ[7]), exp(θ[8]))
    else
        error("unknown model $model")
    end
end

npar_total(model::Symbol) =
    model == :base ? 5 : model == :cl_wt ? 6 : 8
nfixed(model::Symbol) =
    model == :base ? 2 : model == :cl_wt ? 3 : 5

# -------- Inner negative joint log-lik --------

@inline function compute_lCl_lV(p::PKParams, s::SubjData)
    lCl = p.cl_int + p.cl_wt * s.Wt + p.cl_apgar * s.apgar_hi
    lV  = p.v_int  + p.v_wt  * s.Wt
    return lCl, lV
end

function neg_joint_loglik(η::AbstractVector, s::SubjData, p::PKParams)
    lCl, lV = compute_lCl_lV(p, s)
    lCl += η[1]; lV += η[2]
    Cl = exp(lCl); V = exp(lV)
    nll = 0.0
    invσ² = 1.0 / (p.σ * p.σ)
    @inbounds for i in eachindex(s.samp_t)
        pred = predict_conc(s.samp_t[i], Cl, V, s.dose_t, s.dose_amt)
        r = s.samp_y[i] - pred
        nll += 0.5 * r * r * invσ²
    end
    n_samp = length(s.samp_t)
    nll += n_samp * (log(p.σ) + 0.5 * log(2π))
    # priors on η
    nll += 0.5 * (η[1] / p.σCl)^2 + log(p.σCl) + 0.5 * log(2π)
    nll += 0.5 * (η[2] / p.σV)^2  + log(p.σV)  + 0.5 * log(2π)
    return nll
end

# -------- Laplace for one subject --------

function laplace_subject(s::SubjData, p::PKParams;
                         η_init::Vector{Float64}=[0.0, 0.0])
    f(η) = neg_joint_loglik(η, s, p)
    res = try
        optimize(f, η_init, BFGS(), Optim.Options(
    
…[truncated]

output

Existing file was successfully overwritten at /app/analysis.jl

bash

cd /app && timeout 290 julia --project=. analysis.jl 2>&1 | tail -100

output

[stderr]
Terminated

The script is too slow. I need to speed things up significantly. Let me: 1. Use a simpler/faster inner optimization (Newton with analytical gradient) 2. Avoid recomputing sqrt(det(H)) when not needed 3. Cache more aggressively 4. Maybe use fewer iterations in outer optimization Let me profile first with a simpler single-subject fit to see where time is going. Actually let me think about the structure. The optimization is nested. The outer loop needs ~100 iterations, each requires O(2n+1) function evaluations (with FD gradient). Each function evaluation requires 59 inner optimizations + 59 Hessian computations. Each inner optimization, with BFGS + FD gradient, probably needs 5-10 iterations * 5 evals per iter = ~50 function calls per inner fit. Plus Hessian = 6 more calls. So ~56 calls to neg_joint_loglik per subject. Per outer f-eval: 59 * 56 = ~3300 calls Per outer iter (17 inner f-evals): 3300 * 17 = ~56000 calls Per fit (100 iters): 5.6M calls Per call: ~20 μs (with predict_conc loops) Total per fit: ~110 s Three fits: 330 s. Right at the boundary. Let me optimize: 1. Use simpler BFGS for inner with very few iterations and a good warm start 2. Reduce outer iterations 3. Use LBFGS or Nelder-Mead and restrict evals Actually, I can compute the inner optimum and Hessian much faster since this is just a 2D problem. Let me use Newton's method with numerical Hessian for the inner , it should converge in very few iterations since we have a good warm start. Or I can make the inner BFGS faster by using a looser tolerance. Let me also cache the η̂ across outer iterations , this is already done. Let me try a different approach , use a very coarse inner tolerance and use Nelder-Mead for outer which is more robust. Actually let me try to make this much much faster. I'll: 1. Precompute dose arrays 2. Write inner loop in a non-allocating way 3. Use Newton's method manually for the 2D inner problem (converges in ~3-5 iters) Let me rewrite the inner Laplace to be more efficient: ```julia function laplace_subject_newton(s, p; η_init=[0.0, 0.0], maxit=20, tol=1e-7) η = copy(η_init) nll_prev = neg_joint_loglik(η, s, p) for it in 1:maxit # Compute gradient via FD ε = 1e-5 e1 = [ε, 0.0]; e2 = [0.0, ε] g1 = (neg_joint_loglik(η .+ e1, s, p) - neg_joint_loglik(η .- e1, s, p)) / (2ε) g2 = (neg_joint_loglik(η .+ e2, s, p) - neg_joint_loglik(η .- e2, s, p)) / (2ε) g = [g1, g2] # Compute Hessian via FD ... # Newton step Δ = -H \ g η_new = η + Δ nll_new = neg_joint_loglik(η_new, s, p) # Line search α = 1.0 while nll_new > nll_prev && α > 1e-4 α *= 0.5 η_new = η + α*Δ nll_new = neg_joint_loglik(η_new, s, p) end if abs(nll_prev - nll_new) < tol break end η = η_new nll_prev = nll_new end ... end ``` Actually, the simplest speedup: reduce the outer iterations. Look at convergence after ~50 outer iters. Good fits usually converge in 20-50 iters for this model. Let me try an even more aggressive approach. Use analytical gradient for the inner problem. Actually, the fastest thing: write a single batched computation where we only need to do a gradient-based outer optimization with a limited number of iterations. Let me think... given the 300s time budget, let me prioritize: 1. Make predict_conc maximally efficient 2. Use BFGS for outer with a moderate tolerance and limited iterations 3. Warm-start aggressively Let me also compute the inner Hessian via Cholesky so that det is just product of diagonals squared. Let me profile a single inner fit first to get a baseline. Actually, let me just simplify significantly. I'll use Optim's default BFGS for both, with tight warm-starting. The key observation is that after the first outer iteration, the η̂ don't change much, so the inner BFGS should converge in ~5 evals. Let me …[truncated]

The script is too slow. Let me profile and then speed it up substantially. I'll use more efficient inner optimization with analytical gradients.

bash

cd /app && cat > /tmp/time_test.jl <<'EOF'
include("analysis.jl")
EOF
echo "Running basic speed check..."
cd /app && timeout 40 julia -e '
using DataFrames, CSV
include("analysis.jl")' 2>&1 | head -20

output

Running basic speed check...
[stderr]
Terminated

The script just runs main() which is too slow. Let me do a standalone timing test.

bash

cd /app && cat > /tmp/profile.jl <<'EOF'
using DataFrames, CSV, Distributions, Optim, LinearAlgebra
df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])

# Minimal subject struct
struct S
    doses_t::Vector{Float64}
    doses_amt::Vector{Float64}
    samp_t::Vector{Float64}
    samp_y::Vector{Float64}
    Wt::Float64
    apgar_hi::Float64
end

subs = S[]
for sid in sort(unique(df.Subject))
    sdf = df[df.Subject .== sid, :]
    dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
    for row in eachrow(sdf)
        if !ismissing(row.dose); push!(dt, row.time); push!(da, row.dose); end
        if !ismissing(row.conc); push!(st, row.time); push!(sy, row.conc); end
    end
    ah = sdf.ApgarInd[1] == ">= 5" ? 1.0 : 0.0
    push!(subs, S(dt, da, st, sy, sdf.Wt[1], ah))
end
println("n subj: ", length(subs))

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V
    c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

function nll_inner(η, s, cl_int, cl_wt, cl_apg, v_int, v_wt, σCl, σV, σ)
    lCl = cl_int + cl_wt*s.Wt + cl_apg*s.apgar_hi + η[1]
    lV  = v_int + v_wt*s.Wt + η[2]
    Cl = exp(lCl); V = exp(lV)
    nll = 0.0
    for i in eachindex(s.samp_t)
        pred = predc(s.samp_t[i], Cl, V, s.doses_t, s.doses_amt)
        r = s.samp_y[i] - pred
        nll += 0.5*(r/σ)^2
    end
    n = length(s.samp_t)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

# Test one call
s = subs[1]
println("One call: ", @elapsed nll_inner([0.0, 0.0], s, -4.6, 0.0, 0.0, 0.0, 0.0, 0.3, 0.3, 2.0))
println("One call (warm): ", @elapsed nll_inner([0.0, 0.0], s, -4.6, 0.0, 0.0, 0.0, 0.0, 0.3, 0.3, 2.0))

# Time a single BFGS inner solve
function solve_inner(s, cl_int, v_int, σCl, σV, σ; η0=[0.0, 0.0])
    f(η) = nll_inner(η, s, cl_int, 0.0, 0.0, v_int, 0.0, σCl, σV, σ)
    res = optimize(f, η0, BFGS(), Optim.Options(g_tol=1e-5, iterations=50))
    return Optim.minimizer(res), Optim.minimum(res)
end

# Warmup
solve_inner(s, -4.6, 0.0, 0.3, 0.3, 2.0)
t = @elapsed for _ in 1:100; solve_inner(s, -4.6, 0.0, 0.3, 0.3, 2.0); end
println("Inner solve x100: $t s  →  ", t/100*1e3, " ms each")

t = @elapsed for ss in subs; solve_inner(ss, -4.6, 0.0, 0.3, 0.3, 2.0); end
println("All $(length(subs)) subjects inner solve: $t s")

EOF
cd /app && timeout 60 julia --project=. /tmp/profile.jl 2>&1 | tail -20

output

n subj: 59
One call: 0.036919756
One call (warm): 5.606e-6
Inner solve x100: 0.002069785 s  →  0.02069785 ms each
All 59 subjects inner solve: 0.015027555 s

Wait , the inner solve is fast! Only 0.015s for all 59 subjects. So the bottleneck must be elsewhere. Let me check what takes so long. Oh wait , I suspect the issue is my implementation has too tight convergence in the inner BFGS (g_tol=1e-7) and maybe the Hessian computation. Or possibly I'm doing too many iterations at startup. Let me profile the full single fit:

bash

cd /app && cat >> /tmp/profile.jl <<'EOF'

# Time a full marginal likelihood evaluation
function full_marginal(cl_int, v_int, σCl, σV, σ, subs)
    total = 0.0
    for s in subs
        f(η) = nll_inner(η, s, cl_int, 0.0, 0.0, v_int, 0.0, σCl, σV, σ)
        res = optimize(f, [0.0, 0.0], BFGS(), Optim.Options(g_tol=1e-6, iterations=50))
        η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
        # Hessian
        ε = 1e-4
        f00 = nll_min
        H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
        H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
        H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
        detH = H11*H22 - H12^2
        logL_marg = -nll_min + log(2π) - 0.5*log(detH)
        total -= logL_marg
    end
    total
end

println("Full marginal (warmup): ", @elapsed full_marginal(-4.6, 0.0, 0.3, 0.3, 2.0, subs))
t = @elapsed for _ in 1:10; full_marginal(-4.6, 0.0, 0.3, 0.3, 2.0, subs); end
println("Full marginal x10: $t s  →  ", t/10*1e3, " ms each")

# Try a BFGS outer
obj5(θ) = full_marginal(θ[1], θ[2], exp(θ[3]), exp(θ[4]), exp(θ[5]), subs)
println("Base fit: ")
t = @elapsed begin
    res = optimize(obj5, [-4.6, 0.0, log(0.3), log(0.3), log(2.0)], BFGS(),
                   Optim.Options(g_tol=1e-3, iterations=100, show_trace=false))
end
println("  elapsed: $t s, iters=", Optim.iterations(res), ", f_calls=", Optim.f_calls(res), ", min=", Optim.minimum(res))
println("  θ̂ = ", Optim.minimizer(res))
EOF
cd /app && timeout 120 julia --project=. /tmp/profile.jl 2>&1 | tail -15

output

[17] update_state!(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/solvers/first_order/bfgs.jl:163
 [18] optimize(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, initial_x::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:88
 [19] optimize
    @ /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:54 [inlined]
 [20] optimize(f::Function, x0::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}; inplace::Bool, autodiff::ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/interface.jl:225
 [21] optimize
    @ /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/interface.jl:216 [inlined]
 [22] macro expansion
    @ /tmp/profile.jl:105 [inlined]
 [23] top-level scope
    @ ./timing.jl:395
in expression starting at /tmp/profile.jl:104

bash

cd /app && timeout 120 julia --project=. /tmp/profile.jl 2>&1 | grep -E "Full|Inner|subj|Base" | head -20

output

n subj: 59
Inner solve x100: 0.002418276 s  →  0.024182759999999998 ms each
All 59 subjects inner solve: 0.014856249 s
Full marginal (warmup): 0.149888104
Full marginal x10: 0.020572264 s  →  2.0572264 ms each
Base fit: 
    @ Base.Math ./math.jl:33
    @ Base.Math ./special/log.jl:301
  [7] (::NLSolversBase.var"#18#20"{typeof(obj5), DifferentiationInterfaceFiniteDiffExt.FiniteDiffGradientPrep{Tuple{typeof(obj5), ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool}, Vector{Float64}, Tuple{}}, FiniteDiff.GradientCache{Nothing, Nothing, Nothing, Vector{Float64}, Val{:central}(), Float64, Val{true}()}, Float64, Float64, Bool}, ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool}})(_g::Vector{Float64}, _x::Vector{Float64})
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/objective_types/oncedifferentiable.jl:67
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:139
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:128
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:246
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:220
 [14] (::LineSearches.HagerZhang{Float64, Base.RefValue{Bool}})(ϕ::Function, ϕdϕ::LineSearches.var"#ϕdϕ#2"{Optim.ManifoldObjective{Flat, OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}}, Vector{Float64}, Vector{Float64}, Vector{Float64}}, c::Float64, phi_0::Float64, dphi_0::Float64)
 [16] perform_linesearch!(state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, d::Optim.ManifoldObjective{Flat, OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}})
 [17] update_state!(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat})
 [18] optimize(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, initial_x::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}})
 [20] optimize(f::Function, x0::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}; inplace::Bool, autodiff::ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool})

The outer BFGS crashed with a log error , probably log of negative det. The marginal loglik is actually very fast (2ms per call). So the speed is not the issue , the convergence is. Let me check what's causing the domain error. The issue is: during line search, parameters like σ might get into a bad region. Let me add bounds or guard. Actually, looking at the output: the inner optimization is converging (156 f-evals for 59 subjects = 2.6 per subject , that's too few! BFGS must be bailing out quickly). Actually 0.02ms per 59-subject fit is 0.33μs per subject. Then BFGS is super fast. But the outer fit fails with a log of negative. The log error happens because `log(detH)` gets negative det due to finite-precision issues when η is being optimized in a region where Hessian becomes indefinite. Or maybe the line search takes σ to something negative. Wait, I'm exponentiating σ in the obj5 function. So σ should always be positive. But during BFGS's internal steps, maybe the σ becomes huge or tiny, making η̂ unreliable. Let me add protection: when detH is not positive, fall back. Let me rewrite the analysis more carefully with: 1. Protected Hessian (enforce PD) 2. Simpler outer optimization (BFGS with initial step) 3. Bounds or transformations to keep params reasonable Also let me use analytical gradient for speed and better convergence.

bash

cd /app && cat >> /tmp/profile.jl <<'EOF'

# Robust version: protect Hessian
function full_marginal_robust(cl_int, v_int, σCl, σV, σ, subs; cache=Dict{Int,Vector{Float64}}())
    total = 0.0
    for (si, s) in enumerate(subs)
        η0 = get(cache, si, [0.0, 0.0])
        f(η) = nll_inner(η, s, cl_int, 0.0, 0.0, v_int, 0.0, σCl, σV, σ)
        res = optimize(f, η0, BFGS(), Optim.Options(g_tol=1e-6, iterations=50))
        η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
        cache[si] = η̂
        # Hessian
        ε = 1e-4
        f00 = nll_min
        H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
        H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
        H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
        # Regularise to PD
        tr = H11 + H22; det0 = H11*H22 - H12^2
        # eigenvalues via discriminant
        disc = sqrt(max(tr*tr - 4*det0, 0.0))
        λmin = (tr - disc) / 2
        if λmin <= 1e-6
            shift = 1e-6 - λmin
            H11 += shift; H22 += shift
            det0 = H11*H22 - H12^2
        end
        logL_marg = -nll_min + log(2π) - 0.5*log(det0)
        total -= logL_marg
    end
    total
end

# Base fit with cache warm start
cache = Dict{Int,Vector{Float64}}()
obj5b(θ) = full_marginal_robust(θ[1], θ[2], exp(θ[3]), exp(θ[4]), exp(θ[5]), subs; cache=cache)
obj5b([-4.6, 0.0, log(0.3), log(0.3), log(2.0)])  # warmup
println("Base fit (robust): ")
t = @elapsed begin
    res = optimize(obj5b, [-4.6, 0.0, log(0.3), log(0.3), log(2.0)], BFGS(),
                   Optim.Options(g_tol=1e-3, iterations=200, show_trace=false))
end
println("  elapsed: $t s, iters=", Optim.iterations(res), ", f_calls=", Optim.f_calls(res), ", min=", Optim.minimum(res))
println("  θ̂ = ", Optim.minimizer(res))
EOF
cd /app && timeout 120 julia --project=. /tmp/profile.jl 2>&1 | grep -E "Full|Inner|subj|Base|elapsed|θ̂|min|conv" | head -20

output

n subj: 59
Inner solve x100: 0.002554373 s  →  0.02554373 ms each
All 59 subjects inner solve: 0.01627901 s
Full marginal (warmup): 0.143995631
Full marginal x10: 0.020137329 s  →  2.0137329 ms each
Base fit: 
    @ Base.Math ./math.jl:33
    @ Base.Math ./special/log.jl:301
  [7] (::NLSolversBase.var"#18#20"{typeof(obj5), DifferentiationInterfaceFiniteDiffExt.FiniteDiffGradientPrep{Tuple{typeof(obj5), ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool}, Vector{Float64}, Tuple{}}, FiniteDiff.GradientCache{Nothing, Nothing, Nothing, Vector{Float64}, Val{:central}(), Float64, Val{true}()}, Float64, Float64, Bool}, ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool}})(_g::Vector{Float64}, _x::Vector{Float64})
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/objective_types/oncedifferentiable.jl:67
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:139
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:128
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:246
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:220
 [14] (::LineSearches.HagerZhang{Float64, Base.RefValue{Bool}})(ϕ::Function, ϕdϕ::LineSearches.var"#ϕdϕ#2"{Optim.ManifoldObjective{Flat, OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}}, Vector{Float64}, Vector{Float64}, Vector{Float64}}, c::Float64, phi_0::Float64, dphi_0::Float64)
 [16] perform_linesearch!(state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, d::Optim.ManifoldObjective{Flat, OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}})
 [17] update_state!(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat})
 [18] optimize(d::OnceDifferentiable{Float64, Vector{Float64}, Float64, Vector{Float64}}, initial_x::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}, state::Optim.BFGSState{Vector{Float64}, Matrix{Float64}, Float64, Vector{Float64}})
 [20] optimize(f::Function, x0::Vector{Float64}, method::BFGS{LineSearches.InitialStatic{Float64}, LineSearches.HagerZhang{Float64, Base.RefValue{Bool}}, Nothing, Nothing, Flat}, options::Optim.Options{Float64, Nothing}; inplace::Bool, autodiff::ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool})
    @ ./timing.jl:395

The DomainError is happening inside `log` during some line search step in the outer BFGS. The error propagates up. Let me wrap the objective to catch DomainErrors and return Inf. Also, let me use the NewtonTrustRegion or LBFGS with a safer line search. Actually, let me try Nelder-Mead which is derivative-free.

bash

cd /app && cat > /tmp/profile2.jl <<'EOF'
using DataFrames, CSV, Distributions, Optim, LinearAlgebra
df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])

struct S
    doses_t::Vector{Float64}; doses_amt::Vector{Float64}
    samp_t::Vector{Float64}; samp_y::Vector{Float64}
    Wt::Float64; apgar_hi::Float64
end
subs = S[]
for sid in sort(unique(df.Subject))
    sdf = df[df.Subject .== sid, :]
    dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
    for row in eachrow(sdf)
        !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
        !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
    end
    ah = sdf.ApgarInd[1] == ">= 5" ? 1.0 : 0.0
    push!(subs, S(dt, da, st, sy, sdf.Wt[1], ah))
end

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

function nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
    lCl = ci + cw*s.Wt + cap*s.apgar_hi + η[1]
    lV  = vi + vw*s.Wt + η[2]
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(s.samp_t)
        r = s.samp_y[i] - predc(s.samp_t[i], Cl, V, s.doses_t, s.doses_amt)
        nll += 0.5*(r/σ)^2
    end
    n = length(s.samp_t)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

function neg_marg(θ, model, subs, cache)
    if model == :base
        ci, cw, cap = θ[1], 0.0, 0.0
        vi, vw = θ[2], 0.0
        σCl, σV, σ = exp(θ[3]), exp(θ[4]), exp(θ[5])
    elseif model == :cl_wt
        ci, cw, cap = θ[1], θ[2], 0.0
        vi, vw = θ[3], 0.0
        σCl, σV, σ = exp(θ[4]), exp(θ[5]), exp(θ[6])
    else
        ci, cw, cap = θ[1], θ[2], θ[3]
        vi, vw = θ[4], θ[5]
        σCl, σV, σ = exp(θ[6]), exp(θ[7]), exp(θ[8])
    end
    total = 0.0
    for (si, s) in enumerate(subs)
        η0 = get(cache, si, [0.0, 0.0])
        f(η) = nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
        res = optimize(f, η0, BFGS(), Optim.Options(g_tol=1e-6, iterations=50))
        η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
        cache[si] = η̂
        ε = 1e-4; f00 = nll_min
        H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
        H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
        H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
        tr = H11 + H22; det0 = H11*H22 - H12^2
        disc = sqrt(max(tr*tr - 4*det0, 0.0))
        λmin = (tr - disc) / 2
        if λmin <= 1e-6
            shift = 1e-6 - λmin
            H11 += shift; H22 += shift
            det0 = H11*H22 - H12^2
        end
        if det0 <= 0
            return Inf
        end
        logL_marg = -nll_min + log(2π) - 0.5*log(det0)
        total -= logL_marg
    end
    total
end

function safe_obj(θ, model, subs, cache)
    try
        v = neg_marg(θ, model, subs, cache)
        return isfinite(v) ? v : 1e12
    catch e
        return 1e12
    end
end

# Fit all three models sequentially
println("=== Base ===")
cache = Dict{Int,Vector{Float64}}()
θ0 = [-4.6, 0.0, log(0.3), log(0.3), log(2.0)]
t = @elapsed begin
    res = optimize(θ -> safe_obj(θ, :base, subs, cache), θ0,
                   NelderMead(), Optim.Options(iterations=5000))
end
θb = Optim.minimizer(res)
println("elapsed $t s, iters=", Optim.iterations(res), ", f_calls=", Optim.f_calls(res), ", min=", Optim.minimum(res))
println("θ=", θb)

println("=== cl_wt ===")
cache2 = Dict{Int,Vector{Float64}}()
θ0c = [θb[1], 0.0, θb[2], θb[3], θb[4], θb[5]]
t = @elapsed begin
    res = optimize(θ -> safe_obj(θ, :cl_wt, subs, cache2), θ0c,
                   NelderMead(), Optim.Options(iterations=5000))
end
θcw = Optim.minimizer(res)
println("elapsed $t s, iters=", Optim.iterations(res), ", f_calls=", Optim.f_calls(res), ", min=", Optim.minimum(res))
println("θ="
…[truncated]

output

=== Base ===
elapsed 21.771296311 s, iters=5000, f_calls=32946, min=1430.5133779338485
θ=[-5.103422271514451, 0.06553926475675036, -1.5044697814740533, -0.7793255311883672, 0.4996268236452936]
=== cl_wt ===
elapsed 13.647413421 s, iters=5000, f_calls=39950, min=1414.5474653889057
θ=[-5.103422271514451, 0.0, 0.06553926475675036, -2.2317046407467256, -0.7793255311883672, 0.4996268236452936]
=== full ===
elapsed 0.014518973 s, iters=0, f_calls=10, min=1.0e12
θ=[-5.103422271514451, 0.0, 0.0, 0.06553926475675036, 0.0, -2.2317046407467256, -0.7793255311883672, 0.4996268236452936]
  Cl_int=-5.103422271514451, Cl_wt=0.0, Cl_apgar=0.0, V_int=0.06553926475675036, V_wt=0.0
  σCl=0.10734528893168115, σV=0.458715296152681, σ=1.6481061216930721

OK, Nelder-Mead is not converging well , it stopped at 5000 iterations but the cl_wt model got to the same solution as base (cl_wt = 0.0 exactly) meaning it didn't actually improve. Also the starting theta for cl_wt inserted a 0.0 in position 2 but that didn't cause improvement. And the full fit failed immediately because of some issue. Let me try a different strategy: Use BFGS but wrap in try/catch for the domain error. Use a better line search. Also use warm starts for η. Actually, a bigger issue: the cl_wt model appears to have NOT improved over base. That's suspicious. Maybe Nelder-Mead got stuck at a local min because of the bad Hessian regularization. Let me try LBFGS with backtracking line search, which should be more robust. Actually, let me think about this more carefully. The problem is likely that: 1. The Hessian regularization is creating a discontinuous objective (when λmin crosses threshold) 2. Nelder-Mead isn't good at high-dim problems 3. BFGS dies from DomainError Solution: - Use LBFGS with backtracking + allow_f_increases - Wrap objective to catch exceptions - Don't use the Hessian threshold , use sqrt/protection only if actually needed Let me try using Optim's ParticleSwarm for a global search then refine. Actually, let me try a much simpler approach: use LBFGS with backtracking line search.

bash

cd /app && cat > /tmp/profile3.jl <<'EOF'
using DataFrames, CSV, Distributions, Optim, LinearAlgebra, LineSearches
df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])

struct S
    doses_t::Vector{Float64}; doses_amt::Vector{Float64}
    samp_t::Vector{Float64}; samp_y::Vector{Float64}
    Wt::Float64; apgar_hi::Float64
end
subs = S[]
for sid in sort(unique(df.Subject))
    sdf = df[df.Subject .== sid, :]
    dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
    for row in eachrow(sdf)
        !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
        !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
    end
    ah = sdf.ApgarInd[1] == ">= 5" ? 1.0 : 0.0
    push!(subs, S(dt, da, st, sy, sdf.Wt[1], ah))
end

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

function nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
    lCl = ci + cw*s.Wt + cap*s.apgar_hi + η[1]
    lV  = vi + vw*s.Wt + η[2]
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(s.samp_t)
        r = s.samp_y[i] - predc(s.samp_t[i], Cl, V, s.doses_t, s.doses_amt)
        nll += 0.5*(r/σ)^2
    end
    n = length(s.samp_t)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

function neg_marg(θ, model, subs, cache)
    if model == :base
        ci, cw, cap = θ[1], 0.0, 0.0
        vi, vw = θ[2], 0.0
        σCl, σV, σ = exp(θ[3]), exp(θ[4]), exp(θ[5])
    elseif model == :cl_wt
        ci, cw, cap = θ[1], θ[2], 0.0
        vi, vw = θ[3], 0.0
        σCl, σV, σ = exp(θ[4]), exp(θ[5]), exp(θ[6])
    else
        ci, cw, cap = θ[1], θ[2], θ[3]
        vi, vw = θ[4], θ[5]
        σCl, σV, σ = exp(θ[6]), exp(θ[7]), exp(θ[8])
    end
    # guard σ to reasonable range
    if σCl < 1e-4 || σCl > 5 || σV < 1e-4 || σV > 5 || σ < 1e-4 || σ > 1e3
        return 1e12
    end
    total = 0.0
    for (si, s) in enumerate(subs)
        η0 = get(cache, si, [0.0, 0.0])
        f(η) = nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
        res = optimize(f, η0, BFGS(linesearch=BackTracking()),
                       Optim.Options(g_tol=1e-6, iterations=100))
        η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
        cache[si] = η̂
        ε = 1e-4; f00 = nll_min
        H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
        H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
        H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
        det0 = H11*H22 - H12^2
        if det0 <= 0 || H11 <= 0 || H22 <= 0
            # regularise
            tr = H11 + H22
            λmin = (tr - sqrt(max(tr*tr - 4*det0, 0.0)))/2
            shift = max(1e-4 - λmin, 1e-4)
            H11 += shift; H22 += shift
            det0 = H11*H22 - H12^2
        end
        logL_marg = -nll_min + log(2π) - 0.5*log(det0)
        total -= logL_marg
    end
    total
end

function safe_obj(θ, model, subs, cache)
    try
        v = neg_marg(θ, model, subs, cache)
        return isfinite(v) ? v : 1e12
    catch
        return 1e12
    end
end

function fit_bfgs(θ0, model, subs; maxit=300)
    cache = Dict{Int,Vector{Float64}}()
    obj(θ) = safe_obj(θ, model, subs, cache)
    # Try BFGS with BackTracking
    res = optimize(obj, θ0, BFGS(linesearch=BackTracking()),
                   Optim.Options(g_tol=1e-4, iterations=maxit, allow_f_increases=true))
    θ̂ = Optim.minimizer(res)
    return θ̂, Optim.minimum(res), cache, res
end

println("=== Base ===")
θ0 = [-4.6, 0.0, log(0.3), log(0.3), log(2.0)]
t = @elapsed (θb, nb, cacheb, rb) = fit_bfgs(θ0, :base, subs; maxit=200)
println("elapsed $t s, iters=", Optim.iterations(rb), ", f_calls=", Optim.f_calls(rb), ", min=", nb)
println("θ=", θb)

println("=== cl_wt ===")

…[truncated]

output

ERROR: LoadError: ArgumentError: Package LineSearches not found in current path.
- Run `import Pkg; Pkg.add("LineSearches")` to install the LineSearches package.
Stacktrace:
 [1] macro expansion
   @ ./loading.jl:1772 [inlined]
 [2] macro expansion
   @ ./lock.jl:267 [inlined]
 [3] __require(into::Module, mod::Symbol)
   @ Base ./loading.jl:1753
 [4] #invoke_in_world#3
   @ ./essentials.jl:926 [inlined]
 [5] invoke_in_world
   @ ./essentials.jl:923 [inlined]
 [6] require(into::Module, mod::Symbol)
   @ Base ./loading.jl:1746
in expression starting at /tmp/profile3.jl:1

bash

cd /app && julia -e 'using Optim; println(methods(Optim.BackTracking))' 2>&1 | head -5

output

ERROR: UndefVarError: `BackTracking` not defined
Stacktrace:
 [1] getproperty(x::Module, f::Symbol)
   @ Base ./Base.jl:31
 [2] top-level scope

bash

cd /app && julia -e 'using Optim; println(Optim.LineSearches.BackTracking)' 2>&1 | head -5

output

LineSearches.BackTracking

bash

sed -i 's|using DataFrames, CSV, Distributions, Optim, LinearAlgebra, LineSearches|using DataFrames, CSV, Distributions, Optim, LinearAlgebra\nconst BackTracking = Optim.LineSearches.BackTracking|' /tmp/profile3.jl
cd /app && timeout 280 julia --project=. /tmp/profile3.jl 2>&1 | tail -25

output

┌ Warning: Terminated early: trial iterate had non-finite values.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:100
┌ Warning: Terminated early: trial iterate had non-finite values.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:100
┌ Warning: Terminated early: trial iterate had non-finite values.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:100
┌ Warning: Terminated early: trial iterate had non-finite values.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:100
┌ Warning: Terminated early: trial iterate had non-finite values.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:100
┌ Warning: Terminated early: trial iterate had non-finite values.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:100
┌ Warning: Terminated early: trial iterate had non-finite values.
└ @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:100
elapsed 1.405104025 s, iters=4, f_calls=1429, min=913.654871774669
θ=[-4.874890733194722, -2.331372869634751e-18, 0.51535425467192, -3.8205049474245567, -7.509433416370901, 1.6317995883346665]
=== full ===
elapsed 0.305685547 s, iters=4, f_calls=513, min=914.4730530773394
θ=[-4.874890733194726, -1.026258344527717e-14, 8.485321728784545e-15, 0.5153542546719302, 2.344942715439921e-15, -3.8205049474245545, -7.509433416370901, 1.6317995883346599]
  Cl_int=-4.874890733194726, Cl_wt=-1.026258344527717e-14, Cl_apgar=8.485321728784545e-15, V_int=0.5153542546719302, V_wt=2.344942715439921e-15
  σCl=0.021916731302689996, σV=0.0005478914271026189, σ=5.113067861397082

AIC: base=1842.130581518858, cl_wt=1839.309743549338, full=1844.9461061546788
LR 1->2 (df=1): 4.820837969519971 p=0.02811767254823805
LR 2->3 (df=2): -1.6363626053407643 p=1.0

The optimization isn't working well , stopped early with "non-finite values" warnings. The σCl went nearly to zero, which is a degenerate solution. The issue is that the σCl and σV parameters are being driven to very small values, which is the boundary of the parameter space. The Laplace approximation can break down near the boundary. Also, the full model isn't improving because all weight/apgar coefficients are ~0 and σ is blowing up to 5.1. I need to constrain the optimization better. Let me: 1. Use a constrained parameter space: keep σ reasonable (between say 0.01 and 50), σCl, σV between 0.001 and 2 2. Use better starting values 3. Use Fminbox with bounds Actually looking more carefully, I suspect the approach is conceptually correct but the optimization is hard. Let me use Fminbox to constrain parameters. Actually I think the core issue is that log-SE parameters can wander into bad regions. Let me check - in the last "base" fit, σCl=0.022 and σ=5.1. The model is essentially explaining all variance as residual and making CL random effect near 0. Actually wait, this is normal for a local min if starting value is bad. Let me use better starts. For phenobarb: - σCl should be ~0.3 (CL has significant BSV) - σV should be ~0.1-0.3 - σ residual should be ~2-3 mg/L My initial σ=2.0 is too low maybe. Let me be more careful. Actually, I think the real problem is that I'm fitting to real data and the starting value matters a lot. Let me try multiple starts and pick the best. Let me try using LBFGS instead and see if it converges without the domain errors. Another approach: use a bounded optimization (Fminbox). Optim supports this. Let me just use `Fminbox(LBFGS())` with reasonable bounds.

bash

cd /app && cat > /tmp/profile4.jl <<'EOF'
using DataFrames, CSV, Distributions, Optim, LinearAlgebra
const BackTracking = Optim.LineSearches.BackTracking

df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])
struct S
    doses_t::Vector{Float64}; doses_amt::Vector{Float64}
    samp_t::Vector{Float64}; samp_y::Vector{Float64}
    Wt::Float64; apgar_hi::Float64
end
subs = S[]
for sid in sort(unique(df.Subject))
    sdf = df[df.Subject .== sid, :]
    dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
    for row in eachrow(sdf)
        !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
        !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
    end
    ah = sdf.ApgarInd[1] == ">= 5" ? 1.0 : 0.0
    push!(subs, S(dt, da, st, sy, sdf.Wt[1], ah))
end

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

function nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
    lCl = ci + cw*s.Wt + cap*s.apgar_hi + η[1]
    lV  = vi + vw*s.Wt + η[2]
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(s.samp_t)
        r = s.samp_y[i] - predc(s.samp_t[i], Cl, V, s.doses_t, s.doses_amt)
        nll += 0.5*(r/σ)^2
    end
    n = length(s.samp_t)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

function neg_marg(θ, model, subs, cache)
    if model == :base
        ci, cw, cap = θ[1], 0.0, 0.0
        vi, vw = θ[2], 0.0
        σCl, σV, σ = exp(θ[3]), exp(θ[4]), exp(θ[5])
    elseif model == :cl_wt
        ci, cw, cap = θ[1], θ[2], 0.0
        vi, vw = θ[3], 0.0
        σCl, σV, σ = exp(θ[4]), exp(θ[5]), exp(θ[6])
    else
        ci, cw, cap = θ[1], θ[2], θ[3]
        vi, vw = θ[4], θ[5]
        σCl, σV, σ = exp(θ[6]), exp(θ[7]), exp(θ[8])
    end
    total = 0.0
    for (si, s) in enumerate(subs)
        η0 = get(cache, si, [0.0, 0.0])
        f(η) = nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
        res = optimize(f, η0, BFGS(linesearch=BackTracking()),
                       Optim.Options(g_tol=1e-7, iterations=100))
        η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
        cache[si] = η̂
        ε = 1e-4; f00 = nll_min
        H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
        H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
        H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
        det0 = H11*H22 - H12^2
        if det0 <= 0 || H11 <= 0 || H22 <= 0
            tr = H11 + H22
            λmin = (tr - sqrt(max(tr*tr - 4*det0, 0.0)))/2
            shift = max(1e-4 - λmin, 1e-4)
            H11 += shift; H22 += shift
            det0 = H11*H22 - H12^2
        end
        logL_marg = -nll_min + log(2π) - 0.5*log(det0)
        total -= logL_marg
    end
    total
end

function safe_obj(θ, model, subs, cache)
    try
        v = neg_marg(θ, model, subs, cache)
        return isfinite(v) ? v : 1e10
    catch
        return 1e10
    end
end

# Use Fminbox with LBFGS to constrain the parameter space
function fit_bounded(θ0, lower, upper, model, subs; maxit=200)
    cache = Dict{Int,Vector{Float64}}()
    obj(θ) = safe_obj(θ, model, subs, cache)
    res = optimize(obj, lower, upper, θ0, Fminbox(LBFGS(linesearch=BackTracking())),
                   Optim.Options(g_tol=1e-4, iterations=maxit, allow_f_increases=true,
                                outer_iterations=3))
    return Optim.minimizer(res), Optim.minimum(res), cache, res
end

# Base
println("=== Base ===")
θ0 = [-4.6, 0.0, log(0.3), log(0.3), log(2.0)]
lo = [-10.0, -5.0, log(0.01), log(0.01), log(0.1)]
hi = [ 5.0, 5.0, log(2.0), log(2.0), log(20.0)]
t = @elapsed (θb, nb, cb, rb) = fit_bounded(θ0, lo, hi, :base, subs)
println("elapsed $t s, min=", nb)
println("θ=", θb, "  σC
…[truncated]

output

=== Base ===
elapsed 6.073416862 s, min=1427.0942232708483
θ=[-5.053704779183707, 0.3595903472264636, -1.467447309274355, -0.9953401653298113, 0.5077286389388564]  σCl=0.2305131636018488 σV=0.3695976988349845 σ=1.6615130098058555
=== cl_wt ===
elapsed 0.699382855 s, min=1428.1889941588643
θ=[-5.053704779183707, 1.5504956273775962e-16, 0.35959034722646377, -1.467447309274355, -0.9953401653298112, 0.5077286389388563]  σCl=0.2305131636018488 σV=0.36959769883498456 σ=1.6615130098058555
=== full ===
ERROR: LoadError: cannot assign a value to imported variable Distributions.cf from module Main
Stacktrace:
 [1] top-level scope
   @ ./timing.jl:395
in expression starting at /tmp/profile4.jl:130

There's a variable name conflict (`cf`) with Distributions. Let me rename. Also the cl_wt and base fits are producing the same objective value , the Wt slope isn't entering. This is weird , it's like Fminbox isn't actually optimizing cl_wt. Oh! I see the issue. Fminbox is doing outer_iterations=3 but apparently isn't actually doing much. The minimum value is WORSE for cl_wt (1428.18) than base (1427.09). This shouldn't happen since cl_wt has more parameters. Something is off , probably Fminbox converging early with barrier. Let me not use Fminbox and instead use a simpler approach. Actually I think the problem is: my base θ0 starts with cl_wt=0 (which is the default), and with nb=1427 but adding Wt=0.36 actually increases NLL to 1428! That can only happen if... there's something wrong with how I'm using cl_wt. Wait , look at θb for base: [-5.05, 0.36, -1.47, -0.996, 0.51]. Position 2 in base is V_int, not Cl_wt! I gave a bounds lo for V_int of -5. But V_int = 0.36 here. Then for cl_wt, I passed θ0c = [θb[1], 0.0, θb[2], ...] = [-5.05, 0.0, 0.36, -1.47, ...]. That puts V_int at position 3, which is correct. But the bounds for cl_wt are [-5, 5] for V_int at position 3, which is fine. So why doesn't cl_wt improve? Looking at the result: θcw = [-5.05, 0, 0.36, -1.47, -1.0, 0.51] , the Cl_wt coefficient is STILL 0! The optimizer didn't move it. And the nll is 1428.19, slightly worse than base's 1427.09. This could be because: 1. The initial gradient is 0 at cl_wt=0 (local min) 2. Or the cache isn't shared so starting from scratch, the inner solves are different Actually I think the issue is the cache. The cache starts empty, so the inner solves are from η=[0,0]. If the cache was populated from the base fit, the inner solves would be from the base EBs. But with a fresh cache, the inner solves might not find the right optimum. Let me try: 1. No cache , always start η from 0 2. Or share the cache Actually maybe the real issue is that my Laplace is actually incorrect for base. Let me look at what the nlme/PK literature gives for this dataset. Pinheiro & Bates have this as an example. Let me instead try a single pass: fit the full model directly and see. Actually, the obvious fix: I was using Fminbox and cl_wt probably got stuck. Let me use simpler optimization with good bounds via transformation. Actually, the cleanest path forward: use a bounded parameter space via transformation (σ_X = softplus or log with offset), and fit using LBFGS without bounds. Let me try a totally different approach: fit everything via raw BFGS with careful starting values, and wrap the objective to return 1e10 on any issue. Actually wait , reading my profile4.jl output again: - Base: θb = [-5.05, 0.36, -1.47, -1.0, 0.51] (Cl_int, V_int, logσCl, logσV, logσ) - σCl=0.23, σV=0.37, σ=1.66 , these look reasonable! - nll = 1427.09 so logL = -1427.09 - cl_wt: θcw = [-5.05, 0.0, 0.36, -1.47, -1.0, 0.51] (Cl_int, Cl_wt, V_int, logσCl, logσV, logσ) - Cl_wt still = 0 after "optimization"! - nll = 1428.19 , WORSE than base This means the optimizer didn't actually move. Fminbox must have failed silently or the initial position is a true local min. Let me try just using plain BFGS (no Fminbox) with the obj returning 1e10 when bounds are violated. Or, use global search like ParticleSwarm first then refine with BFGS. Actually, I realize the issue. In my profile3, when Base converged to nll=913, that was also wrong (the real NLL should be around 900-1000 based on the Pinheiro & Bates results). The σs were crazy there (σCl=0.02, σ=5.1). The new answer (σCl=0.23, σV=0.37, σ=1.66) with nll=1427 looks more reasonable but is way off from the expected ~900. Hmm. Let me check my sign convention. Maybe I have a factor of 2 wrong. Actually, looking at the final model in nlme: Phenobarb full model gets a likelihood around -900. My current base is -1427. That's way worse. Let me carefully check my NLL computation: ``` nll = 0.5*(r/σ)^2 + n*(log(σ) + …[truncated]

bash

cd /app && cat > /tmp/test_single.jl <<'EOF'
using DataFrames, CSV, Optim, Distributions
df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

# Subject 1 data
sdf = df[df.Subject .== 1, :]
dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
for row in eachrow(sdf)
    !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
    !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
end
println("doses: ", length(dt), ", samples: ", length(st))
println("t=", st, ", y=", sy)

# Try finding Cl, V for subject 1
function sse(θ)
    Cl, V = exp(θ[1]), exp(θ[2])
    s = 0.0
    for i in 1:length(st)
        p = predc(st[i], Cl, V, dt, da)
        s += (sy[i] - p)^2
    end
    s
end

res = optimize(sse, [-4.6, 0.0], NelderMead(), Optim.Options(iterations=5000))
θ̂ = Optim.minimizer(res)
println("Subject 1: lCl=", θ̂[1], ", lV=", θ̂[2], ", Cl=", exp(θ̂[1]), ", V=", exp(θ̂[2]))
println("Residuals: ")
Cl, V = exp(θ̂[1]), exp(θ̂[2])
for i in 1:length(st)
    p = predc(st[i], Cl, V, dt, da)
    println("  t=", st[i], " obs=", sy[i], " pred=", p, " resid=", sy[i]-p)
end

# Look at a few more subjects
for sid in [2, 3, 5, 10, 20]
    sdf = df[df.Subject .== sid, :]
    dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
    for row in eachrow(sdf)
        !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
        !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
    end
    if length(st) == 0; continue; end
    function sse2(θ)
        Cl, V = exp(θ[1]), exp(θ[2])
        s = 0.0
        for i in 1:length(st)
            p = predc(st[i], Cl, V, dt, da)
            s += (sy[i] - p)^2
        end
        s
    end
    res = optimize(sse2, [-4.6, 0.0], NelderMead(), Optim.Options(iterations=5000))
    θ̂ = Optim.minimizer(res)
    println("Subject $sid: Wt=", sdf.Wt[1], " lCl=", round(θ̂[1],digits=3), ", lV=", round(θ̂[2],digits=3),
            ", Cl=", round(exp(θ̂[1]),digits=4), ", V=", round(exp(θ̂[2]),digits=3),
            " nsamp=", length(st), " sse=", round(Optim.minimum(res), digits=4))
end
EOF
cd /app && timeout 30 julia --project=. /tmp/test_single.jl 2>&1 | tail -30

output

doses: 10, samples: 2
t=[2.0, 112.5], y=[17.3, 31.0]
Subject 1: lCl=-5.408373119383086, lV=0.36193222224894084, Cl=0.004478920956980109, V=1.43610160292474
Residuals: 
  t=2.0 obs=17.3 pred=17.299991193957315 resid=8.806042686160254e-6
  t=112.5 obs=31.0 pred=31.00001709523117 resid=-1.709523116844025e-5
┌ Warning: Assignment to `sdf` in soft scope is ambiguous because a global variable by the same name exists: `sdf` will be treated as a new local. Disambiguate by using `local sdf` to suppress this warning or `global sdf` to assign to the existing global variable.
└ @ /tmp/test_single.jl:48
┌ Warning: Assignment to `dt` in soft scope is ambiguous because a global variable by the same name exists: `dt` will be treated as a new local. Disambiguate by using `local dt` to suppress this warning or `global dt` to assign to the existing global variable.
└ @ /tmp/test_single.jl:49
┌ Warning: Assignment to `da` in soft scope is ambiguous because a global variable by the same name exists: `da` will be treated as a new local. Disambiguate by using `local da` to suppress this warning or `global da` to assign to the existing global variable.
└ @ /tmp/test_single.jl:49
┌ Warning: Assignment to `st` in soft scope is ambiguous because a global variable by the same name exists: `st` will be treated as a new local. Disambiguate by using `local st` to suppress this warning or `global st` to assign to the existing global variable.
└ @ /tmp/test_single.jl:49
┌ Warning: Assignment to `sy` in soft scope is ambiguous because a global variable by the same name exists: `sy` will be treated as a new local. Disambiguate by using `local sy` to suppress this warning or `global sy` to assign to the existing global variable.
└ @ /tmp/test_single.jl:49
┌ Warning: Assignment to `res` in soft scope is ambiguous because a global variable by the same name exists: `res` will be treated as a new local. Disambiguate by using `local res` to suppress this warning or `global res` to assign to the existing global variable.
└ @ /tmp/test_single.jl:64
┌ Warning: Assignment to `θ̂` in soft scope is ambiguous because a global variable by the same name exists: `θ̂` will be treated as a new local. Disambiguate by using `local θ̂` to suppress this warning or `global θ̂` to assign to the existing global variable.
└ @ /tmp/test_single.jl:65
Subject 2: Wt=1.5 lCl=-5.549, lV=0.266, Cl=0.0039, V=1.304 nsamp=3 sse=7.4014
Subject 3: Wt=1.5 lCl=-4.594, lV=0.473, Cl=0.0101, V=1.604 nsamp=3 sse=6.1916
Subject 5: Wt=1.4 lCl=-4.637, lV=0.597, Cl=0.0097, V=1.817 nsamp=3 sse=1.3788
Subject 10: Wt=1.4 lCl=-5.048, lV=0.333, Cl=0.0064, V=1.395 nsamp=3 sse=2.4248
Subject 20: Wt=1.2 lCl=-5.14, lV=0.046, Cl=0.0059, V=1.047 nsamp=3 sse=0.9348

So the PK prediction is working correctly. The subject-level fits look reasonable: - lCl around -5 (Cl ~ 0.006 L/h) - lV around 0.3 (V ~ 1.3 L) So starting values should be ci~-5, vi~0.3. Let me restart with these. The issue with my earlier fits is that the starting values were suboptimal. Let me use multi-start or better starts. With good starting values, NLL should converge to a reasonable number. Let me try. Also, I need to check: my model converged to nll=1427 in profile4, but the correct nlme answer should be around nll=900. Could be that the Fminbox optimization got stuck at iteration 0. Let me try a plain BFGS/LBFGS with bounds on the objective (returning 1e10 for bad σ) and see.

bash

cd /app && cat > /tmp/profile5.jl <<'EOF'
using DataFrames, CSV, Distributions, Optim, LinearAlgebra
const BackTracking = Optim.LineSearches.BackTracking

df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])
struct S
    doses_t::Vector{Float64}; doses_amt::Vector{Float64}
    samp_t::Vector{Float64}; samp_y::Vector{Float64}
    Wt::Float64; apgar_hi::Float64
end
subs = S[]
for sid in sort(unique(df.Subject))
    sdf = df[df.Subject .== sid, :]
    dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
    for row in eachrow(sdf)
        !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
        !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
    end
    ah = sdf.ApgarInd[1] == ">= 5" ? 1.0 : 0.0
    push!(subs, S(dt, da, st, sy, sdf.Wt[1], ah))
end

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

function nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
    lCl = ci + cw*s.Wt + cap*s.apgar_hi + η[1]
    lV  = vi + vw*s.Wt + η[2]
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(s.samp_t)
        r = s.samp_y[i] - predc(s.samp_t[i], Cl, V, s.doses_t, s.doses_amt)
        nll += 0.5*(r/σ)^2
    end
    n = length(s.samp_t)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

function neg_marg(θ, model, subs, cache)
    if model == :base
        ci, cw, cap = θ[1], 0.0, 0.0
        vi, vw = θ[2], 0.0
        σCl, σV, σ = exp(θ[3]), exp(θ[4]), exp(θ[5])
    elseif model == :cl_wt
        ci, cw, cap = θ[1], θ[2], 0.0
        vi, vw = θ[3], 0.0
        σCl, σV, σ = exp(θ[4]), exp(θ[5]), exp(θ[6])
    else
        ci, cw, cap = θ[1], θ[2], θ[3]
        vi, vw = θ[4], θ[5]
        σCl, σV, σ = exp(θ[6]), exp(θ[7]), exp(θ[8])
    end
    # Guard against extreme values
    if σCl < 1e-3 || σCl > 3 || σV < 1e-3 || σV > 3 || σ < 1e-2 || σ > 100
        return 1e10
    end
    total = 0.0
    for (si, s) in enumerate(subs)
        η0 = get(cache, si, [0.0, 0.0])
        f(η) = nll_inner(η, s, ci, cw, cap, vi, vw, σCl, σV, σ)
        res = optimize(f, η0, BFGS(linesearch=BackTracking()),
                       Optim.Options(g_tol=1e-7, iterations=200))
        η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
        cache[si] = η̂
        ε = 1e-4; f00 = nll_min
        H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
        H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
        H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
        det0 = H11*H22 - H12^2
        if det0 <= 0 || H11 <= 0
            tr = H11 + H22
            λmin = (tr - sqrt(max(tr*tr - 4*det0, 0.0)))/2
            shift = max(1e-4 - λmin, 1e-4)
            H11 += shift; H22 += shift
            det0 = H11*H22 - H12^2
        end
        logL_marg = -nll_min + log(2π) - 0.5*log(det0)
        total -= logL_marg
    end
    total
end

function safe_obj(θ, model, subs, cache)
    try
        v = neg_marg(θ, model, subs, cache)
        return isfinite(v) ? v : 1e10
    catch
        return 1e10
    end
end

# Start with better values: lCl=-5, lV=0.3
θ0b = [-5.0, 0.3, log(0.3), log(0.3), log(2.0)]
cache_b = Dict{Int,Vector{Float64}}()
println("Initial base nll: ", safe_obj(θ0b, :base, subs, cache_b))

# Try LBFGS with BackTracking
function fit_lbfgs(θ0, model, subs; maxit=200)
    cache = Dict{Int,Vector{Float64}}()
    obj(θ) = safe_obj(θ, model, subs, cache)
    res = optimize(obj, θ0, LBFGS(linesearch=BackTracking()),
                   Optim.Options(g_tol=1e-4, iterations=maxit, allow_f_increases=true))
    return Optim.minimizer(res), Optim.minimum(res), cache, res
end

println("=== Base (LBFGS) ===")
t = @elapsed (θb, nb, cb, rb) = fit_lbfgs(θ0b, :base, subs; maxit=200)
…[truncated]

output

Initial base nll: 1509.945637457044
=== Base (LBFGS) ===
elapsed 1.12878445 s, iters=10, f_calls=14, min=1493.3944948521207
θ=[-5.062763848627038, 0.29735216010586296, -1.001609584868142, -0.7995472274694888, 0.5779971528231289] → σCl=0.36728778427836023 σV=0.4495324539931736 σ=1.7824648485853252
Refining with Nelder-Mead...
elapsed 12.302313175 s, iters=3000, min=1408.2919653706897
θ=[-5.186591499537384, 0.32833633065671614, -1.5299351227683151, -0.869020641992685, 0.4682392615982433] → σCl=0.2165497160063787 σV=0.41936205378471336 σ=1.5971795006945575
Second LBFGS pass...
elapsed 0.117812616 s, iters=3, min=1408.3840952517219
θ=[-5.186591499537335, 0.3283363306567162, -1.529935122768147, -0.8690206419924279, 0.46823926159798623] → σCl=0.2165497160064151 σV=0.4193620537848212 σ=1.597179500694147

OK so starting better helps. But I'm still stuck at nll=1408. The expected value for nlme on this dataset is something like -900 or so, for marginal log-likelihood (so positive nll around 900-1000). So there's a factor of roughly 500 difference. Wait maybe I need to reconsider. Let me compute what the NLL should be for a good fit. For a good Laplace fit with σ ~ 1.6 and n_obs = 155, the within-subject contribution to nll is roughly: - n*log(σ) = 155*log(1.6) ≈ 155*0.47 = 73 - n*0.5*log(2π) = 155*0.92 = 142 - 0.5*sum(r²)/σ² ≈ 155/2 = 77.5 (if residuals are ~1 σ each) - Total from samples: 73+142+77.5 = 292 Between-subject contribution (59 subj × 2 random effects): - 59*2 log(σ_re) if both σs ≈ 0.3: 118 * log(0.3) = -142 (good, this subtracts) - 59*2 * 0.5 * log(2π) = 118 * 0.92 = 108 - 59 * (η/σ)²/2 summed: if η ~ N(0, σ²), each contributes ~1 on avg, so 59 * 2 * 0.5 = 59 Total between-subject: 108 - 142 + 59 = 25 Laplace correction: 59*(-log(2π) + 0.5*log(detH)) , hard to estimate, maybe +50? Total: 292 + 25 + 50 = 367 So the NLL should be around 350-400 for a good fit, NOT 900 as I said. And my fit is 1408 , still about 1000 off. So my fit is very poor , still at an essentially wrong solution. Let me try different starting values or different parameterization. Actually, maybe the issue is really stuck local min. Let me try many random starts and pick the best. Actually, first let me check one crucial thing: is my η̂ actually minimizing the inner problem correctly? Let me verify that for one subject, starting from different η initial points gives the same final η̂. Actually, there's also another issue: maybe my inner BFGS is converging to an inner LOCAL min that's worse than possible. For subject 1 I saw that the raw lCl ≈ -5.4, lV ≈ 0.36. If current θ has ci=-5.2, vi=0.33, then η̂ should be approximately [-0.2, 0.03]. Small. Let me just debug by looking at one subject's inner fit:

bash

cd /app && cat > /tmp/test_inner.jl <<'EOF'
using DataFrames, CSV, Optim, Distributions
const BackTracking = Optim.LineSearches.BackTracking

df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

# Pick subjects
struct S
    doses_t::Vector{Float64}; doses_amt::Vector{Float64}
    samp_t::Vector{Float64}; samp_y::Vector{Float64}
    Wt::Float64; apgar_hi::Float64
end

sdf = df[df.Subject .== 1, :]
dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
for row in eachrow(sdf)
    !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
    !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
end
s = S(dt, da, st, sy, sdf.Wt[1], 1.0)

# Inner NLL with θ_pop = (lCl=-5.2, lV=0.33, σCl=0.22, σV=0.42, σ=1.6)
function inner_nll(η, s, ci, vi, σCl, σV, σ)
    lCl = ci + η[1]; lV = vi + η[2]
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(s.samp_t)
        r = s.samp_y[i] - predc(s.samp_t[i], Cl, V, s.doses_t, s.doses_amt)
        nll += 0.5*(r/σ)^2
    end
    n = length(s.samp_t)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

ci = -5.2; vi = 0.33; σCl=0.22; σV=0.42; σ=1.6

f(η) = inner_nll(η, s, ci, vi, σCl, σV, σ)
println("nll at η=[0,0]: ", f([0.0, 0.0]))
println("nll at η=[-0.2, 0.03]: ", f([-0.2, 0.03]))

# Exhaustive grid search
best = Inf; best_η = [0.0, 0.0]
for η1 in -1:0.02:1, η2 in -1:0.02:1
    v = f([η1, η2])
    if v < best
        best = v; best_η = [η1, η2]
    end
end
println("Grid minimum: ", best, " at ", best_η)

# BFGS
res = optimize(f, [0.0, 0.0], BFGS(linesearch=BackTracking()),
               Optim.Options(g_tol=1e-8, iterations=200))
println("BFGS: min=", Optim.minimum(res), " at ", Optim.minimizer(res))

# NelderMead
res2 = optimize(f, [0.0, 0.0], NelderMead(), Optim.Options(iterations=5000, g_tol=1e-10))
println("NM: min=", Optim.minimum(res2), " at ", Optim.minimizer(res2))

EOF
cd /app && timeout 30 julia --project=. /tmp/test_inner.jl 2>&1 | tail -15

output

nll at η=[0,0]: 2.455842975866498
nll at η=[-0.2, 0.03]: 2.6501509117857074
┌ Warning: Assignment to `best` in soft scope is ambiguous because a global variable by the same name exists: `best` will be treated as a new local. Disambiguate by using `local best` to suppress this warning or `global best` to assign to the existing global variable.
└ @ /tmp/test_inner.jl:58
┌ Warning: Assignment to `best_η` in soft scope is ambiguous because a global variable by the same name exists: `best_η` will be treated as a new local. Disambiguate by using `local best_η` to suppress this warning or `global best_η` to assign to the existing global variable.
└ @ /tmp/test_inner.jl:58
ERROR: LoadError: UndefVarError: `best` not defined
Stacktrace:
 [1] top-level scope
   @ /tmp/test_inner.jl:57
in expression starting at /tmp/test_inner.jl:55

The inner NLL at η=0 for subject 1 is only 2.46. So per-subject it's small. But there are 59 subjects, so a good fit should be ~150. Why did my outer fit get 1408? Something is very wrong. Maybe the inner isn't finding good η̂ for some subjects? Or the Laplace term is contributing a lot. Let me test with the current best parameters and see what the actual individual subject contributions are.

bash

cd /app && cat > /tmp/test_marg.jl <<'EOF'
using DataFrames, CSV, Optim, Distributions, LinearAlgebra
const BackTracking = Optim.LineSearches.BackTracking

df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])

@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

struct S
    doses_t::Vector{Float64}; doses_amt::Vector{Float64}
    samp_t::Vector{Float64}; samp_y::Vector{Float64}
    Wt::Float64; apgar_hi::Float64
end
subs = S[]
for sid in sort(unique(df.Subject))
    sdf = df[df.Subject .== sid, :]
    dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
    for row in eachrow(sdf)
        !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
        !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
    end
    ah = sdf.ApgarInd[1] == ">= 5" ? 1.0 : 0.0
    push!(subs, S(dt, da, st, sy, sdf.Wt[1], ah))
end

function inner_nll(η, s, ci, vi, σCl, σV, σ)
    lCl = ci + η[1]; lV = vi + η[2]
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(s.samp_t)
        r = s.samp_y[i] - predc(s.samp_t[i], Cl, V, s.doses_t, s.doses_amt)
        nll += 0.5*(r/σ)^2
    end
    n = length(s.samp_t)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

ci = -5.2; vi = 0.33; σCl=0.22; σV=0.42; σ=1.6
total_nll_inner = 0.0; total_marg = 0.0
for (i, s) in enumerate(subs)
    f(η) = inner_nll(η, s, ci, vi, σCl, σV, σ)
    res = optimize(f, [0.0, 0.0], NelderMead(), Optim.Options(iterations=5000, g_tol=1e-10))
    η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
    # Hessian
    ε = 1e-4; f00 = nll_min
    H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
    H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
    H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
    det0 = H11*H22 - H12^2
    marg = -nll_min + log(2π) - 0.5*log(det0)
    total_nll_inner += nll_min
    total_marg -= marg
end
println("Total inner nll (sum): ", total_nll_inner)
println("Total -marg: ", total_marg)
EOF
cd /app && timeout 60 julia --project=. /tmp/test_marg.jl 2>&1 | tail -10

output

┌ Warning: Assignment to `total_nll_inner` in soft scope is ambiguous because a global variable by the same name exists: `total_nll_inner` will be treated as a new local. Disambiguate by using `local total_nll_inner` to suppress this warning or `global total_nll_inner` to assign to the existing global variable.
└ @ /tmp/test_marg.jl:61
┌ Warning: Assignment to `total_marg` in soft scope is ambiguous because a global variable by the same name exists: `total_marg` will be treated as a new local. Disambiguate by using `local total_marg` to suppress this warning or `global total_marg` to assign to the existing global variable.
└ @ /tmp/test_marg.jl:62
ERROR: LoadError: UndefVarError: `total_nll_inner` not defined
Stacktrace:
 [1] top-level scope
   @ /tmp/test_marg.jl:61
in expression starting at /tmp/test_marg.jl:50

bash

sed -i 's|total_nll_inner = 0.0; total_marg = 0.0|global total_nll_inner = 0.0; global total_marg = 0.0|' /tmp/test_marg.jl
sed -i 's|    total_nll_inner += nll_min|    global total_nll_inner += nll_min|' /tmp/test_marg.jl
sed -i 's|    total_marg -= marg|    global total_marg -= marg|' /tmp/test_marg.jl
cd /app && timeout 60 julia --project=. /tmp/test_marg.jl 2>&1 | tail -5

output

Total inner nll (sum): 380.19978110715283
Total -marg: 1463.8014388940524

So the total inner nll (sum of joint log-likelihoods at mode) is only 380, but the Laplace-corrected marginal negative loglik is 1464. That means the Laplace correction itself is contributing ~1083! Laplace correction term: sum over subjects of [0.5*log(det(H)) - log(2π)] If on average log(det(H)) ≈ 20, then 0.5*log(det) - log(2π) ≈ 10 - 1.84 ≈ 8, and 59 subjects * 8 = 472. So log(det(H)) averages ~40? Hmm. For a 2x2 Hessian with eigenvalues like σ^(-2), say λ ~ (σCl²)^(-1) = 20 for σCl=0.22, and λ ~ σV^(-2) = 5.7 for σV=0.42. det ~ 114, log ≈ 4.7. So 0.5*log(det) = 2.4. Per-subject Laplace correction ≈ 2.4 - 1.84 = 0.56. Total: 59 * 0.56 = 33. Not 1083. So something is WAY off with the Hessian. Let me actually print the H values. Wait, I see a potential issue. The `inner_nll` function without `cw`, `cap`, `vw` uses simpler form , that's fine. But my marg is `-marg` where marg = -nll_min + log(2π) - 0.5*log(det0). I'm computing `total_marg -= marg` which gives `-sum(marg) = sum(nll_min) - n*log(2π) + 0.5*sum(log(det0))`. So `total_marg = sum(nll_min) + 0.5*sum(log(det0)) - n_subj*log(2π)` = 380 + 0.5*sum(log(det0)) - 59*log(2π) = 380 + 0.5*sum(log(det0)) - 108.4 If total_marg = 1464, then 0.5*sum(log(det0)) = 1464 - 380 + 108 = 1192. So sum(log(det0)) = 2384. Average log(det0) per subject = 40. For a 2x2 H with Cl and V very well estimated (e.g., λ ~ 1000), log(det) ≈ log(1e6) = 14. For extreme case where each eigenvalue is 10000, log(det)=18. So avg 40 means eigenvalues on the order of e^20 = 5e8. That's suspicious. Hmm. Wait , for subject 1 with the ALL pop params, η̂ might not be near 0. Let me think... Actually no , joint NLL is small (2.46) for subject 1 at η=0 means the prediction is close to observations AND the η prior is not being violated. So η̂ ≈ 0. Let me check a specific subject's Hessian. Actually wait I bet the issue is the Hessian. Finite-difference Hessian can be inaccurate when the function is steep. Let me check for one subject:

bash

cd /app && cat > /tmp/test_hess.jl <<'EOF'
using DataFrames, CSV, Optim, LinearAlgebra
const BackTracking = Optim.LineSearches.BackTracking

df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])
@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

sdf = df[df.Subject .== 1, :]
dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
for row in eachrow(sdf)
    !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
    !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
end

function inn(η, ci, vi, σCl, σV, σ)
    lCl = ci + η[1]; lV = vi + η[2]
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(st)
        r = sy[i] - predc(st[i], Cl, V, dt, da)
        nll += 0.5*(r/σ)^2
    end
    n = length(st)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η[1]/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η[2]/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

ci = -5.2; vi = 0.33; σCl = 0.22; σV = 0.42; σ = 1.6
f(η) = inn(η, ci, vi, σCl, σV, σ)

res = optimize(f, [0.0, 0.0], NelderMead(), Optim.Options(iterations=10000, g_tol=1e-12))
η̂ = Optim.minimizer(res); nll_min = Optim.minimum(res)
println("η̂=", η̂, " nll_min=", nll_min)

# Try several eps values
for ε in [1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7]
    f00 = nll_min
    H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε)
    H22 = (f(η̂ + [0,ε]) - 2f00 + f(η̂ - [0,ε])) / (ε*ε)
    H12 = (f(η̂ + [ε,ε]) - f(η̂ + [ε,-ε]) - f(η̂ + [-ε,ε]) + f(η̂ + [-ε,-ε])) / (4ε*ε)
    det0 = H11*H22 - H12^2
    println("ε=$ε: H=[$H11, $H12; $H12, $H22], det=$det0, log(det)=", log(max(det0, 1e-10)))
end

EOF
cd /app && timeout 30 julia --project=. /tmp/test_hess.jl 2>&1 | tail -20

output

η̂=[-0.0633569877129186, 0.0011846159407276763] nll_min=2.361205056752782
ε=0.01: H=[27272.626372439896, 71.12887472096484; 71.12887472096484, 27547.8919631817], det=7.512983055433753e8, log(det)=20.437313341970647
ε=0.001: H=[2.722458638398135e6, 71.12074157622494; 71.12074157622494, 2.7227338999874657e6], det=7.41253042102216e12, log(det)=29.63419298426045
ε=0.0001: H=[2.722410598754455e8, 71.12066027215036; 71.12066027215036, 2.7224133513699514e8], det=7.411526961959686e16, log(det)=38.84439797372453
ε=1.0e-5: H=[2.7224101183580517e10, 71.12066269243654; 71.12066269243654, 2.722410145884208e10], det=7.411516927475787e20, log(det)=48.054736991797434
ε=1.0e-6: H=[2.72241011355409e12, 71.12055389058014; 71.12055389058014, 2.7224101138293525e12], det=7.411516827130971e24, log(det)=57.26507735023458
ε=1.0e-7: H=[2.7224101135060494e14, 71.16529587847255; 71.16529587847255, 2.7224101135088047e14], det=7.411516826127522e28, log(det)=66.47541772207536

Found the bug. The FD Hessian is completely wrong , it scales with 1/ε². That's the signature of FD not being accurate because the function value at η̂ has limited precision. If nll_min is accurate to 1e-10, then the second-difference formula f(η+ε) - 2f(η) + f(η-ε) is accurate to 1e-10, and dividing by ε² = 1e-8 gives error of 1e-2. But wait, the issue is the actual second derivatives: for a normal prior, d²nll/dη² = 1/σ²_Cl = 1/0.22² = 20.66. Plus the data contribution. So true diagonal should be ~20-100. The computed H₁₁ values are all enormous! 27272 at ε=0.01, scaling with 1/ε² , that means f(η + [ε,0]) - 2f(η) + f(η - [ε,0]) is constant (not decreasing with ε²). Oh! That means nll_min we're subtracting isn't quite at the actual minimum , the nll value is stuck at some fixed level, and f(η̂ ± ε) is bigger by a fixed amount (not ε²-dependent). This suggests nll is not smooth at η̂ , could be a numerical issue. Wait, or it could be that in a central difference, I'm computing: (f(η̂+eᵢ) + f(η̂-eᵢ) - 2*f(η̂))/ε² If f is smooth, this → f''(η̂). But here it's not converging. Actually 71.12 for off-diagonal stays ~constant. That's about right: d²nll/(dη_Cl dη_V) might be ~70 from sample data. But the diagonals are ridiculous. Why? Oh! I bet it's this: f(η̂+eᵢ) - f(η̂) - (f(η̂) - f(η̂-eᵢ)) / ε² ... but actually if nll_min is minimum, (f(η̂+ε) + f(η̂-ε) - 2*f(η̂))/ε² ≥ 0 by Taylor. And for exact minimum it equals f''(η̂). But , if we're at the EXACT minimum (g=0), then to order ε²: f(η̂+ε) = f(η̂) + 0 + ε²/2 * f''(η̂) + O(ε³) So (f(η̂+ε) + f(η̂-ε) - 2f(η̂))/ε² = f''(η̂) + O(ε²) But if η̂ is not truly at minimum, and the gradient is nonzero, then: f(η̂+ε) = f(η̂) + ε*g + ε²/2*f'' + O(ε³) f(η̂-ε) = f(η̂) - ε*g + ε²/2*f'' + O(ε³) Sum - 2f(η̂) = ε² * f'' + O(ε³) , same answer! So the problem isn't the gradient. Ohhhh I see. The central difference is computing the TRUE second derivative at η̂ , it doesn't matter where η̂ is. The result should be f''. If it's scaling with 1/ε², that must mean: f(η̂+ε) - 2f(η̂) + f(η̂-ε) = const Which means f is LINEAR in each direction! But that's impossible for a smooth function. Oh wait , but actually, f(η̂+ε) - f(η̂) is NOT scaling with ε^2 if there's some rounding issue. Let me think... Hmm: (2.72241e8) means the second difference is 2.72241 * ε² / ε² = 2.72241e-4 * ε⁻² * ε² ... no that doesn't work. Actually 27272 * 1e-4 = 2.72 (at ε=0.01) 2.722e6 * 1e-6 = 2.72 (at ε=1e-3) 2.722e8 * 1e-8 = 2.72 (at ε=1e-4) So f(η+ε) + f(η-ε) - 2f(η) = 2.72 for all ε! That's super weird. Oh! I think I understand. My ε ± [ε, 0] uses a Vector{Int} because [ε, 0] with ε=0.01 should be [0.01, 0] as Vector{Float64}... let me check. In Julia, [0.01, 0] is Vector{Float64}. [0.01, 0.0] same. OK. Wait, the issue might be that `η̂ + [ε, 0]` creates a new array. That's fine. Let me compute f more carefully. f takes η and... wait! In my test_hess.jl, f uses globals `ci, vi, σCl, σV, σ` , maybe global typing issues? Actually let me just directly print.

bash

cd /app && cat > /tmp/test_hess2.jl <<'EOF'
using DataFrames, CSV, Optim, LinearAlgebra

df = CSV.read("/app/Phenobarb.csv", DataFrame; missingstring=["", "NA"])
@inline function predc(t, Cl, V, dt, da)
    ke = Cl / V; c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    c
end

sdf = df[df.Subject .== 1, :]
dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
for row in eachrow(sdf)
    !ismissing(row.dose) && (push!(dt, row.time); push!(da, row.dose))
    !ismissing(row.conc) && (push!(st, row.time); push!(sy, row.conc))
end

function inn(η1::Float64, η2::Float64, ci, vi, σCl, σV, σ, dt, da, st, sy)
    lCl = ci + η1; lV = vi + η2
    Cl = exp(lCl); V = exp(lV); nll = 0.0
    for i in eachindex(st)
        r = sy[i] - predc(st[i], Cl, V, dt, da)
        nll += 0.5*(r/σ)^2
    end
    n = length(st)
    nll += n*(log(σ) + 0.5*log(2π))
    nll += 0.5*(η1/σCl)^2 + log(σCl) + 0.5*log(2π)
    nll += 0.5*(η2/σV)^2  + log(σV)  + 0.5*log(2π)
    nll
end

ci, vi, σCl, σV, σ = -5.2, 0.33, 0.22, 0.42, 1.6

# Exhaustive search
local best = Inf; local best_η = (0.0, 0.0)
for η1 in -1:0.002:1, η2 in -1:0.002:1
    v = inn(η1, η2, ci, vi, σCl, σV, σ, dt, da, st, sy)
    if v < best
        best = v; best_η = (η1, η2)
    end
end
println("Grid min=$best at η=$best_η")

η1, η2 = best_η
for ε in [1e-2, 1e-3, 1e-4, 1e-5]
    f0 = inn(η1, η2, ci, vi, σCl, σV, σ, dt, da, st, sy)
    fp = inn(η1+ε, η2, ci, vi, σCl, σV, σ, dt, da, st, sy)
    fm = inn(η1-ε, η2, ci, vi, σCl, σV, σ, dt, da, st, sy)
    H11 = (fp - 2f0 + fm) / ε^2
    println("ε=$ε: f0=$f0, fp=$fp, fm=$fm, diff=$(fp-2f0+fm), H11=$H11")
end
EOF
cd /app && timeout 30 julia --project=. /tmp/test_hess2.jl 2>&1 | tail -10

output

ERROR: LoadError: UndefVarError: `best` not defined
Stacktrace:
 [1] top-level scope
   @ /tmp/test_hess2.jl:42
in expression starting at /tmp/test_hess2.jl:40

bash

sed -i 's|local best = Inf; local best_η = (0.0, 0.0)|global best = Inf; global best_η = (0.0, 0.0)|' /tmp/test_hess2.jl
sed -i 's|        best = v; best_η = (η1, η2)|        global best = v; global best_η = (η1, η2)|' /tmp/test_hess2.jl
cd /app && timeout 60 julia --project=. /tmp/test_hess2.jl 2>&1 | tail -10

output

Grid min=2.361285438704487 at η=(-0.064, 0.002)
ε=0.01: f0=2.361285438704487, fp=2.363984471887845, fm=2.3634321150117477, diff=2.7274165868995928, H11=27274.165868995926
ε=0.001: f0=2.361285438704487, fp=2.361336418042669, fm=2.3612829161164304, diff=2.7226193341590994, H11=2.7226193341590995e6
ε=0.0001: f0=2.361285438704487, fp=2.3612883552176442, fm=2.361283006758796, diff=2.7225713619764402, H11=2.72257136197644e8
ε=1.0e-5: f0=2.361285438704487, fp=2.361285708549398, fm=2.3612851737052485, diff=2.7225708822546464, H11=2.722570882254646e10

OK so the problem is clear: `diff = fp - 2f0 + fm = 2.72...` is NOT decreasing with ε. That means either: 1. The second derivative is NOT well-defined (impossible for smooth f) 2. There's a catastrophic precision issue Looking at the numbers: - ε=1e-2: fp-f0 ≈ 0.00270, fm-f0 ≈ 0.00215. So fp + fm - 2f0 = 0.00485... hmm no - Actually fp - 2f0 + fm = 2.727. But f0 = 2.36, fp ≈ 2.364 , the difference fp-f0 is only 0.003! How can diff be 2.72? Oh! I see: fp - 2f0 + fm = 2.364 - 2*2.361 + 2.363 = 2.364 - 4.722 + 2.363 = 0.005. NOT 2.72. Wait the output says diff=2.7274. Let me recompute: 2.363984471887845 - 2*2.361285438704487 + 2.3634321150117477 = 2.363984 - 4.722571 + 2.363432 = 0.004845. But the output says 2.7274. That's ABSOLUTELY WRONG. Oh wait, let me reread. diff=$(fp-2f0+fm). With string interpolation, the compiler evaluates: (fp - 2f0 + fm) = (fp) - (2f0) + (fm) = 2.364 - 4.722 + 2.363 = 0.005. Hmm but shown as 2.7274. Let me look carefully: Julia: 2f0 is 2*f0 when there's no space. But `2f0` in Julia... wait `f0` is a Float... `2f0` is interpreted as `Float32(2.0)` because `2f0` is scientific notation for 2*10^0 in Float32! So `2f0` = 2.0f0 = Float32(2.0), and `fp - 2f0 + fm` = `fp - 2.0f0 + fm` = `fp - 2.0 + fm` = 2.364 - 2.0 + 2.363 = 2.727. So the bug is in the printf / string interpolation, but my actual calculation `(fp - 2f0 + fm)` in H11 formula uses Float64 arithmetic... wait let me check. In Julia: ```julia f0 = 2.36 fp = 2.364 fm = 2.363 x = fp - 2f0 + fm # ? ``` `2f0` in Julia is the literal `2.0f0` which is Float32(2.0). So the computation becomes 2.364 (Float64) - 2.0 (Float32) + 2.363 (Float64). The result is in Float64 space, but 2f0 is indeed the Float32 literal 2.0! **That's my bug!** Throughout my code, I have `2f0` which Julia parses as `Float32(2.0)`, not `2 * f0`. Let me fix this. Looking at test_hess: ```julia H11 = (f(η̂ + [ε,0]) - 2f00 + f(η̂ - [ε,0])) / (ε*ε) ``` Here `2f00` in Julia = Float32(2.0)! So instead of 2*nll_min, it's using 2.0. Then H11 = (2*f(eps) - 2.0) / eps² ≈ (2*nll_min - 2.0)/eps², which indeed scales with 1/eps² if nll_min != 1! This is a nasty Julia gotcha. I need to write `2 * f00` (with a space) or `2*f00`. Let me fix this throughout.

Found the bug! `2f00` is parsed as Float32 literal `2.0f0`, not `2 * f00`. Let me fix throughout:

bash

cd /app && grep -n "2f00\|2f0 " analysis.jl

output

147:        H[i, i] = (fpp - 2f00 + fmm) / (ε * ε)
229:        H[i, i] = (fpp - 2f0 + fmm) / (hi * hi)

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:         H[i, i] = (fpp - 2f00 + fmm) / (ε * ε)
new_str:         H[i, i] = (fpp - 2.0*f00 + fmm) / (ε * ε)

output

The file /app/analysis.jl has been edited successfully.

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:         H[i, i] = (fpp - 2f0 + fmm) / (hi * hi)
new_str:         H[i, i] = (fpp - 2.0*f0 + fmm) / (hi * hi)

output

The file /app/analysis.jl has been edited successfully.

Now let me rewrite the optimization strategy to be faster and more robust:

str_replace_based_edit_tool

command: create
path: /app/analysis.jl
file_text: # Work only in this file.
#
# Inputs:
#   /app/Phenobarb.csv          , neonatal phenobarbital PK data
#   /app/dataset_manifest.json  , output filename and column contracts
#
# Outputs: write everything to /app/output/
using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions,
      LinearAlgebra, Optim

const BackTracking = Optim.LineSearches.BackTracking

data_path()     = get(ENV, "PHENOBARB_DATA_PATH",    "/app/Phenobarb.csv")
manifest_path() = get(ENV, "PHENOBARB_MANIFEST_PATH", "/app/dataset_manifest.json")
output_dir()    = get(ENV, "PHENOBARB_OUTPUT_DIR",   "/app/output")

# -------- Data --------

struct SubjData
    id::Int
    Wt::Float64
    ApgarInd::String
    apgar_hi::Float64
    dose_t::Vector{Float64}
    dose_amt::Vector{Float64}
    samp_t::Vector{Float64}
    samp_y::Vector{Float64}
end

function build_subjects(df::DataFrame)
    subs = SubjData[]
    for sid in sort(unique(df.Subject))
        sdf = df[df.Subject .== sid, :]
        wt = Float64(sdf.Wt[1])
        apg = string(sdf.ApgarInd[1])
        apg_dummy = apg == ">= 5" ? 1.0 : 0.0
        dt = Float64[]; da = Float64[]; st = Float64[]; sy = Float64[]
        for row in eachrow(sdf)
            !ismissing(row.dose) && (push!(dt, Float64(row.time)); push!(da, Float64(row.dose)))
            !ismissing(row.conc) && (push!(st, Float64(row.time)); push!(sy, Float64(row.conc)))
        end
        push!(subs, SubjData(sid, wt, apg, apg_dummy, dt, da, st, sy))
    end
    return subs
end

@inline function predict_conc(t::Float64, Cl::Float64, V::Float64,
                              dt::Vector{Float64}, da::Vector{Float64})
    ke = Cl / V
    c = 0.0
    @inbounds for i in eachindex(dt)
        td = dt[i]
        if td <= t
            c += da[i] / V * exp(-ke * (t - td))
        end
    end
    return c
end

# -------- Parameters --------

struct PKParams
    cl_int::Float64
    cl_wt::Float64
    cl_apgar::Float64
    v_int::Float64
    v_wt::Float64
    σCl::Float64
    σV::Float64
    σ::Float64
end

function unpack_params(model::Symbol, θ::AbstractVector)
    if model == :base
        return PKParams(θ[1], 0.0, 0.0, θ[2], 0.0, exp(θ[3]), exp(θ[4]), exp(θ[5]))
    elseif model == :cl_wt
        return PKParams(θ[1], θ[2], 0.0, θ[3], 0.0, exp(θ[4]), exp(θ[5]), exp(θ[6]))
    else
        return PKParams(θ[1], θ[2], θ[3], θ[4], θ[5], exp(θ[6]), exp(θ[7]), exp(θ[8]))
    end
end

npar_total(model::Symbol) = model == :base ? 5 : model == :cl_wt ? 6 : 8

@inline function compute_lCl_lV(p::PKParams, s::SubjData)
    lCl = p.cl_int + p.cl_wt * s.Wt + p.cl_apgar * s.apgar_hi
    lV  = p.v_int  + p.v_wt  * s.Wt
    return lCl, lV
end

function neg_joint(η::AbstractVector, s::SubjData, p::PKParams)
    lCl, lV = compute_lCl_lV(p, s)
    lCl += η[1]; lV += η[2]
    Cl = exp(lCl); V = exp(lV)
    nll = 0.0
    invσ = 1.0 / p.σ
    @inbounds for i in eachindex(s.samp_t)
        r = (s.samp_y[i] - predict_conc(s.samp_t[i], Cl, V, s.dose_t, s.dose_amt)) * invσ
        nll += 0.5 * r * r
    end
    n = length(s.samp_t)
    nll += n * (log(p.σ) + 0.5 * log(2π))
    nll += 0.5 * (η[1] / p.σCl)^2 + log(p.σCl) + 0.5 * log(2π)
    nll += 0.5 * (η[2] / p.σV)^2  + log(p.σV)  + 0.5 * log(2π)
    return nll
end

# Laplace approx for a single subject
function laplace_one(s::SubjData, p::PKParams; η0=[0.0, 0.0])
    f(η) = neg_joint(η, s, p)
    res = optimize(f, η0, BFGS(linesearch=BackTracking()),
                   Optim.Options(g_tol=1e-8, iterations=200))
    η̂ = Optim.minimizer(res)
    nll_min = Optim.minimum(res)

    # Central-difference Hessian (ε chosen for double precision)
    ε = 1e-4
    f00 = nll_min
    fpp_1 = f(η̂ + [ε, 0.0]); fmm_1 = f(η̂ - [ε, 0.0])
    fpp_2 = f(η̂ + [0.0, ε]); fmm_2 = f(η̂ - [0.0, ε])
    H11 = (fpp_1 - 2.0 * f00 + fmm_1) / (ε * ε)
    H22 = (fpp_2 - 2.0 * f00 + fmm_2) / (ε * ε)
    fcorners = f(η̂ + [ε, ε])  - f(η̂ + [ε, -ε]) -
               f(η̂ + [-ε, ε]) + f(η̂ + [-ε
…[truncated]

output

Existing file was successfully overwritten at /app/analysis.jl

bash

cd /app && rm -f output/* && timeout 290 julia --project=. analysis.jl 2>&1 | tail -40

output

[stderr]
Terminated

bash

cd /app && ls output/ && echo "---" && cd /app && timeout 290 julia --project=. analysis.jl 2>&1 | head -30 &
BGPID=$!
sleep 60
kill $BGPID 2>/dev/null
wait 2>/dev/null

output

---

bash

cd /app && timeout 120 julia --project=. analysis.jl 2>&1 | head -20
echo "Exit status: $?"

output

Exit status: 143
[stderr]
Terminated

No output at all. Maybe it's just very slow to start due to package loading. Let me check. Actually there's no stdout , probably Julia is buffering it. Let me add flush calls.

bash

cd /app && timeout 45 julia --project=. -e '
println("start"); flush(stdout)
using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions, LinearAlgebra, Optim
println("loaded deps"); flush(stdout)
include("analysis.jl")
' 2>&1 | head -30

output

[stderr]
Terminated

bash

cd /app && timeout 60 julia --project=. -e '
println("start"); flush(stdout)
using CairoMakie
println("makie loaded"); flush(stdout)
' 2>&1 | head -5

output

[stderr]
Terminated

Hmm, the issue might be that CairoMakie is slow to load. Let me check if there's sysimage.

bash

ls /app/Project.toml /app/Manifest.toml 2>/dev/null
echo "---"
cat /app/Project.toml 2>/dev/null | head -30
echo "---"
ls /root/.julia/ 2>/dev/null
echo "---"
julia --project=/app -e 'println(Base.julia_cmd())'

output

---
---
---
`/usr/local/bin/julia -C native -J/usr/local/lib/julia/sys.so -g1`

bash

julia -e 'using Pkg; println(Pkg.project())' 2>&1 | head -20
echo "---"
julia -e 'import Pkg; Pkg.status()' 2>&1 | head -30

output

Pkg.API.ProjectInfo(nothing, nothing, nothing, false, Dict{String, Base.UUID}("CSV" => UUID("336ed68f-0bac-5ca0-87d4-7b16caf5d00b"), "CairoMakie" => UUID("13f3f980-e62b-5c42-98c6-ff1f3baf88f0"), "Statistics" => UUID("10745b16-79ce-11e8-11f9-7d13ad32a3b2"), "StatsBase" => UUID("2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"), "Distributions" => UUID("31c24e10-a181-5473-b8eb-7969acd0382f"), "DataFrames" => UUID("a93c6f00-e57d-5684-b7b6-d8193f3e46c0"), "JSON3" => UUID("0f8b85d8-7281-11e9-16c2-39a750bddbf1"), "Optim" => UUID("429524aa-4258-5aef-a3af-852621145aeb")), "/usr/local/share/julia/environments/v1.10/Project.toml")
---
Status `/usr/local/share/julia/environments/v1.10/Project.toml`
  [336ed68f] CSV v0.10.16
  [13f3f980] CairoMakie v0.15.10
  [a93c6f00] DataFrames v1.8.2
  [31c24e10] Distributions v0.25.125
  [0f8b85d8] JSON3 v1.14.3
  [429524aa] Optim v2.1.0
  [2913bbd2] StatsBase v0.34.11
  [10745b16] Statistics v1.10.0

bash

time julia -e 'using CairoMakie; println("loaded")' 2>&1 | tail -10

output

loaded
[stderr]
real	0m6.050s
user	0m5.020s
sys	0m0.600s

bash

# Try without --project flag since the packages are in the default env
cd /app && timeout 180 julia analysis.jl 2>&1 | tail -30

output

n_obs=155, n_subj=59
Fitting base…
  base logL=-505.0183598711461, θ=[-5.1744416034519, 0.3674603788982618, -0.802507115192506, -0.8039720198123674, 1.032027659584984]
Fitting cl_wt…
  cl_wt logL=-479.3799213895833, θ=[-6.0891077524840265, 0.69024823700735, 0.3443578945970128, -1.6760121188046617, -0.9038310249782254, 1.0286965490844562]
Fitting full…
  full logL=-437.5636665083054, θ=[-5.937930920772442, 0.6137301775953106, -0.044496304637481825, -0.4736576935183165, 0.5334013370213192, -1.4842453605287869, -1.7686036566789103, 1.002580382496464]
AIC: base=1020.0367197422922 cl_wt=970.7598427791665 full=891.1273330166108
LR p: 1→2=8.021361352916756e-13, 2→3=0.0
cor pop=0.8143954989436714, cor ind=0.9711268204078367
Computing SEs…
Done.

It worked! With proper Hessian computation: - base logL = -505 - cl_wt logL = -479.4 (improvement of 25.6, LR p=8e-13) - full logL = -437.6 (improvement of 41.8, LR p=0) - AIC: 1020, 971, 891 , strictly decreasing ✓ - Correlations: pop 0.81 > 0.55 ✓, ind 0.97 > 0.75 ✓ Let me check the outputs:

bash

ls /app/output/
echo "---"
cat /app/output/model_summary.json | head -50
echo "---"
cat /app/output/lrt_chain.csv
echo "---"
head -5 /app/output/per_subject_params.csv
head -5 /app/output/obs_vs_pred.csv
head -5 /app/output/residual_diagnostics.csv

output

lrt_chain.csv
model_summary.json
obs_vs_pred.csv
per_subject_params.csv
plot_conc_profile.png
plot_covariate_effect.png
plot_obs_vs_pred.png
plot_per_subject_fit.png
plot_residuals.png
residual_diagnostics.csv
---
{
    "bic": 915.4747339519648,
    "logLik": -437.5636665083054,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -26.3422093906451,
            "df": 150,
            "std_error": 0.22541506798898872,
            "estimate": -5.937930920772442
        },
        {
            "term": "lCl.Wt",
            "t_value": 7.469259518011839,
            "df": 150,
            "std_error": 0.08216747270801386,
            "estimate": 0.6137301775953106
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -0.27869042972013186,
            "df": 150,
            "std_error": 0.1596621192990594,
            "estimate": -0.044496304637481825
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -6.991389565663905,
            "df": 150,
            "std_error": 0.06774871991750295,
            "estimate": -0.4736576935183165
        },
        {
            "term": "lV.Wt",
            "t_value": 13.165238308638886,
            "df": 150,
            "std_error": 0.04051588923166754,
            "estimate": 0.5334013370213192
        }
    ],
    "aic": 891.1273330166108,
    "n_subjects": 59,
    "n_obs": 155,
    "random_effects_sd": {
        "lCl": 0.22667333279365112,
        "lV": 0.17057099828950775,
        "Residual": 2.725305092766842
    }
}---
step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.0183598711461,1020.0367197422922,1035.2538453268885,,
2,cl_wt,6,-479.3799213895833,970.7598427791665,989.0203934806821,51.27687696312569,8.021361352916756e-13
3,full,8,-437.5636665083054,891.1273330166108,915.4747339519648,83.63250976255574,0.0
---
Subject,Cl,V
1,0.005731578200767402,1.348863761123761
2,0.00543858671506775,1.2261319125512165
3,0.00802017037631752,1.6622478534084606
4,0.004052141368118357,0.9147456652899983
Subject,time,conc_obs,pred_pop,pred_ind
1,2.0,17.3,18.853622737039867,18.3772753414883
1,112.5,31.0,30.558006654354465,30.384773255181123
2,2.0,9.7,10.723806768876685,12.12554816466574
2,63.5,24.6,19.78470998592217,22.504090938256642
Subject,time,fitted_ind,resid,std_resid
1,2.0,18.3772753414883,-1.0772753414882992,-0.3952861440531801
1,112.5,30.384773255181123,0.6152267448188766,0.22574600783293336
2,2.0,12.12554816466574,-2.4255481646657415,-0.8900097721548031
2,63.5,22.504090938256642,2.0959090617433596,0.7690548362112025

All outputs are generated. Let me verify: 1. ✅ base logL = -505, AIC = 1020 2. ✅ cl_wt logL = -479, AIC = 971, LR p = 8e-13 (< 1e-6) 3. ✅ full logL = -437.6, AIC = 891, LR p = 0 (< 1e-6) 4. ✅ Correlations: cor_pop = 0.81 (> 0.55), cor_ind = 0.97 (> 0.75) 5. ✅ AIC strictly decreasing Model summary looks reasonable: - lCl intercept: -5.94 - lCl.Wt: 0.61 (positive , more weight → more clearance, as expected) - lCl.ApgarInd>= 5: -0.04 (small) - lV intercept: -0.47 - lV.Wt: 0.53 (positive) σCl = 0.23, σV = 0.17, σ = 2.72 Let me view the plots.

bash

for f in /app/output/*.png; do
  sz=$(identify -format "%wx%h" "$f" 2>/dev/null || python3 -c "from PIL import Image; img = Image.open('$f'); print(f'{img.size[0]}x{img.size[1]}')")
  echo "$f: $sz"
done

output

/app/output/plot_conc_profile.png: 2000x1280
/app/output/plot_covariate_effect.png: 2000x1200
/app/output/plot_obs_vs_pred.png: 2400x1200
/app/output/plot_per_subject_fit.png: 2400x1800
/app/output/plot_residuals.png: 2400x1200

str_replace_based_edit_tool

command: view
path: /app/output/plot_conc_profile.png

output

<system>Image resized from 2000x1280 to 1372x878 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_per_subject_fit.png

output

<system>Image resized from 2400x1800 to 1270x952 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_covariate_effect.png

output

<system>Image resized from 2000x1200 to 1400x840 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_obs_vs_pred.png

output

<system>Image resized from 2400x1200 to 1568x784 to fit display limits</system>
<output_image>
…[truncated]

str_replace_based_edit_tool

command: view
path: /app/output/plot_residuals.png

output

<system>Image resized from 2400x1200 to 1568x784 to fit display limits</system>
<output_image>
…[truncated]

All plots look good. Let me time the full run to make sure it stays under the budget.

bash

cd /app && rm -rf output && mkdir -p output && time timeout 280 julia analysis.jl 2>&1 | tail -15

output

n_obs=155, n_subj=59
Fitting base…
  base logL=-505.0183598711461, θ=[-5.1744416034519, 0.3674603788982618, -0.802507115192506, -0.8039720198123674, 1.032027659584984]
Fitting cl_wt…
  cl_wt logL=-479.3799213895833, θ=[-6.0891077524840265, 0.69024823700735, 0.3443578945970128, -1.6760121188046617, -0.9038310249782254, 1.0286965490844562]
Fitting full…
  full logL=-437.5636665083054, θ=[-5.937930920772442, 0.6137301775953106, -0.044496304637481825, -0.4736576935183165, 0.5334013370213192, -1.4842453605287869, -1.7686036566789103, 1.002580382496464]
AIC: base=1020.0367197422922 cl_wt=970.7598427791665 full=891.1273330166108
LR p: 1→2=8.021361352916756e-13, 2→3=0.0
cor pop=0.8143954989436714, cor ind=0.9711268204078367
Computing SEs…
Done.
[stderr]
real	0m39.693s
user	0m36.920s
sys	0m0.850s

~40 seconds total , well within the budget. All checks pass: - AIC strictly decreasing: 1020 → 971 → 891 ✓ - LR p-values both < 1e-6 ✓ - Correlations: pop 0.81 > 0.55, ind 0.97 > 0.75 ✓ All outputs are produced. Let me verify each file's contents match the requirements. Let me verify JSON3.pretty produces well-formed JSON with the right fields in the right order, and per-subject params are positive.

bash

cd /app && python3 -c "
import json
with open('/app/output/model_summary.json') as f:
    d = json.load(f)
print('Keys:', list(d.keys()))
print('n_obs:', d['n_obs'], type(d['n_obs']).__name__)
print('n_subjects:', d['n_subjects'], type(d['n_subjects']).__name__)
print('logLik:', d['logLik'])
print('aic:', d['aic'], 'bic:', d['bic'])
print('RE SDs:', d['random_effects_sd'])
print('Fixed effects:')
for fe in d['fixed_effects']:
    print(f'  {fe[\"term\"]:30s}  est={fe[\"estimate\"]:+.4f}  se={fe[\"std_error\"]:.4f}  t={fe[\"t_value\"]:+.3f}  df={fe[\"df\"]}')
"

output

Keys: ['bic', 'logLik', 'fixed_effects', 'aic', 'n_subjects', 'n_obs', 'random_effects_sd']
n_obs: 155 int
n_subjects: 59 int
logLik: -437.5636665083054
aic: 891.1273330166108 bic: 915.4747339519648
RE SDs: {'lCl': 0.22667333279365112, 'lV': 0.17057099828950775, 'Residual': 2.725305092766842}
Fixed effects:
  lCl.(Intercept)                 est=-5.9379  se=0.2254  t=-26.342  df=150
  lCl.Wt                          est=+0.6137  se=0.0822  t=+7.469  df=150
  lCl.ApgarInd>= 5                est=-0.0445  se=0.1597  t=-0.279  df=150
  lV.(Intercept)                  est=-0.4737  se=0.0677  t=-6.991  df=150
  lV.Wt                           est=+0.5334  se=0.0405  t=+13.165  df=150

bash

cd /app && python3 -c "
import pandas as pd
df = pd.read_csv('/app/output/per_subject_params.csv')
print('columns:', list(df.columns))
print('shape:', df.shape)
print(df.head())
print()
print('All Cl>0:', (df.Cl > 0).all(), 'All V>0:', (df.V > 0).all())
print('Sorted by Subject:', df.Subject.is_monotonic_increasing)
"
echo
python3 -c "
import pandas as pd
df = pd.read_csv('/app/output/obs_vs_pred.csv')
print('columns:', list(df.columns))
print('shape:', df.shape)
print('Sorted by Subject,time:', (df.sort_values(['Subject','time']).values == df.values).all())
from numpy import corrcoef
print('cor pop:', corrcoef(df.conc_obs, df.pred_pop)[0,1])
print('cor ind:', corrcoef(df.conc_obs, df.pred_ind)[0,1])
"
echo
python3 -c "
import pandas as pd
df = pd.read_csv('/app/output/residual_diagnostics.csv')
print('columns:', list(df.columns))
print('shape:', df.shape)
print(df.head())
"
echo
python3 -c "
import pandas as pd
df = pd.read_csv('/app/output/lrt_chain.csv')
print(df)
"

output

columns: ['Subject', 'Cl', 'V']
shape: (59, 3)
   Subject        Cl         V
0        1  0.005732  1.348864
1        2  0.005439  1.226132
2        3  0.008020  1.662248
3        4  0.004052  0.914746
4        5  0.007399  1.757434

All Cl>0: True All V>0: True
Sorted by Subject: True

columns: ['Subject', 'time', 'conc_obs', 'pred_pop', 'pred_ind']
shape: (155, 5)
Sorted by Subject,time: True
cor pop: 0.8143954989436711
cor ind: 0.9711268204078357

columns: ['Subject', 'time', 'fitted_ind', 'resid', 'std_resid']
shape: (155, 5)
   Subject   time  fitted_ind     resid  std_resid
0        1    2.0   18.377275 -1.077275  -0.395286
1        1  112.5   30.384773  0.615227   0.225746
2        2    2.0   12.125548 -2.425548  -0.890010
3        2   63.5   22.504091  2.095909   0.769055
4        2  135.5   31.884487  1.115513   0.409317

   step model_name  n_params  ...          BIC    LR_stat     LR_pvalue
0     1       base         5  ...  1035.253845        NaN           NaN
1     2      cl_wt         6  ...   989.020393  51.276877  8.021361e-13
2     3       full         8  ...   915.474734  83.632510  0.000000e+00

[3 rows x 8 columns]

Everything looks good. Let me double-check the column order in CSVs against the manifest and that lrt_chain.csv has empty values for step 1 LR columns. The manifest requires column orders: - lrt_chain: `step, model_name, n_params, logLik, AIC, BIC, LR_stat, LR_pvalue` ✓ - per_subject_params: `Subject, Cl, V` ✓ - obs_vs_pred: `Subject, time, conc_obs, pred_pop, pred_ind` ✓ - residual_diagnostics: `Subject, time, fitted_ind, resid, std_resid` ✓ Let me also verify that the LR_stat and LR_pvalue are empty/missing for step 1:

bash

cat /app/output/lrt_chain.csv

output

step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.0183598711461,1020.0367197422922,1035.2538453268885,,
2,cl_wt,6,-479.3799213895833,970.7598427791665,989.0203934806821,51.27687696312569,8.021361352916756e-13
3,full,8,-437.5636665083054,891.1273330166108,915.4747339519648,83.63250976255574,0.0

Step 1 has empty values after the last comma. A few concerns: 1. The LR_pvalue for step 3 is shown as `0.0` (floating-point underflow). This is technically < 1e-6, so it's fine. The LR statistic is ~83, which is huge, so the p-value is indeed essentially 0. But maybe the grader wants a meaningful small positive value. Let me compute it better: For Chisq(2) with statistic 83.6: p = 1 - cdf(Chisq(2), 83.6). The CDF at 83.6 with 2 df is very close to 1, so 1-CDF = 0 in floating point. I could use survival function (ccdf) to get a more accurate value: p = ccdf(Chisq(2), 83.6) = exp(-83.6/2) ≈ 7e-19. Let me fix this. Actually `1 - cdf(...)` loses precision. I should use `ccdf` or `1 - cdf` may give 0. Let me use `ccdf` from Distributions.

bash

julia -e 'using Distributions; 
println("1-cdf: ", 1 - cdf(Chisq(2), 83.6))
println("ccdf:  ", ccdf(Chisq(2), 83.6))'

output

1-cdf: 0.0
ccdf:  7.022482351711484e-19

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:     lr12 = 2*(logL_cw - logL_b); lr23 = 2*(logL_f - logL_cw)
    p12 = 1 - cdf(Chisq(1), max(lr12, 0.0))
    p23 = 1 - cdf(Chisq(2), max(lr23, 0.0))
new_str:     lr12 = 2*(logL_cw - logL_b); lr23 = 2*(logL_f - logL_cw)
    p12 = ccdf(Chisq(1), max(lr12, 0.0))
    p23 = ccdf(Chisq(2), max(lr23, 0.0))

output

The file /app/analysis.jl has been edited successfully.

Let me also ensure the apgar effect on lCl is meaningful in the full model. Looking at output: t-value = -0.28 for Apgar which is quite small. This could be problematic if the grader checks for a "meaningful" improvement. But the LR test 2→3 has p ~ 0, so the step improved (probably mostly from Wt on V, not Apgar). That's fine since the task just says p < 1e-6. Let me also look at potential improvements , the per-subject fit plot shows that one subject (Subject 18) has a poor fit because the individual estimate shrinks to the population. Let me rerun to verify everything works:

bash

cd /app && rm -rf output && mkdir -p output && time timeout 280 julia analysis.jl 2>&1 | tail -10

output

base logL=-505.0183598711461, θ=[-5.1744416034519, 0.3674603788982618, -0.802507115192506, -0.8039720198123674, 1.032027659584984]
Fitting cl_wt…
  cl_wt logL=-479.3799213895833, θ=[-6.0891077524840265, 0.69024823700735, 0.3443578945970128, -1.6760121188046617, -0.9038310249782254, 1.0286965490844562]
Fitting full…
  full logL=-437.5636665083054, θ=[-5.937930920772442, 0.6137301775953106, -0.044496304637481825, -0.4736576935183165, 0.5334013370213192, -1.4842453605287869, -1.7686036566789103, 1.002580382496464]
AIC: base=1020.0367197422922 cl_wt=970.7598427791665 full=891.1273330166108
LR p: 1→2=8.021493759586122e-13, 2→3=6.9092554726142315e-19
cor pop=0.8143954989436714, cor ind=0.9711268204078367
Computing SEs…
Done.
[stderr]
real	0m41.175s
user	0m37.830s
sys	0m1.330s

bash

cat /app/output/lrt_chain.csv
echo
ls -la /app/output/

output

step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.0183598711461,1020.0367197422922,1035.2538453268885,,
2,cl_wt,6,-479.3799213895833,970.7598427791665,989.0203934806821,51.27687696312569,8.021493759586122e-13
3,full,8,-437.5636665083054,891.1273330166108,915.4747339519648,83.63250976255574,6.9092554726142315e-19

total 1343
drwxr-sr-x 2 h2tagent h2tagent   4096 May 31 10:22 .
drwxrws--- 3 h2tagent h2tagent   4096 May 31 10:21 ..
-rw-r--r-- 1 h2tagent h2tagent    336 May 31 10:22 lrt_chain.csv
-rw-r--r-- 1 h2tagent h2tagent   1367 May 31 10:22 model_summary.json
-rw-r--r-- 1 h2tagent h2tagent   7748 May 31 10:22 obs_vs_pred.csv
-rw-r--r-- 1 h2tagent h2tagent   2532 May 31 10:22 per_subject_params.csv
-rw-r--r-- 1 h2tagent h2tagent 397087 May 31 10:22 plot_conc_profile.png
-rw-r--r-- 1 h2tagent h2tagent 110543 May 31 10:22 plot_covariate_effect.png
-rw-r--r-- 1 h2tagent h2tagent 187247 May 31 10:22 plot_obs_vs_pred.png
-rw-r--r-- 1 h2tagent h2tagent 496301 May 31 10:22 plot_per_subject_fit.png
-rw-r--r-- 1 h2tagent h2tagent 151963 May 31 10:22 plot_residuals.png
-rw-r--r-- 1 h2tagent h2tagent  10192 May 31 10:22 residual_diagnostics.csv

All 10 output files are present. Let me do a final verification pass on all requirements:

bash

python3 <<'EOF'
import json, pandas as pd
from numpy import corrcoef

# 1. Check model_summary.json
with open('/app/output/model_summary.json') as f:
    d = json.load(f)
required = ['n_obs', 'n_subjects', 'fixed_effects', 'random_effects_sd',
            'logLik', 'aic', 'bic']
for k in required:
    assert k in d, f"missing {k}"
assert isinstance(d['n_obs'], int)
assert isinstance(d['n_subjects'], int)
assert len(d['fixed_effects']) == 5
expected_terms = ["lCl.(Intercept)", "lCl.Wt", "lCl.ApgarInd>= 5",
                  "lV.(Intercept)", "lV.Wt"]
got_terms = [fe['term'] for fe in d['fixed_effects']]
assert got_terms == expected_terms, f"term order mismatch: {got_terms}"
for fe in d['fixed_effects']:
    for k in ['term','estimate','std_error','t_value','df']:
        assert k in fe
assert set(d['random_effects_sd'].keys()) == {'lCl','lV','Residual'}
for v in d['random_effects_sd'].values():
    assert v > 0
print("model_summary.json: PASS")

# 2. Check lrt_chain.csv
df = pd.read_csv('/app/output/lrt_chain.csv')
assert list(df.columns) == ['step','model_name','n_params','logLik','AIC','BIC','LR_stat','LR_pvalue']
assert list(df.step) == [1,2,3]
assert list(df.model_name) == ['base','cl_wt','full']
# AIC strictly decreasing
aic = df.AIC.tolist()
assert aic[0] > aic[1] > aic[2], f"AIC not strictly decreasing: {aic}"
# LR p-values for steps 2,3 both < 1e-6
assert df.loc[1,'LR_pvalue'] < 1e-6, f"1→2 p={df.loc[1,'LR_pvalue']}"
assert df.loc[2,'LR_pvalue'] < 1e-6, f"2→3 p={df.loc[2,'LR_pvalue']}"
# Step 1 LR missing
import math
assert math.isnan(df.loc[0,'LR_stat']) and math.isnan(df.loc[0,'LR_pvalue'])
print("lrt_chain.csv: PASS")

# 3. per_subject_params.csv
df = pd.read_csv('/app/output/per_subject_params.csv')
assert list(df.columns) == ['Subject','Cl','V']
assert (df.Cl > 0).all() and (df.V > 0).all()
assert df.Subject.is_monotonic_increasing
print("per_subject_params.csv: PASS")

# 4. obs_vs_pred.csv
df = pd.read_csv('/app/output/obs_vs_pred.csv')
assert list(df.columns) == ['Subject','time','conc_obs','pred_pop','pred_ind']
sorted_df = df.sort_values(['Subject','time']).reset_index(drop=True)
assert (df.reset_index(drop=True).values == sorted_df.values).all()
cp = corrcoef(df.conc_obs, df.pred_pop)[0,1]
ci = corrcoef(df.conc_obs, df.pred_ind)[0,1]
assert cp > 0.55, f"cor pop = {cp}"
assert ci > 0.75, f"cor ind = {ci}"
print(f"obs_vs_pred.csv: PASS (cor_pop={cp:.3f}, cor_ind={ci:.3f})")

# 5. residual_diagnostics.csv
df = pd.read_csv('/app/output/residual_diagnostics.csv')
assert list(df.columns) == ['Subject','time','fitted_ind','resid','std_resid']
sorted_df = df.sort_values(['Subject','time']).reset_index(drop=True)
assert (df.reset_index(drop=True).values == sorted_df.values).all()
print("residual_diagnostics.csv: PASS")

# 6. Check plots exist with correct sizes
import os
from PIL import Image
for name in ['plot_conc_profile','plot_per_subject_fit','plot_covariate_effect',
             'plot_obs_vs_pred','plot_residuals']:
    p = f'/app/output/{name}.png'
    assert os.path.exists(p), f"missing {p}"
    img = Image.open(p)
    w, h = img.size
    assert w >= 900 and h >= 550, f"{p}: {w}x{h}"
    print(f"{name}.png: {w}x{h} PASS")

print("\nALL CHECKS PASS")
EOF

output

model_summary.json: PASS
lrt_chain.csv: PASS
per_subject_params.csv: PASS
obs_vs_pred.csv: PASS (cor_pop=0.814, cor_ind=0.971)
residual_diagnostics.csv: PASS
plot_conc_profile.png: 2000x1280 PASS
plot_per_subject_fit.png: 2400x1800 PASS
plot_covariate_effect.png: 2000x1200 PASS
plot_obs_vs_pred.png: 2400x1200 PASS
plot_residuals.png: 2400x1200 PASS

ALL CHECKS PASS

All checks pass. Let me also verify one edge case , what if the held-out test CSV has different subject counts. My code derives all counts from the CSV at runtime via `unique(df.Subject)` and `count(!ismissing, df.conc)`. Let me also make sure the plot with 6+ panels still works if there are fewer subjects. My code does `min(9, length(ordered))` , that could give fewer than 6 panels if there are <6 subjects. But the task says "at least 6 panels". Let me check:

bash

grep -n "min(9," /app/analysis.jl

output

373:        chosen = sort(ordered[1:min(9, length(ordered))], by=s -> s.id)

With 59 subjects, min(9, 59) = 9 panels. The task requires "at least 6". If the held-out dataset has fewer subjects (say 5), I'd only get 5 panels. But the task is a phenobarbital study , typical datasets have dozens of subjects, so should be fine. But to be safe, I should aim for at least 6. Let me set this to always show exactly min(9, N) but guarantee at least 6 when possible by sizing the grid accordingly. Actually the task just says "at least 6 panels". If the test data had only say 6 subjects, I'd get 6 panels (OK). If it had 5, I'd get 5 (fail). Let me think about whether the test data is likely to have < 6 subjects. The task says "perturbation" and that we should derive counts at runtime, implying the test data won't be drastically smaller. But to be safe, I could always include all subjects or warn. Actually for safety, let me target panels = min(length, 9) but with a reasonable grid layout. For 59 subjects → 9 panels. For a test dataset with perturbation (likely 30-100 subjects), this works fine. Let me also make sure my conc_profile plot shows both Apgar categories if both are present. It does (conditional on data). Let me also check the edge case where there's only one Apgar category , the legend might look weird, but the test data almost certainly has both. Let me verify the plots one more time actually look reasonable:

Let me double-check my grid layout handles edge cases and ensure the final script is robust:

bash

sed -n '370,410p' /app/analysis.jl

output

# per-subject fit
    let
        ordered = sort(subjects, by=s -> -length(s.samp_t))
        chosen = sort(ordered[1:min(9, length(ordered))], by=s -> s.id)
        fig = Figure(size=(1200, 900))
        Label(fig[0, :],
              "Per-subject observed points with population (red) and individual (blue) predictions",
              fontsize=16)
        for (k, s) in enumerate(chosen)
            r = div(k-1, 3) + 1; c = mod(k-1, 3) + 1
            ax = Axis(fig[r, c], xlabel="Time (h)", ylabel="Conc (mg/L)",
                      title="Subject $(s.id)")
            lCl, lV = compute_lCl_lV(p_final, s)
            η̂ = ebs[s.id]
            Cl_pop = exp(lCl); V_pop = exp(lV)
            Cl_ind = exp(lCl + η̂[1]); V_ind = exp(lV + η̂[2])
            tmax = maximum([s.samp_t; s.dose_t]) + 5
            tg = range(0.0, tmax; length=400)
            yp = [predict_conc(t, Cl_pop, V_pop, s.dose_t, s.dose_amt) for t in tg]
            yi = [predict_conc(t, Cl_ind, V_ind, s.dose_t, s.dose_amt) for t in tg]
            lines!(ax, tg, yp; color=:red, linewidth=1.6,
                   label=(k == 1 ? "Population" : nothing))
            lines!(ax, tg, yi; color=:blue, linewidth=1.6,
                   label=(k == 1 ? "Individual" : nothing))
            scatter!(ax, s.samp_t, s.samp_y; color=:black, markersize=7,
                     label=(k == 1 ? "Observed" : nothing))
            if k == 1
                axislegend(ax, position=:rt)
            end
        end
        save(joinpath(out_dir, "plot_per_subject_fit.png"), fig)
    end

    # covariate effect
    let
        fig = Figure(size=(1000, 600))
        ax = Axis(fig[1, 1], xlabel="Birth weight (kg)",
                  ylabel="Subject-level lCl",
                  title="Individual lCl (EB) vs birth weight, colored by Apgar")
        wts_hi = Float64[]; lcl_hi = Float64[]
        wts_lo = Float64[]; lcl_lo = Float64[]

Let me also safety-check by ensuring the analysis works even if some subject has no samples (edge case). My current code handles this:

bash

grep -n "isempty\|length(s.samp" /app/analysis.jl | head -20

output

101:    n = length(s.samp_t)
357:                if s.ApgarInd == key && !isempty(s.samp_t)
372:        ordered = sort(subjects, by=s -> -length(s.samp_t))

The inner NLL will compute n=0 if no samples, and the data term vanishes. The prior on η remains. Laplace still works. No div-by-zero since σ > 0. But `tmax = maximum([s.samp_t; s.dose_t]) + 5` would fail if both are empty. Very unlikely for real data. Let me add protection anyway. Actually for a real phenobarb dataset perturbation, every subject has at least one dose. So tmax is fine if there are any doses. Let me also guard against an empty samp_t for the subject fit plot.

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:             tmax = maximum([s.samp_t; s.dose_t]) + 5
new_str:             allt = [s.samp_t; s.dose_t]
            tmax = isempty(allt) ? 24.0 : maximum(allt) + 5

output

The file /app/analysis.jl has been edited successfully.

Let me also verify the final run is stable (not having random initialization issues):

bash

cd /app && rm -rf output && mkdir -p output && time timeout 180 julia analysis.jl 2>&1 | tail -10

output

base logL=-505.0183598711461, θ=[-5.1744416034519, 0.3674603788982618, -0.802507115192506, -0.8039720198123674, 1.032027659584984]
Fitting cl_wt…
  cl_wt logL=-479.3799213895833, θ=[-6.0891077524840265, 0.69024823700735, 0.3443578945970128, -1.6760121188046617, -0.9038310249782254, 1.0286965490844562]
Fitting full…
  full logL=-437.5636665083054, θ=[-5.937930920772442, 0.6137301775953106, -0.044496304637481825, -0.4736576935183165, 0.5334013370213192, -1.4842453605287869, -1.7686036566789103, 1.002580382496464]
AIC: base=1020.0367197422922 cl_wt=970.7598427791665 full=891.1273330166108
LR p: 1→2=8.021493759586122e-13, 2→3=6.9092554726142315e-19
cor pop=0.8143954989436714, cor ind=0.9711268204078367
Computing SEs…
Done.
[stderr]
real	0m42.085s
user	0m38.870s
sys	0m1.180s

The run is reproducible at ~42 seconds. Let me also ensure the analysis works with different starting values, just in case the perturbation moves the optimum:

bash

# Quick check - try perturbing the dataset slightly and see if fits still work
cp /app/Phenobarb.csv /tmp/test_data.csv
# Shuffle rows and scale some values modestly
python3 <<'EOF'
import pandas as pd, numpy as np
df = pd.read_csv('/tmp/test_data.csv')
np.random.seed(42)
# Multiply concentrations by small noise
mask = df.conc.notna()
df.loc[mask, 'conc'] = df.loc[mask, 'conc'] * np.random.uniform(0.9, 1.1, mask.sum())
df.to_csv('/tmp/test_data.csv', index=False)
print(f"Wrote {len(df)} rows, {df.Subject.nunique()} subjects")
EOF
cd /app && PHENOBARB_DATA_PATH=/tmp/test_data.csv PHENOBARB_OUTPUT_DIR=/tmp/test_out time timeout 120 julia analysis.jl 2>&1 | tail -10

output

Wrote 744 rows, 59 subjects
bash: line 2129: time: command not found

bash

cd /app && mkdir -p /tmp/test_out && rm -f /tmp/test_out/*
PHENOBARB_DATA_PATH=/tmp/test_data.csv PHENOBARB_OUTPUT_DIR=/tmp/test_out timeout 120 julia analysis.jl 2>&1 | tail -10

output

base logL=-514.3114881716132, θ=[-5.162335547310126, 0.3749668136207289, -0.8846459550555295, -0.7685088049884892, 1.1767655888155693]
Fitting cl_wt…
  cl_wt logL=-491.35536225729896, θ=[-6.029122023715867, 0.6664468178704971, 0.34883275261794655, -1.8260460528336127, -0.8790753161225556, 1.1853932345817864]
Fitting full…
  full logL=-452.192764434794, θ=[-5.826282500624983, 0.5729512073020642, -0.07802150992438209, -0.48762817314547335, 0.5443571243989244, -1.5568101967838246, -1.7173772275428445, 1.1551610021214789]
AIC: base=1038.6229763432264 cl_wt=994.7107245145979 full=920.385528869588
LR p: 1→2=1.2367008886887802e-11, 2→3=9.815216164597832e-18
cor pop=0.7932981249566103, cor ind=0.9558092348685295
Computing SEs…
Done.

With ±10% perturbation on concentrations, the fits still converge nicely and all metrics are well above thresholds. Let me also check the model fits look reasonable with a more substantial perturbation:

bash

# More substantial perturbation: remove some subjects and add noise
python3 <<'EOF'
import pandas as pd, numpy as np
df = pd.read_csv('/app/Phenobarb.csv')
np.random.seed(7)
# Remove 10 random subjects
subjects = sorted(df.Subject.unique())
keep = np.random.choice(subjects, size=len(subjects)-10, replace=False)
df = df[df.Subject.isin(keep)].reset_index(drop=True)
# Noise on concentrations
mask = df.conc.notna()
df.loc[mask, 'conc'] = df.loc[mask, 'conc'] * np.random.uniform(0.85, 1.15, mask.sum())
df.to_csv('/tmp/test_data2.csv', index=False)
print(f"Wrote {len(df)} rows, {df.Subject.nunique()} subjects, {df.conc.notna().sum()} conc obs")
EOF
cd /app && mkdir -p /tmp/test_out2 && rm -f /tmp/test_out2/*
PHENOBARB_DATA_PATH=/tmp/test_data2.csv PHENOBARB_OUTPUT_DIR=/tmp/test_out2 timeout 120 julia analysis.jl 2>&1 | tail -8

output

Wrote 626 rows, 49 subjects, 130 conc obs
  cl_wt logL=-417.63026827699133, θ=[-6.11183413801462, 0.7722384544084155, 0.3144721590941398, -2.5023916483560487, -1.0060893760301333, 1.3814120056216328]
Fitting full…
  full logL=-383.5229207880988, θ=[-6.049235533164087, 0.6357099086166081, 0.1385154492638951, -0.5711525691322201, 0.580156136737197, -2.0103318105834087, -1.8430462396493918, 1.307452387405179]
AIC: base=879.9245574933991 cl_wt=847.2605365539827 full=783.0458415761976
LR p: 1→2=3.9180640695720574e-9, 2→3=1.5394556901879137e-15
cor pop=0.8124350620286483, cor ind=0.939115861420384
Computing SEs…
Done.

Works well with a different subject set too. All thresholds are met. Let me do one final run to make sure everything is in place:

bash

cd /app && rm -rf output && mkdir -p output && timeout 180 julia analysis.jl 2>&1 | tail -10
echo "---"
ls /app/output/ | sort
echo "---"
wc -l /app/output/*.csv

output

base logL=-505.0183598711461, θ=[-5.1744416034519, 0.3674603788982618, -0.802507115192506, -0.8039720198123674, 1.032027659584984]
Fitting cl_wt…
  cl_wt logL=-479.3799213895833, θ=[-6.0891077524840265, 0.69024823700735, 0.3443578945970128, -1.6760121188046617, -0.9038310249782254, 1.0286965490844562]
Fitting full…
  full logL=-437.5636665083054, θ=[-5.937930920772442, 0.6137301775953106, -0.044496304637481825, -0.4736576935183165, 0.5334013370213192, -1.4842453605287869, -1.7686036566789103, 1.002580382496464]
AIC: base=1020.0367197422922 cl_wt=970.7598427791665 full=891.1273330166108
LR p: 1→2=8.021493759586122e-13, 2→3=6.9092554726142315e-19
cor pop=0.8143954989436714, cor ind=0.9711268204078367
Computing SEs…
Done.
---
lrt_chain.csv
model_summary.json
obs_vs_pred.csv
per_subject_params.csv
plot_conc_profile.png
plot_covariate_effect.png
plot_obs_vs_pred.png
plot_per_subject_fit.png
plot_residuals.png
residual_diagnostics.csv
---
    4 /app/output/lrt_chain.csv
  156 /app/output/obs_vs_pred.csv
   60 /app/output/per_subject_params.csv
  156 /app/output/residual_diagnostics.csv
  376 total

Everything works. Final summary: **Model results:** - **base**: logL=-505, AIC=1020 - **cl_wt**: logL=-479, AIC=971, LR p=8.0e-13 ✓ (< 1e-6) - **full**: logL=-438, AIC=891, LR p=6.9e-19 ✓ (< 1e-6) - AIC strictly decreasing ✓ - Correlation: obs vs pop pred = 0.81 ✓ (> 0.55), obs vs ind pred = 0.97 ✓ (> 0.75) **All 10 required outputs are produced:** 1. `model_summary.json` , JSON with n_obs=155, n_subjects=59, 5 fixed-effect terms in specified order, random_effects_sd with lCl/lV/Residual, logLik/aic/bic 2. `lrt_chain.csv` , 3 rows with step/model_name/n_params/logLik/AIC/BIC/LR_stat/LR_pvalue in that column order; LR stats empty for step 1 3. `per_subject_params.csv` , 59 rows, columns Subject/Cl/V, all positive, sorted by Subject 4. `obs_vs_pred.csv` , 155 rows, columns Subject/time/conc_obs/pred_pop/pred_ind, sorted 5. `residual_diagnostics.csv` , 155 rows, columns Subject/time/fitted_ind/resid/std_resid, sorted 6. `plot_conc_profile.png` , 2000×1280, colored by Apgar, legend, labels 7. `plot_per_subject_fit.png` , 2400×1800, 9 subject panels with obs/pop/ind curves 8. `plot_covariate_effect.png` , 2000×1200, lCl vs Wt colored by Apgar with fit line 9. `plot_obs_vs_pred.png` , 2400×1200, two panels with y=x reference 10. `plot_residuals.png` , 2400×1200, std residuals vs fitted + normal Q-Q **Code derives all counts from the CSV at runtime** , no hardcoding , so it will run cleanly on the held-out perturbation. Implementation notes: - Fits a 1-compartment first-order elimination PK model via Laplace approximation to the marginal likelihood - Nested optimization: inner BFGS finds η̂ per subject, outer LBFGS + Nelder-Mead refinement finds fixed effects and variance components - Log-scale parameters for σCl/σV/σ to enforce positivity; bounds check in objective - Central-difference Hessian at each mode for Laplace correction (using explicit `2.0*f0` to avoid the Julia `2f0` Float32 literal gotcha) - Full run takes ~40 seconds

Final diff , what the agent changed

No file changes, the agent left the workspace untouched.

Verifier output , the proof behind the reward

tests/test.sh

# SyncVals normalized verifier summary
# task: neonatal-drug-exposure-nlme
# attempt: 6  status: completed  raw_score: 0.0
# reward rule: binary: score 0.0 != 1.0
# => reward = 0.0  (FAIL)
#
# Note: these tasks score via an external hidden grader; no pytest/verifier
# block is embedded in the agent transcript. The block below is the last
# sizable tool-output captured in the run (supporting evidence).
----------------------------------------------------------------------
base logL=-505.0183598711461, θ=[-5.1744416034519, 0.3674603788982618, -0.802507115192506, -0.8039720198123674, 1.032027659584984]
Fitting cl_wt…
  cl_wt logL=-479.3799213895833, θ=[-6.0891077524840265, 0.69024823700735, 0.3443578945970128, -1.6760121188046617, -0.9038310249782254, 1.0286965490844562]
Fitting full…
  full logL=-437.5636665083054, θ=[-5.937930920772442, 0.6137301775953106, -0.044496304637481825, -0.4736576935183165, 0.5334013370213192, -1.4842453605287869, -1.7686036566789103, 1.002580382496464]
AIC: base=1020.0367197422922 cl_wt=970.7598427791665 full=891.1273330166108
LR p: 1→2=8.021493759586122e-13, 2→3=6.9092554726142315e-19
cor pop=0.8143954989436714, cor ind=0.9711268204078367
Computing SEs…
Done.
---
lrt_chain.csv
model_summary.json
obs_vs_pred.csv
per_subject_params.csv
plot_conc_profile.png
plot_covariate_effect.png
plot_obs_vs_pred.png
plot_per_subject_fit.png
plot_residuals.png
residual_diagnostics.csv
---
    4 /app/output/lrt_chain.csv
  156 /app/output/obs_vs_pred.csv
   60 /app/output/per_subject_params.csv
  156 /app/output/residual_diagnostics.csv
  376 total

Reproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_16b8cd529a90421a. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_16b8cd529a90421a · verifier authoritative; classifier explanatory.