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.

SubtypeEnvironment Issues

EvidenceThe test pipeline (test.sh line 39) calls `python3 /tests/llm_judge.py` which requires GEMINI_API_KEY environment variable to be set. Without this key, llm_judge.py exits with error code 1 (line 86: 'if not api_key: exit(1)'). The agent correctly generated all 10 required output files with valid mathematical results (AIC strictly decreasing, LR p-values 5.67e-13 and 7.73e-19 both < 1e-6 threshold, correlation metrics above minima). The failure occurred not because the agent's solution was wrong, but because the test infrastructure depends on external API credentials that were not available in the execution environment.

Root causeThe task's test suite uses Gemini API for LLM-based plot evaluation (llm_judge.py), but the GEMINI_API_KEY environment variable was not set in the trial environment, causing test.sh to abort at the plot grading step before it could assess whether the agent's actual outputs were correct.

RecommendationFix the task's test environment setup: (1) Provide GEMINI_API_KEY in the trial environment, OR (2) Mock/stub the Gemini API call in the test for offline evaluation, OR (3) Replace LLM-based plot grading with deterministic validation (check PNG properties, verify column names, validate numeric ranges). The agent's implementation is mathematically sound, the failure is purely a test infrastructure issue, not a task specification problem."

Trajectory

Tool-by-tool agent trajectory

176 tool calls · 3 tool types · 176 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 analyze this task carefully. I need to: 1. Read `Phenobarb.csv` and `dataset_manifest.json` 2. Fit three PK models with increasing complexity 3. Output tables and plots as specified Let me start by exploring the data.

bash

ls /app/ && cat /app/dataset_manifest.json

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"
  }
}

bash

head -50 /app/Phenobarb.csv && echo "---" && wc -l /app/Phenobarb.csv

output

"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
3,1.5,6,">= 5",11.5,3.7,
3,1.5,6,">= 5",23.5,3.7,
3,1.5,6,">= 5",35.5,3.7,
3,1.5,6,">= 5",47.5,3.7,
3,1.5,6,">= 5",59.3,3.7,
3,1.5,6,">= 5",73,3.7,
3,1.5,6,">= 5",83.5,,23.8
3,1.5,6,">= 5",84,3.7,
3,1.5,6,">= 5",96.5,3.7,
3,1.5,6,">= 5",108.5,3.7,
3,1.5,6,">= 5",120,3.7,
3,1.5,6,">= 5",132,3.7,
3,1.5,6,">= 5",134.3,,24.3
4,0.9,6,">= 5",0,18.6,
4,0.9,6,">= 5",1.8,,20.8
4,0.9,6,">= 5",12,2.3,
4,0.9,6,">= 5",24.3,2.3,
4,0.9,6,">= 5",35.8,2.3,
4,0.9,6,">= 5",48.1,2.3,
4,0.9,6,">= 5",59.3,,23.9
---
745 /app/Phenobarb.csv

bash

ls /app/output/ 2>/dev/null || mkdir -p /app/output; julia --version

output

julia version 1.10.4

bash

cat /app/analysis.jl 2>/dev/null | head -20

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.

Let me design the approach: **Model structure:** One-compartment PK with first-order elimination, multiple bolus doses: For each subject i with dose events at times $t_d$ and doses $D_d$: $$C_i(t) = \sum_{d: t_d \le t} \frac{D_d}{V_i} \exp(-k_i (t - t_d))$$ where $k_i = Cl_i / V_i$. Parameters on log scale: - $\log(Cl_i) = \beta_0 + \beta_1 \cdot Wt_i + \beta_2 \cdot [Apgar \ge 5]_i + \eta_{Cl,i}$ - $\log(V_i) = \gamma_0 + \gamma_1 \cdot Wt_i + \eta_{V,i}$ - $\eta \sim N(0, \text{diag}(\sigma_{Cl}^2, \sigma_V^2))$ - $y_{ij} - C_i(t_{ij}) \sim N(0, \sigma^2)$ Fitting: Use Laplace approximation. For each subject, given fixed effects, find the mode of $\eta$ then use Laplace for the marginal likelihood. Actually, given the complexity, let me use FOCE or a first-order approximation. Let me go with Laplace approximation which is well-defined. **Laplace approximation:** $\ell(\theta) = \sum_i \log \int f(y_i | \eta_i, \theta) f(\eta_i | \theta) d\eta_i$ Laplace approximation: $\log \int \approx \log f(y_i | \hat\eta_i, \theta) + \log f(\hat\eta_i | \theta) + \frac{p}{2}\log(2\pi) - \frac{1}{2}\log|H_i|$ where $H_i$ is the negative Hessian of $-\log f(y_i,\eta_i|\theta)$ at $\hat\eta_i$. This is getting complex. Let me simplify: - For each subject, inner optimization on 2-dim $\eta_i$ - Outer optimization on fixed effects + variance components Given that this is a well-known dataset and the model is straightforward, Laplace should work. Let me also think about what "df" means in the fixed_effects output. Let me use n_obs - n_params for df. For pharmacometric mixed models, this is typically what's reported for fixed effect tests. Actually, looking more carefully , mixed model output usually doesn't report df for fixed effects straightforwardly. Let me use a reasonable value like total observations minus number of fixed effects (n_obs - n_fixed). Let me code this up. I'll use a relatively small number of inner iterations and a decent number of outer iterations. Let me structure the code: ```julia using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions, LinearAlgebra, Optim # Load data # Split per subject, gather dose events and sample events # Model prediction function # Laplace approximation for -2LL # Optimize # Extract standard errors via numerical Hessian # Output ``` Let me write this. For prediction, given a subject's dose schedule (time, amount) and sample times, compute concentrations: ``` C(t) = sum over past doses D[j] / V * exp(-Cl/V * (t - td[j])) ``` For the Laplace approximation: - Objective: -log p(y|η,θ) - log p(η|θ) = (1/2) sum (y-f(η))^2/σ^2 + (n_obs/2)*log(2π σ^2) + (1/2) η^T Ω^{-1} η + (1/2) log|2π Ω| Actually let me just minimize over fixed effects and variance components jointly using Laplace for the marginal LL. Let me think about parameterization: - log(Cl) ~ β0 + β1*Wt + β2*Apgar>=5 (β2 zero if ApgarInd = "< 5", since "< 5" is reference... actually let's use "< 5" as 0 and ">= 5" as 1 , wait, which way? Let's use the ">= 5" level, with "< 5" being reference. The term name "lCl.ApgarInd>= 5" suggests ">= 5" is the non-reference level.) Let me code this step by step. For numerical Hessian for SE, I can use ForwardDiff but it's not in the allowed list. Let me use finite differences. Actually wait , I don't have ForwardDiff in the list. I'll need to use finite differences for gradient/Hessian. Let me plan: 1. Parse CSV 2. Build per-subject data: doses (time, amount) and samples (time, conc) 3. Implement model prediction 4. Implement inner optimization (per subject random effects) 5. Implement Laplace marginal log-likelihood 6. Optimize over fixed effects + variance components 7. Compute SEs via numerical Hessian 8. LRT chain 9. Output tables and plots Let me start writing. ```julia # Model: Cl = exp(lCl), V = exp(lV), k = Cl/V # C(t) = sum over dose events before t of D_j / V * exp(-k * (t - td_j)) function predict_conc(sample_times, dose_times, dose_amts, Cl, V) k = …[truncated]

bash

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

output

bash

awk -F, 'NR>1 && $7!=""' /app/Phenobarb.csv | wc -l; awk -F, 'NR>1 && $6!=""' /app/Phenobarb.csv | wc -l

output

155
589

So 59 subjects, 155 concentration observations, 589 dose events in the original. Let me write the 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")

# --- subject data container ---------------------------------------------------
struct SubjData
    id::Int
    wt::Float64
    apgar_high::Float64         # 1.0 if ApgarInd == ">= 5", else 0.0
    dose_times::Vector{Float64}
    dose_amts::Vector{Float64}
    samp_times::Vector{Float64}
    samp_conc::Vector{Float64}
end

function load_subjects(df::DataFrame)
    subs = SubjData[]
    for sid in sort(unique(df.Subject))
        rows = df[df.Subject .== sid, :]
        wt  = Float64(first(rows.Wt))
        apg = String(first(rows.ApgarInd))
        apgar_high = (strip(apg) == ">= 5") ? 1.0 : 0.0
        dts = Float64[]; damts = Float64[]
        sts = Float64[]; scs  = Float64[]
        for r in eachrow(rows)
            has_dose = !ismissing(r.dose)
            has_conc = !ismissing(r.conc)
            if has_dose
                push!(dts,  Float64(r.time))
                push!(damts, Float64(r.dose))
            end
            if has_conc
                push!(sts, Float64(r.time))
                push!(scs, Float64(r.conc))
            end
        end
        push!(subs, SubjData(Int(sid), wt, apgar_high, dts, damts, sts, scs))
    end
    return subs
end

# --- 1-compartment IV bolus (superposition of past doses) ---------------------
function predict_conc(stimes::Vector{Float64},
                      dtimes::Vector{Float64}, damts::Vector{Float64},
                      Cl::Float64, V::Float64)
    k = Cl / V
    C = zeros(length(stimes))
    @inbounds for i in eachindex(stimes)
        t = stimes[i]
        s = 0.0
        for j in eachindex(dtimes)
            if dtimes[j] <= t
                s += damts[j] * exp(-k * (t - dtimes[j]))
            end
        end
        C[i] = s / V
    end
    return C
end

# --- model spec flags ---------------------------------------------------------
# each model has: lCl intercept, optional lCl:Wt, optional lCl:Apgar,
#                 lV intercept, optional lV:Wt, plus ωCl, ωV, σ
struct ModelSpec
    name::String
    clwt::Bool      # include Wt on lCl
    clapgar::Bool   # include ApgarInd on lCl
    vwt::Bool       # include Wt on lV
end

function param_layout(spec::ModelSpec)
    names = String["lCl.(Intercept)"]
    spec.clwt    && push!(names, "lCl.Wt")
    spec.clapgar && push!(names, "lCl.ApgarInd>= 5")
    push!(names, "lV.(Intercept)")
    spec.vwt     && push!(names, "lV.Wt")
    return names
end

# Unpack θ vector into (fixed effect dict, ωCl, ωV, σ).  The last three
# variance components are passed on the log scale to keep them positive.
function unpack(θ::AbstractVector, spec::ModelSpec)
    idx = 1
    lCl0 = θ[idx]; idx += 1
    lCl_wt = 0.0; lCl_apg = 0.0
    if spec.clwt;    lCl_wt  = θ[idx]; idx += 1; end
    if spec.clapgar; lCl_apg = θ[idx]; idx += 1; end
    lV0 = θ[idx]; idx += 1
    lV_wt = 0.0
    if spec.vwt;     lV_wt = θ[idx]; idx += 1; end
    ωCl = exp(θ[idx]); idx += 1
    ωV  = exp(θ[idx]); idx += 1
    σ   = exp(θ[idx])
    return (lCl0=lCl0, lCl_wt=lCl_wt, lCl_apg=lCl_apg,
            lV0=lV0, lV_wt=lV_wt, ωCl=ωCl, ωV=ωV, σ=σ)
end

n_fixed(spec) = length(param_layout(spec))
n_params(spec) = n_fixed(spec) + 3       # + ωCl, ωV, σ

# --- inner objective (per subject) --------------------------------------------
function inner_nll(η::AbstractVector, s::SubjData, p)
    lCl = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high + η[1]
    lV  = p.lV0  + p.lV_wt*s.w
…[truncated]

output

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

bash

cd /app && timeout 280 julia --project=. analysis.jl 2>&1 | tail -60

output

[stderr]
Terminated

Execution was terminated (took too long). The optimization is too slow. Let me optimize by: 1. Using analytical gradient for the inner optimization 2. Reducing outer iterations 3. Better initial values Actually the main slowness is likely the Nelder-Mead outer then BFGS with finite differences, combined with inner optimization done with NelderMead. Let me: - Use analytical gradient of inner obj - Use Newton's method for inner optimization (only 2D) - Reduce outer iterations Actually the inner optimization with Nelder-Mead followed by BFGS is expensive. Let me use a simpler inner method. Since it's 2D, Newton-Raphson with analytical gradient should converge in <10 iterations. Inner gradient w.r.t. η: ∂q/∂η[1] = -sum((y-f)/σ² * ∂f/∂η1) + η[1]/ωCl² ∂q/∂η[2] = -sum((y-f)/σ² * ∂f/∂η2) + η[2]/ωV² Where f depends on Cl = exp(lCl0 + β1*Wt + β2*Apgar + η1) and V = exp(lV0 + β3*Wt + η2). ∂Cl/∂η1 = Cl ∂V/∂η2 = V C_j = sum_d D_d / V * exp(-Cl/V * (t_j - t_d)) ∂C_j/∂Cl = sum_d D_d / V * (-(t_j-t_d)/V) * exp(-k(t_j-t_d)) = -(1/V) * sum_d D_d * (t_j-t_d)/V * exp(...) ∂C_j/∂V = sum_d D_d * [-1/V² * exp(...) + 1/V * (Cl*(t_j-t_d)/V²) * exp(...)] = (1/V²) * sum_d D_d * exp(...) * (k*(t_j-t_d) - 1) ∂C_j/∂η1 = ∂C_j/∂Cl * ∂Cl/∂η1 = Cl * ∂C_j/∂Cl ∂C_j/∂η2 = ∂C_j/∂V * ∂V/∂η2 = V * ∂C_j/∂V Actually, let me simplify the approach. Instead of doing full Laplace with numerical inner + Hessian, maybe use a simpler first-order approach that still works? Or use the fact that we can do each subject's inner optimization very fast. Let me just use a tight, fast inner Newton loop with analytical gradient and Hessian. Actually, let's try a different approach: since each subject only has a small number of observations, and η is just 2D, I can write a fast custom Newton-Raphson solver. Let me also cache predictions efficiently. I'll try to make the code run faster. Let me also reduce the Nelder-Mead iterations. Key optimization ideas: 1. Use Newton-Raphson inner loop (few iterations, analytical derivs) 2. Reduce outer iterations (especially Nelder-Mead) 3. Reduce Hessian FD calls Actually , maybe the simplest big win is to use autodiff for the inner problem. But we don't have ForwardDiff in the allowed list. Let me write analytic gradient + Hessian for the inner problem. Since it's only 2D, it's not bad. Inner objective: Q(η1, η2) = 0.5/σ² * sum_j (y_j - C_j)² + 0.5*(η1²/ωCl² + η2²/ωV²) Let u = Cl, v = V where Cl = Cl0 * exp(η1), V = V0 * exp(η2), with Cl0 = exp(lCl0 + β1*Wt + β2*Apgar), V0 = exp(lV0 + β3*Wt). C_j = (1/V) * sum_d D_d * exp(-k(t_j-t_d)) where k = Cl/V Let a_j = sum_d D_d * exp(-(Cl/V)*(t_j - t_d)) Then C_j = a_j / V ∂C_j/∂η1 = ∂(a_j/V)/∂η1 ∂a_j/∂η1 = sum_d D_d * exp(...) * (-(t_j-t_d) * Cl/V) [since ∂Cl/∂η1 = Cl] = -Cl/V * sum_d D_d * (t_j-t_d) * exp(...) Let b_j = sum_d D_d * (t_j - t_d) * exp(-(Cl/V)(t_j-t_d)) Then ∂a_j/∂η1 = -(Cl/V) * b_j, so ∂C_j/∂η1 = -(Cl/V²) * b_j = -k/V * b_j ∂C_j/∂η2 = ? V depends on η2. ∂V/∂η2 = V. a_j also depends on η2 through k = Cl/V. ∂a_j/∂η2 = sum_d D_d * exp(...) * (-(t_j-t_d) * ∂k/∂η2) ∂k/∂η2 = ∂(Cl/V)/∂η2 = -Cl/V² * V = -Cl/V = -k So ∂a_j/∂η2 = sum_d D_d * exp(...) * (-(t_j-t_d) * (-k)) = k * b_j ∂C_j/∂η2 = [∂a_j/∂η2 * V - a_j * V] / V² = [k*b_j - a_j] / V = k*b_j/V - C_j = (k*b_j - a_j)/V Ugh OK let me just use finite differences but with much fewer function evals. Or let me simplify the approach. Alternative: use a First-Order (FO) approximation instead of Laplace. FO linearizes the model around η=0, so you don't need per-subject inner optimization. This is much faster. FO approach: For each subject, linearize: y_j ≈ f(0) + ∂f/∂η|_{η=0} * η + ε Marginal distribution: y_i ~ N(f_i(0), J_i Ω J_i^T + σ² I) Log likelihood for subject i: -logL_i = 0.5 * [log|2π Σ_i| + (y_i - f_i(0))^T Σ_i^{-1} (y_i - f_i(0))] where Σ_i = J_i Ω J_i^T + σ² I, J_i is n_i × 2 Jacobian. With this, we only need J_i computed at η=0 for each subject. Much simple …[truncated]

The script is too slow. Let me rewrite with analytic gradients for the inner problem and a faster outer optimization strategy.

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")

# --- subject data container ---------------------------------------------------
struct SubjData
    id::Int
    wt::Float64
    apgar_high::Float64
    dose_times::Vector{Float64}
    dose_amts::Vector{Float64}
    samp_times::Vector{Float64}
    samp_conc::Vector{Float64}
end

function load_subjects(df::DataFrame)
    subs = SubjData[]
    for sid in sort(unique(df.Subject))
        rows = df[df.Subject .== sid, :]
        wt  = Float64(first(rows.Wt))
        apg = String(strip(String(first(rows.ApgarInd))))
        apgar_high = (apg == ">= 5") ? 1.0 : 0.0
        dts = Float64[]; damts = Float64[]
        sts = Float64[]; scs  = Float64[]
        for r in eachrow(rows)
            if !ismissing(r.dose)
                push!(dts,  Float64(r.time))
                push!(damts, Float64(r.dose))
            end
            if !ismissing(r.conc)
                push!(sts, Float64(r.time))
                push!(scs, Float64(r.conc))
            end
        end
        push!(subs, SubjData(Int(sid), wt, apgar_high, dts, damts, sts, scs))
    end
    return subs
end

# --- predictions and analytic derivatives -------------------------------------
# Given Cl, V for a subject, return (C, ∂C/∂η1, ∂C/∂η2) vectors where
# Cl = Cl0 * exp(η1), V = V0 * exp(η2).
# C_j = (1/V) Σ_d D_d exp(-k (t_j - t_d))
#   a_j = Σ_d D_d exp(-k τ), b_j = Σ_d D_d τ exp(-k τ)   (τ = t_j-t_d ≥ 0)
#   C_j = a_j / V
#   ∂C/∂η1 = -k * b_j / V                  (since ∂k/∂η1 = k, ∂V/∂η1 = 0)
#   ∂C/∂η2 = (k b_j - a_j) / V             (since ∂k/∂η2 = -k, ∂V/∂η2 = V)
function pred_and_jac(stimes::Vector{Float64},
                      dtimes::Vector{Float64}, damts::Vector{Float64},
                      Cl::Float64, V::Float64)
    n = length(stimes); k = Cl / V
    C  = zeros(n); dC1 = zeros(n); dC2 = zeros(n)
    @inbounds for i in 1:n
        t = stimes[i]; a = 0.0; b = 0.0
        for j in eachindex(dtimes)
            τ = t - dtimes[j]
            if τ >= 0
                e = damts[j] * exp(-k*τ)
                a += e; b += τ*e
            end
        end
        C[i]  = a/V
        dC1[i] = -k*b/V
        dC2[i] = (k*b - a)/V
    end
    return C, dC1, dC2
end

predict_conc(st, dt, da, Cl, V) = pred_and_jac(st, dt, da, Cl, V)[1]

# --- model spec ---------------------------------------------------------------
struct ModelSpec
    name::String
    clwt::Bool
    clapgar::Bool
    vwt::Bool
end

function param_layout(spec::ModelSpec)
    names = String["lCl.(Intercept)"]
    spec.clwt    && push!(names, "lCl.Wt")
    spec.clapgar && push!(names, "lCl.ApgarInd>= 5")
    push!(names, "lV.(Intercept)")
    spec.vwt     && push!(names, "lV.Wt")
    return names
end

function unpack(θ::AbstractVector, spec::ModelSpec)
    i = 1
    lCl0 = θ[i]; i += 1
    lCl_wt = 0.0; lCl_apg = 0.0
    if spec.clwt;    lCl_wt  = θ[i]; i += 1; end
    if spec.clapgar; lCl_apg = θ[i]; i += 1; end
    lV0 = θ[i]; i += 1
    lV_wt = 0.0
    if spec.vwt;     lV_wt = θ[i]; i += 1; end
    ωCl = exp(θ[i]); i += 1
    ωV  = exp(θ[i]); i += 1
    σ   = exp(θ[i])
    return (lCl0=lCl0, lCl_wt=lCl_wt, lCl_apg=lCl_apg,
            lV0=lV0, lV_wt=lV_wt, ωCl=ωCl, ωV=ωV, σ=σ)
end

n_fixed(spec)  = length(param_layout(spec))
n_params(spec) = n_fixed(spec) + 3

# inner nll + analytic gradient + Hessian at η (Gauss-Newton approx Hessian).
# Returns (q, g, H) where g is 2-vec, H is 2x2.
function inner_all(η::
…[truncated]

output

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

bash

cd /app && timeout 280 julia --project=. analysis.jl 2>&1 | tail -40

output

[stderr]
Terminated

Still too slow. Let me see how long a single evaluation takes.

bash

cd /app && timeout 60 julia --project=. -e '
include("analysis.jl") 
' 2>&1 | tail -5 &
sleep 55 && echo "--- killing after 55s ---" && kill %1 2>/dev/null; wait

output

--- killing after 55s ---
[stderr]
[1]+  Terminated              cd /app && timeout 60 julia --project=. -e '
include("analysis.jl") 
' 2>&1 | tail -5

bash

cd /app && timeout 90 julia --project=. -e '
using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions, LinearAlgebra, Optim
println("startup done at ", round(time()))
' 2>&1

output

[1709] signal (15): Terminated
in expression starting at /usr/local/share/julia/packages/CairoMakie/hql6v/src/CairoMakie.jl:3
epoll_wait at /lib/x86_64-linux-gnu/libc.so.6 (unknown line)
uv__io_poll at /workspace/srcdir/libuv/src/unix/epoll.c:236
uv_run at /workspace/srcdir/libuv/src/unix/core.c:400
ijl_task_get_next at /cache/build/builder-amdci4-0/julialang/julia-release-1-dot-10/src/partr.c:478

[1712] signal (15): Terminated
in expression starting at /usr/local/share/julia/packages/Makie/p9K7f/precompile/shared-precompile.jl:14
issimplertype at ./compiler/typelimits.jl:301
tmerge at ./compiler/typelimits.jl:609

CairoMakie load alone takes > 90s of precompilation. Let me check if there's a precompile cache already, or we need to precompile once.

bash

ls /root/.julia/compiled/v1.10/ 2>&1 | head

output

ls: cannot access '/root/.julia/compiled/v1.10/': Permission denied

bash

echo "HOME=$HOME"; ls ~/.julia/compiled/v1.10/ 2>&1 | head; ls /app/.julia/compiled/v1.10/ 2>&1 | head 2>&1; ls ~/Makie*/ 2>&1; du -sh ~/.julia 2>/dev/null; find / -name "Makie.ji" 2>/dev/null | head

output

HOME=/home/h2tagent
ls: cannot access '/home/h2tagent/.julia/compiled/v1.10/': No such file or directory
ls: cannot access '/app/.julia/compiled/v1.10/': No such file or directory
ls: cannot access '/home/h2tagent/Makie*/': No such file or directory

bash

find / -name "*.ji" 2>/dev/null | grep -E "(CairoMakie|Makie)" | head; ls /app/ -la; find / -name "Project.toml" 2>/dev/null | head

output

/usr/local/share/julia/compiled/v1.10/CairoMakie/9mSey_NWwp1.ji
/usr/local/share/julia/compiled/v1.10/Makie/iZ1Bl_NWwp1.ji
total 54
drwxrws---  3 h2tagent h2tagent  4096 May 31 10:00 .
drwxr-xr-x 26 root     root      4096 May 31 09:51 ..
-rw-rw----  1 h2tagent h2tagent 18132 May 30 22:35 Phenobarb.csv
-rw-rw----  1 h2tagent h2tagent 22141 May 31 10:00 analysis.jl
-rw-rw----  1 h2tagent h2tagent  1508 May 30 22:35 dataset_manifest.json
drwxrws---  2 h2tagent h2tagent  4096 May 30 22:39 output
/usr/local/share/julia/stdlib/v1.10/LibGit2_jll/Project.toml
/usr/local/share/julia/stdlib/v1.10/GMP_jll/Project.toml
/usr/local/share/julia/stdlib/v1.10/TOML/benchmark/Project.toml
/usr/local/share/julia/stdlib/v1.10/TOML/docs/Project.toml
/usr/local/share/julia/stdlib/v1.10/TOML/Project.toml
/usr/local/share/julia/stdlib/v1.10/Artifacts/Project.toml
/usr/local/share/julia/stdlib/v1.10/Unicode/Project.toml
/usr/local/share/julia/stdlib/v1.10/Mmap/Project.toml
/usr/local/share/julia/stdlib/v1.10/Profile/Project.toml
/usr/local/share/julia/stdlib/v1.10/Sockets/Project.toml

bash

cd /app && timeout 240 julia -e '
@time using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions, LinearAlgebra, Optim
println("done")
' 2>&1 | tail -5

output

[stderr]
Terminated

bash

cd /app && julia -e '
t0 = time()
using CairoMakie
println("CairoMakie load: ", round(time()-t0, digits=2), "s")
' 2>&1 &
BGPID=$!
# let it run up to 250s
for i in $(seq 1 25); do sleep 10; if ! kill -0 $BGPID 2>/dev/null; then echo "done at ${i}0s"; break; fi; done
wait $BGPID 2>/dev/null
echo "---"

output

[stderr]
Shell command timed out.
Tool interaction exceeded 300 seconds.

bash

restart: true

output

<system>tool has been restarted.</system>

bash

ls /usr/local/share/julia/compiled/v1.10/ | head -20; echo "---"; ls /usr/local/share/julia/environments/ 2>/dev/null | head

output

ADTypes
ADTypesChainRulesCoreExt
ADTypesConstructionBaseExt
AbstractFFTs
AbstractFFTsChainRulesCoreExt
AbstractTrees
Adapt
AdaptSparseArraysExt
AdaptStaticArraysExt
AdaptivePredicates
AliasTables
Animations
ArrayInterface
ArrayInterfaceChainRulesCoreExt
ArrayInterfaceSparseArraysExt
ArrayInterfaceStaticArraysCoreExt
Automa
AxisAlgorithms
AxisArrays
BaseDirs
---
v1.10

bash

ls /usr/local/share/julia/environments/v1.10/

output

Manifest.toml
Project.toml

bash

cat /usr/local/share/julia/environments/v1.10/Project.toml

output

[deps]
CSV = "336ed68f-0bac-5ca0-87d4-7b16caf5d00b"
CairoMakie = "13f3f980-e62b-5c42-98c6-ff1f3baf88f0"
DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
JSON3 = "0f8b85d8-7281-11e9-16c2-39a750bddbf1"
Optim = "429524aa-4258-5aef-a3af-852621145aeb"
Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"

bash

cd /app && time julia --startup-file=no -e 'using CSV, DataFrames; println("loaded")' 2>&1 | tail -5

output

loaded
[stderr]
real	0m1.644s
user	0m1.400s
sys	0m0.130s

bash

cd /app && time julia --startup-file=no -e 'using CairoMakie; println("loaded")' 2>&1 | tail -5

output

└ @ FileWatching.Pidfile /usr/local/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:244
┌ Warning: attempting to remove probably stale pidfile
│   path = "/tmp/julia-depot/compiled/v1.10/Makie/iZ1Bl_MJWkB.ji.pidfile"
└ @ FileWatching.Pidfile /usr/local/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:244
loaded
[stderr]
real	4m53.955s
user	4m32.250s
sys	0m5.410s

OK CairoMakie takes 5 minutes to precompile because `/tmp/julia-depot` is the depot path and isn't pre-compiled. But after first compile, it should be faster. Let me check again:

bash

cd /app && time julia --startup-file=no -e 'using CairoMakie; println("loaded")' 2>&1 | tail -5

output

loaded
[stderr]
real	0m6.214s
user	0m4.950s
sys	0m0.810s

OK so the first time precompiles takes ~5min, subsequent load is 6s. Now let me try the full analysis and see where we stand.

bash

cd /app && time julia --startup-file=no -e 'using DataFrames, CSV, JSON3, CairoMakie, Statistics, Distributions, LinearAlgebra, Optim; println("loaded")' 2>&1 | tail -5

output

loaded
[stderr]
real	0m22.915s
user	0m18.890s
sys	0m2.680s

bash

cd /app && time julia --startup-file=no analysis.jl 2>&1 | tail -40 &
BGPID=$!
# wait up to 270s
for i in $(seq 1 27); do
  sleep 10
  if ! kill -0 $BGPID 2>/dev/null; then break; fi
done
if kill -0 $BGPID 2>/dev/null; then kill $BGPID 2>/dev/null; echo "KILLED"; fi
wait

output

Fitting base model...
ERROR: LoadError: TypeError: in keyword argument autodiff, expected ADTypes.AbstractADType, got a value of type Symbol
Stacktrace:
 [1] fit_model(subs::Vector{SubjData}, spec::ModelSpec; θ0::Nothing, verbose::Bool)
   @ Main /app/analysis.jl:231
 [2] fit_model(subs::Vector{SubjData}, spec::ModelSpec)
   @ Main /app/analysis.jl:202
 [3] main()
   @ Main /app/analysis.jl:404
 [4] top-level scope
   @ /app/analysis.jl:553
in expression starting at /app/analysis.jl:553
[stderr]
real	0m17.413s
user	0m15.540s
sys	0m0.750s

bash

cd /app && julia --startup-file=no -e 'using Optim; println(Optim.Options); @show propertynames(Optim.BFGS())' 2>&1 | tail -5

output

Optim.Options
propertynames(Optim.BFGS()) = (:alphaguess!, :linesearch!, :initial_invH, :initial_stepnorm, :manifold)

The `autodiff = :finite` option for `optimize` isn't supported in this Optim version. The `autodiff` keyword expects an `ADTypes.AbstractADType`. I'll need to pass the gradient explicitly or remove the autodiff option and have Optim use default finite differences. Actually in Optim, BFGS without autodiff uses the default NLSolversBase finite-difference gradient. Let me just remove the `autodiff` keyword.

bash

cd /app && sed -i 's/;\s*autodiff = :finite//g' analysis.jl
grep -n autodiff analysis.jl

output

234:                    autodiff = :finite)

bash

cd /app && sed -n '225,240p' analysis.jl

output

# BFGS with finite-difference gradient is usually fast for this size.
    res = optimize(f, θ0, NelderMead(),
                   Optim.Options(iterations = 800, g_tol = 1e-5,
                                 show_trace = verbose))
    θ1 = Optim.minimizer(res)
    res2 = optimize(f, θ1, BFGS(),
                    Optim.Options(iterations = 150, g_tol = 1e-5,
                                  show_trace = verbose);
                    autodiff = :finite)
    θhat = Optim.minimizer(res2)
    nll_fin, etas = laplace_nll(θhat, subs, spec; etas_cache = etas_cache,
                                return_etas = true)
    return (θ = θhat, nll = nll_fin, etas = etas, spec = spec)
end

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:     res2 = optimize(f, θ1, BFGS(),
                    Optim.Options(iterations = 150, g_tol = 1e-5,
                                  show_trace = verbose);
                    autodiff = :finite)
new_str:     res2 = optimize(f, θ1, BFGS(),
                    Optim.Options(iterations = 150, g_tol = 1e-5,
                                  show_trace = verbose))

output

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

bash

cd /app && time julia --startup-file=no analysis.jl 2>&1 | tail -40 &
BGPID=$!
for i in $(seq 1 27); do
  sleep 10
  if ! kill -0 $BGPID 2>/dev/null; then break; fi
done
if kill -0 $BGPID 2>/dev/null; then kill $BGPID 2>/dev/null; echo "KILLED at 270s"; fi
wait 2>/dev/null

output

Fitting base model...
  -logL = 505.2363234577585  (6.7s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.2s)
Fitting full model...
  -logL = 437.55226628753263  (7.4s)
┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Computing standard errors (FD Hessian)...
  (0.3 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 35.6 s.
[stderr]
real	0m57.871s
user	0m53.150s
sys	0m1.360s

Excellent! The analysis completes in ~58 seconds and meets all the specified thresholds: - AIC decreasing with each step (base → cl_wt → full) - LRT p-values < 1e-6 for both steps (5.67e-13 and 7.73e-19) - cor(obs, pop_pred) = 0.815 > 0.55 - cor(obs, ind_pred) = 0.971 > 0.75 Let me check all outputs.

bash

ls /app/output/ -la

output

total 583
drwxrws--- 2 h2tagent h2tagent   4096 May 31 10:24 .
drwxrws--- 3 h2tagent h2tagent   4096 May 31 10:23 ..
-rw-r--r-- 1 h2tagent h2tagent    336 May 31 10:24 lrt_chain.csv
-rw-r--r-- 1 h2tagent h2tagent   1384 May 31 10:24 model_summary.json
-rw-r--r-- 1 h2tagent h2tagent   7779 May 31 10:24 obs_vs_pred.csv
-rw-r--r-- 1 h2tagent h2tagent   2523 May 31 10:24 per_subject_params.csv
-rw-r--r-- 1 h2tagent h2tagent 159650 May 31 10:24 plot_conc_profile.png
-rw-r--r-- 1 h2tagent h2tagent  51257 May 31 10:24 plot_covariate_effect.png
-rw-r--r-- 1 h2tagent h2tagent  86382 May 31 10:24 plot_obs_vs_pred.png
-rw-r--r-- 1 h2tagent h2tagent 200127 May 31 10:24 plot_per_subject_fit.png
-rw-r--r-- 1 h2tagent h2tagent  66874 May 31 10:24 plot_residuals.png
-rw-r--r-- 1 h2tagent h2tagent  10208 May 31 10:24 residual_diagnostics.csv

bash

cat /app/output/model_summary.json

output

{
    "bic": 915.4519335104193,
    "logLik": -437.55226628753263,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -5910.999299831098,
            "df": 150,
            "std_error": 0.0010012206900087684,
            "estimate": -5.918214797618239
        },
        {
            "term": "lCl.Wt",
            "t_value": 3616.9087822935126,
            "df": 150,
            "std_error": 0.00016921130770482194,
            "estimate": 0.6120218649009403
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -271.01529910934664,
            "df": 150,
            "std_error": 0.00016921327430915675,
            "estimate": -0.04585938615016804
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -2809.1220470274075,
            "df": 150,
            "std_error": 0.00016921076990575773,
            "estimate": -0.4753337043367458
        },
        {
            "term": "lV.Wt",
            "t_value": 3153.2869875189235,
            "df": 150,
            "std_error": 0.00016920457244097565,
            "estimate": 0.5335505765068316
        }
    ],
    "aic": 891.1045325750653,
    "n_subjects": 59,
    "n_obs": 155,
    "random_effects_sd": {
        "lCl": 0.22024795745539982,
        "lV": 0.17207043945418615,
        "Residual": 2.729216144684834
    }
}

The standard errors are unreasonably small (1e-4 level), leading to huge t-values. This means the finite-difference Hessian has too large a step size (5e-3 on the log-scale) or too small. Let me investigate , when θ is around -5 or -0.5, using h = max(5e-3, 5e-3*|θ|), hs would be 5e-3 * 5 = 0.025 for lCl intercept. But the SEs are ~1e-4. Wait, the Hessian is probably poorly conditioned. Let me think: if SE is 1e-4, then variance = 1e-8, so Vcov diagonal = 1e-8, meaning H diagonal ≈ 1e8. That's huge curvature. Hmm, this is likely because `laplace_nll` uses cached η values as starting points for inner optimization, and when we perturb θ by a small h, the inner optimization gets stuck near the cached value without exploring far enough, giving a sharp apparent objective surface. Actually wait , the inner Newton-Raphson should converge regardless of the starting point. Let me think again. Oh, I see. The Hessian h is 5e-3 but relative. For θ[i] = -5, h = 5e-3 * 5 = 0.025. For θ[i] = 0.5, h = 5e-3 (since 5e-3 * 0.5 = 2.5e-3 < 5e-3). These should be fine. Let me check the actual Hessian values and see if there's a sign issue. Also, maybe the issue is `Vcov[i,i]` is being computed but giving ~1e-8 due to an error. Let me add some diagnostics. Actually, wait , maybe the problem is that inside `fd_hessian`, `f(θ)` calls `laplace_nll(θ; etas_cache=etas_cache)` which modifies the cache in place (no , looking at laplace_nll, it doesn't modify the passed cache; it just reads initial values from it). So that's fine. Hmm, but `optimise_eta` returns a fresh η̂ each call. So the cache provides good warm starts. Let me test with a coarser Hessian step to confirm. Actually, let me also check , maybe my inner optimization isn't exactly converging and there's noise in the objective at perturbed points. That would inflate the second derivative. Let me increase h for the Hessian to 0.01 and also try 0.02 and see if SEs stabilize. Wait, actually I realize , maybe these SEs are valid! If the effect is super strong (e.g., estimate ≈ -5.9 with tiny noise), maybe the data really does constrain it that well. But lCl.Wt SE = 1.7e-4 with estimate ≈ 0.6 would give t ≈ 3600 , that's unrealistic. Nearly all SEs are about 1.7e-4, suggesting something is off. Let me check: maybe the Hessian matrix is essentially rank deficient with those diagonals equal to the inverse of the largest eigenvalue? No, that doesn't make sense. Let me debug.

bash

cat /app/output/lrt_chain.csv

output

step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.2363234577585,1020.472646915517,1035.6897725001131,,
2,cl_wt,6,-479.25681389029324,970.5136277805865,988.774178482102,51.959019134930486,5.667114691486915e-13
3,full,8,-437.55226628753263,891.1045325750653,915.4519335104193,83.40909520552123,7.725829256376352e-19

bash

head -5 /app/output/per_subject_params.csv; echo ---; head -5 /app/output/obs_vs_pred.csv

output

Subject,Cl,V
1,0.005809672574136265,1.3451739052990421
2,0.005526203883629521,1.2204301509401663
3,0.008028379432021,1.6621753628199207
4,0.004107320913490431,0.9114793297607127
---
Subject,time,conc_obs,pred_pop,pred_ind
1,2.0,17.3,18.878293258096793,18.42511576460975
1,112.5,31.0,30.428298474741705,30.31508134693467
2,2.0,9.7,10.737683680502412,12.17994399522294
2,63.5,24.6,19.740855622506512,22.51271891888647

The SEs look too small. Let me investigate the Hessian computation.

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 
' 2>&1 &
BGPID=$!
sleep 90
kill $BGPID 2>/dev/null
wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (6.4s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.2s)
Fitting full model...
  -logL = 437.55226628753263  (7.4s)
Computing standard errors (FD Hessian)...
  (0.4 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 35.7 s.

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 

println("Debug Hessian...")
df = CSV.read(data_path(), DataFrame)
subs = load_subjects(df)
spec_full = ModelSpec("full", true, true, true)
# Refit
ff = fit_model(subs, spec_full)
println("θhat = ", ff.θ)
etas_cache = deepcopy(ff.etas)
f = θ -> laplace_nll(θ, subs, spec_full; etas_cache = etas_cache)
# test perturbations
for h in (0.001, 0.005, 0.01, 0.05, 0.1)
    H = fd_hessian(f, ff.θ; h=h)
    V = inv(Symmetric(H))
    nfx = n_fixed(spec_full)
    SE = [V[i,i] > 0 ? sqrt(V[i,i]) : NaN for i in 1:nfx]
    println("h=", h, "  SE = ", round.(SE; digits=4))
end
' 2>&1 &
BGPID=$!
sleep 200
kill $BGPID 2>/dev/null
wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (7.0s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.6s)
Fitting full model...
  -logL = 437.55226628753263  (8.2s)
Computing standard errors (FD Hessian)...
  (0.3 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 37.7 s.
Debug Hessian...
θhat = [-5.918214786740397, 0.612021841959712, -0.04585936167733609, -0.475333758300474, 0.5335506210318381, -1.513001299870201, -1.7598513227222106, 1.004014452041777]
h=0.001  SE = [0.0002, 0.0, 0.0, 0.0, 0.0]
h=0.005  SE = [0.001, 0.0002, 0.0002, 0.0002, 0.0002]
h=0.01  SE = [0.002, 0.0003, 0.0003, 0.0003, 0.0003]
h=0.05  SE = [0.0098, 0.0017, 0.0017, 0.0017, 0.0017]
h=0.1  SE = [0.0185, 0.0034, 0.0034, 0.0034, 0.0033]

The SE scales linearly with h, which means the Hessian is artificially inflated: the finite-difference Hessian isn't reflecting the true curvature. Something is wrong with my inner optimization , the inner problem probably isn't fully converging, making f(θ) noisy. Actually the issue might be that my inner Newton-Raphson exits too early. Let me check by computing the gradient at the optimum , is it actually zero? But more importantly, why does SE scale ~linearly with h? For a smooth function, FD Hessian should be independent of h (at least within range). Linear scaling suggests f(θ±h) depends linearly on h rather than quadratically. That would happen if the function has a kink or discontinuity. Actually, I think I see it. In my inner optimization, the `optimise_eta` exits either after maxit iterations or when ||g|| < tol. When we perturb θ slightly, each inner problem can have slightly different converged values. The issue: if the converged η shifts by δη ~ h, then the additional difference in q is O(δη * grad_q_inner) ~ h * residual_grad. But at the true optimum, grad_q_inner = 0, so this should be O(h²) correction, not O(h). Unless inner is not converged. Let me tighten the inner tolerance and see. Also, maybe I need to think about the Laplace formula. Actually, I realize there might be a different issue. The inner Newton loop I wrote has a termination check after updating g, H. Let me review: ``` for _ in 1:maxit # solve H*d = -g d = -(H \ g) step = 1.0 ...find step... η .= η_new q_new2, g, H = inner_all(η, s, p) if norm(g) < tol q = q_new2 break end q = q_new2 end ``` The tolerance is 1e-8. Should be good enough. Let me check more directly. Actually I wonder if my Hessian formula is wrong. Let me double check. For Laplace approximation to ∫ exp(-Q(η)) dη: log ∫ exp(-Q(η)) dη ≈ -Q(η̂) + (p/2) log(2π) - (1/2) log |Q''(η̂)| Then the full integral p(y) = exp(-ℓ_y|η - ℓ_η) integrated, where -ℓ_y|η = 0.5 * Σ (y-f)²/σ² + (n/2) log(2π σ²) -ℓ_η = 0.5 * η'Ω⁻¹η + 0.5 * log|2π Ω| Hmm so: p(y|η) * p(η) = exp(-0.5 Σ (y-f)²/σ² - (n/2)log(2π σ²) - 0.5 η'Ω⁻¹η - 0.5 log|2π Ω|) Let Q(η) = 0.5 * Σ (y-f)²/σ² + 0.5 * η'Ω⁻¹η (what I use). Const(θ) = (n/2)log(2π σ²) + 0.5 log|2π Ω| p(y|η) p(η) = exp(-Q(η)) * exp(-Const(θ)) p(y) = ∫ p(y|η) p(η) dη ≈ exp(-Const) * exp(-Q(η̂)) * (2π)^{p/2} / sqrt(|Q''|) log p(y) = -Const - Q(η̂) + (p/2)log(2π) - 0.5 log|Q''| - log p(y) = Const + Q(η̂) - (p/2)log(2π) + 0.5 log|Q''| = (n/2)log(2π σ²) + 0.5 log|2π Ω| + Q(η̂) - (p/2)log(2π) + 0.5 log|Q''| = (n/2)log(2π σ²) + 0.5 log|Ω| + (p/2)log(2π) + Q(η̂) - (p/2)log(2π) + 0.5 log|Q''| = (n/2)log(2π σ²) + 0.5 log|Ω| + Q(η̂) + 0.5 log|Q''| OK good, matches what I have. So the formula is right. The issue is numerical , the function values at perturbed θ aren't smooth enough. The linear scaling of SE with h tells us σ(f, h) ~ c*h (i.e. f is linear in h near optimum). That's weird for a smooth function. Unless... ah , maybe the optimization path in the inner loop produces a discontinuous surface. Like when step size in inner halving kicks in differently. Let me reduce the inner tolerance to 1e-12 and test again, and also see if Richardson extrapolation improves. Actually another thought , maybe my BFGS outer loop didn't converge. Let me check , the gradient at optimum should be zero. If not, then we're not at a local min, and H might be misleading. Actually, the fact that the numerical Hessian gives wildly inflated values suggests the cached η values are "locking in" the inner solution too tightly when we perturb θ. When we perturb θ by a small amount, the inner optimization converges quickly (using warm start) but to a slightly different optimum, and this causes noise in Q. Let me test: don't use cached η in Hessian computation. Start fresh each time. Or: use a MUCH tighter tolerance and higher max iterations in the inner loop. Actually, the simplest thing: use a non-warm-start inner fo …[truncated]

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 

df = CSV.read(data_path(), DataFrame)
subs = load_subjects(df)
spec_full = ModelSpec("full", true, true, true)
ff = fit_model(subs, spec_full)
println("θhat = ", ff.θ)
# Try with no cache and tighter tolerance
f = θ -> laplace_nll(θ, subs, spec_full)  # no cache
for h in (0.01, 0.02, 0.05, 0.1, 0.2)
    H = fd_hessian(f, ff.θ; h=h)
    V = inv(Symmetric(H))
    nfx = n_fixed(spec_full)
    SE = [V[i,i] > 0 ? sqrt(V[i,i]) : NaN for i in 1:nfx]
    println("h=", h, "  SE = ", round.(SE; digits=5))
end
' 2>&1 &
BGPID=$!
sleep 240
kill $BGPID 2>/dev/null
wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (11.7s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (10.0s)
Fitting full model...
  -logL = 437.55226628753263  (13.3s)
Computing standard errors (FD Hessian)...
  (0.4 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 51.2 s.
θhat = [-5.918214786740397, 0.612021841959712, -0.04585936167733609, -0.475333758300474, 0.5335506210318381, -1.513001299870201, -1.7598513227222106, 1.004014452041777]
h=0.01  SE = [0.002, 0.00034, 0.00034, 0.00034, 0.00034]
h=0.02  SE = [0.00399, 0.00068, 0.00068, 0.00068, 0.00068]
h=0.05  SE = [0.0098, 0.00169, 0.00169, 0.00169, 0.00168]
h=0.1  SE = [0.01848, 0.00336, 0.00338, 0.00336, 0.00331]
h=0.2  SE = [0.03128, 0.00664, 0.00673, 0.00659, 0.00626]

The SE scales exactly linearly with h. This means the function value near optimum is truly linear in the perturbation, not quadratic. That can only happen if we're not at a local minimum. Looking at the θhat: `[-5.92, 0.612, -0.046, -0.475, 0.534, -1.513, -1.76, 1.004]` with last three being log(ω_Cl), log(ω_V), log(σ). So σ = exp(1.004) ≈ 2.73. Wait... my inner optimization might not be converging properly. If inner η̂ isn't at its minimum, the gradient of the outer w.r.t. θ has an extra term from ∂η̂/∂θ. But at inner optimum this term vanishes by envelope theorem. Hmm. Let me check if the actual outer optimum has been reached. Perhaps the BFGS with finite differences didn't converge tightly enough. Actually the gradient test shows the outer might not be at optimum. Actually, the linear behavior suggests the outer isn't converged. If ∂f/∂θ_i = a ≠ 0 at θhat, then near θhat, f(θ ± h e_i) = f(θhat) ± ah + O(h²), so: (f(θ+h) - 2f(θ) + f(θ-h))/h² = O(1) That gives a constant Hessian independent of h, with SE = 1/√H independent of h. But we see SE proportional to h. That means (f+ - 2f0 + f-)/h² ~ 1/h², i.e., (f+ - 2f0 + f-) ~ constant. That's like a discontinuity at θhat (f has a jump/kink of size c), OR the inner loop is producing discontinuous results. Ohhh, I bet I know. The issue is that `optimise_eta` starts fresh each time when no cache, and Newton-Raphson can converge to slightly different values based on starting point or step halving details. The noise in the output is ~10^{-4} per subject summed over 59 subjects, giving a ~10^{-2.5} level of noise in f. Let me look at the noise scale. If constant "noise" in f is ~1, then h²*H = 1, H = 1/h². SE = h. Matches linear behavior. So there's inherent noise of O(1) in f, independent of h. That's a huge noise. I must be doing something very wrong in optimise_eta. Wait, let me check if my inner Newton-Raphson is actually converging. The formula: ``` for _ in 1:maxit d = -(H \ g) step = 1.0 for _ in 1:20 η_new = η .+ step .* d q_new, _, _ = inner_all(η_new, s, p) if q_new <= q - 1e-10*step*dot(g, d) || step < 1e-6 break end step *= 0.5 end η .= η_new q_new2, g, H = inner_all(η, s, p) if norm(g) < tol; break; end q = q_new2 end ``` Wait wait, the Armijo condition uses `dot(g, d)` but d = -(H\g), so g'd = -g'(H\g) < 0 typically (if H is PD). So we want q_new ≤ q + 1e-10 * step * g'd = q - 1e-10 * step * g'(H\g). My check `q_new <= q - 1e-10*step*dot(g, d)` has a sign error! I wrote `q - 1e-10*step*dot(g, d)` where dot(g,d) is negative (since d is descent). Subtracting a negative means adding. So it requires q_new ≤ q + (small positive), which is essentially any small decrease or even slight increase. That's weak but should still work. Actually, the critical problem is: the Hessian `H` returned by `inner_all` is GAUSS-NEWTON with `sum(dC1^2)/σ2 + 1/ωCl^2`, which doesn't match the exact Hessian perfectly. This works for Newton (we just need descent direction). Should be fine. I think the issue is numerical. Each call to optimise_eta gives subtly different η̂ due to accumulated floating-point errors in Newton steps. When f is evaluated at θ+h vs θ-h, the inner solutions differ, adding noise. Solution: use a very tight inner convergence (tolerance 1e-12), and do final polishing without cache. Actually, let me re-examine. With warm start from θhat cache: - At exactly θhat, q = q_hat. - Perturbing by +h, inner η̂ shifts slightly, giving q' ≈ q_hat + O(h²). - But if my inner tol is 1e-8, and optimal q_hat is maybe 100, then my q_hat is measured to 8 significant digits. OK let me try a really really tight inner tolerance. Actually, wait. I have another theory. I'm starting from warm-start cache after the fit. But after the fit, the cache has etas from a slightly different optimization path. So at θhat, the cache may already give η̂_cached ≠ η̂_true. Then when we compute f(θhat), we get q_cach …[truncated]

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 

df = CSV.read(data_path(), DataFrame)
subs = load_subjects(df)
spec = ModelSpec("full", true, true, true)
ff = fit_model(subs, spec)
println("θhat = ", ff.θ)
# check inner convergence quality
p = unpack(ff.θ, spec)
grads = Float64[]
for (i,s) in enumerate(subs)
    η̂ = optimise_eta(s, p)
    _, g, _ = inner_all(η̂, s, p)
    push!(grads, norm(g))
end
println("max inner gradient norm = ", maximum(grads))
println("mean inner gradient norm = ", mean(grads))

# try directly with high-precision inner
function opt_eta_tight(s::SubjData, p)
    res = optimize(η -> inner_all(η, s, p)[1], zeros(2), NelderMead(),
                   Optim.Options(iterations = 2000, g_tol = 1e-14))
    η1 = Optim.minimizer(res)
    res2 = optimize(η -> inner_all(η, s, p)[1], η1, NelderMead(),
                   Optim.Options(iterations = 4000, g_tol = 1e-14))
    Optim.minimizer(res2)
end
println("try high precision inner on 3 subjects")
for i in 1:3
    s = subs[i]
    η_n = optimise_eta(s, p)
    η_nm = opt_eta_tight(s, p)
    q_n = inner_all(η_n, s, p)[1]
    q_nm = inner_all(η_nm, s, p)[1]
    println("subj $i: Newton q=$q_n  η=$η_n;  NM q=$q_nm  η=$η_nm")
end
' 2>&1 &
BGPID=$!
sleep 150
kill $BGPID 2>/dev/null; wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (6.0s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.1s)
Fitting full model...
  -logL = 437.55226628753263  (8.0s)
Computing standard errors (FD Hessian)...
  (0.4 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 36.0 s.
θhat = [-5.918214786740397, 0.612021841959712, -0.04585936167733609, -0.475333758300474, 0.5335506210318381, -1.513001299870201, -1.7598513227222106, 1.004014452041777]
max inner gradient norm = 9.892861195205622e-9
mean inner gradient norm = 3.724662583487667e-9
try high precision inner on 3 subjects
subj 1: Newton q=0.14423912276077616  η=[-0.04098749416539037, 0.024886193252263183];  NM q=0.14423912276077633  η=[-0.04098748791338282, 0.024886192680066126]
subj 2: Newton q=1.3083448895260805  η=[-0.15221276946626422, -0.12578879294924925];  NM q=1.3083448895260814  η=[-0.1522127751931937, -0.12578879278772054]
subj 3: Newton q=1.9634028655459033  η=[0.22126878466361577, 0.18313504023909];  NM q=1.96340286554591  η=[0.22126877649559112, 0.18313504271758943]

The inner is converging quite well (gradient norm ~1e-9 max). So the function value should be accurate to double-precision level. So why is the FD Hessian scaling linearly with h? Wait, maybe the issue is that my fit_model isn't fully converged at the outer level. The outer optimum may not have gradient = 0, causing the FD Hessian to behave oddly. Let me check , compute outer gradient at θhat numerically.

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 

df = CSV.read(data_path(), DataFrame)
subs = load_subjects(df)
spec = ModelSpec("full", true, true, true)
ff = fit_model(subs, spec)
f = θ -> laplace_nll(θ, subs, spec)
# compute outer gradient at θhat
f0 = f(ff.θ)
println("f0 = ", f0)
for h in (1e-4, 1e-3, 1e-2)
    println("h=$h")
    for i in 1:length(ff.θ)
        ep = copy(ff.θ); ep[i] += h; em = copy(ff.θ); em[i] -= h
        grad_i = (f(ep) - f(em)) / (2h)
        hess_i = (f(ep) - 2f0 + f(em)) / h^2
        println("  i=$i  grad=$grad_i  hess_diag=$hess_i")
    end
end
' 2>&1 &
BGPID=$!
sleep 200
kill $BGPID 2>/dev/null; wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (7.0s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.9s)
Fitting full model...
  -logL = 437.55226628753263  (7.8s)
Computing standard errors (FD Hessian)...
  (0.4 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 37.6 s.
f0 = 437.5522662871405
h=0.0001
  i=1  grad=3.63144181392272e-6  hess_diag=8.731045370666962e10
  i=2  grad=1.6362946553272195e-5  hess_diag=8.731045446437057e10
  i=3  grad=4.34198454968282e-6  hess_diag=8.731045365226445e10
  i=4  grad=0.00010907626801781589  hess_diag=8.731045468607552e10
  i=5  grad=0.00017313851685685222  hess_diag=8.731045724465082e10
  i=6  grad=9.661846434028121e-5  hess_diag=8.731045327840457e10
  i=7  grad=3.552855787347653e-5  hess_diag=8.731045331394394e10
  i=8  grad=-6.898829951751395e-5  hess_diag=8.731045340689357e10
h=0.001
  i=1  grad=6.475025315921812e-5  hess_diag=8.73104981761235e8
  i=2  grad=0.0003888428921072773  hess_diag=8.731057394963605e8
  i=3  grad=5.684381676474004e-5  hess_diag=8.731049273802513e8
  i=4  grad=0.00010089391366818745  hess_diag=8.731059612139925e8
  i=5  grad=8.763853998061677e-5  hess_diag=8.731085197880323e8
  i=6  grad=9.748563911671226e-5  hess_diag=8.731045535250763e8
  i=7  grad=3.868166231768555e-5  hess_diag=8.731045890920697e8
  i=8  grad=-9.906827358463488e-5  hess_diag=8.731046820446978e8
h=0.01
  i=1  grad=0.00638814896092299  hess_diag=8.731494510313485e6
  i=2  grad=0.037726845468455394  hess_diag=8.732252235232206e6
  i=3  grad=0.005471136705637036  hess_diag=8.73144012975439e6
  i=4  grad=-0.0008057679366402226  hess_diag=8.732473963738007e6
  i=5  grad=-0.008358604290492622  hess_diag=8.735032507130126e6
  i=6  grad=0.0003218309757357929  hess_diag=8.73106627576599e6
  i=7  grad=0.0002508525966504749  hess_diag=8.731101841774365e6
  i=8  grad=-0.0032168442231750305  hess_diag=8.731194799720109e6

The Hessian diagonal is ~8.73e10 / h^2 regardless of parameter. That's clearly a fixed noise floor of about 8.73e6 * h^2 absolute noise, i.e., the f(θ+h) + f(θ-h) - 2 f(θ) is constant ~873, independent of h. Actually look: with h=1e-4, diagonal is 8.73e10, so (f+ + f- - 2f0) = 8.73e10 * 1e-8 = 873. With h=1e-3, diagonal is 8.73e8, so (f+ + f- - 2f0) = 8.73e8 * 1e-6 = 873. With h=1e-2, diagonal is 8.73e6, so (f+ + f- - 2f0) = 8.73e6 * 1e-4 = 873. So there's a constant additive noise of 873 in f at θhat vs θhat ± h. That's a huge bias, not numerical noise. This means: at θhat, f(θhat) = 437.55, but at θhat ± h even tiny h, f ≈ 437.55 + 436.5. The function jumps discontinuously! Let me check f at exactly θhat vs θhat + [1e-8, 0, ...]:

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 

df = CSV.read(data_path(), DataFrame)
subs = load_subjects(df)
spec = ModelSpec("full", true, true, true)
ff = fit_model(subs, spec)
f = θ -> laplace_nll(θ, subs, spec)
f0 = f(ff.θ)
println("f(θhat) = $f0")
# Try with tiny and varied perturbations
for h in (1e-10, 1e-8, 1e-6, 1e-4, 1e-3)
    for i in (1, 5)
        ep = copy(ff.θ); ep[i] += h; em = copy(ff.θ); em[i] -= h
        println("h=$h i=$i f+=$(f(ep))  f-=$(f(em))")
    end
end
# Try also calling f at θhat multiple times , is it deterministic?
println("repeat f0: ", f(ff.θ), "  ", f(ff.θ))
' 2>&1 &
BGPID=$!
sleep 200
kill $BGPID 2>/dev/null; wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (6.4s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.1s)
Fitting full model...
  -logL = 437.55226628753263  (7.6s)
Computing standard errors (FD Hessian)...
  (0.4 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 36.7 s.
f(θhat) = 437.5522662871405
h=1.0e-10 i=1 f+=437.55226628697324  f-=437.55226628724716
h=1.0e-10 i=5 f+=437.55226628702167  f-=437.5522662871095
h=1.0e-8 i=1 f+=437.55226628735215  f-=437.55226628708596
h=1.0e-8 i=5 f+=437.55226628751626  f-=437.5522662873713
h=1.0e-6 i=1 f+=437.55226628744043  f-=437.5522662875009
h=1.0e-6 i=5 f+=437.5522662891019  f-=437.5522662890163
h=0.0001 i=1 f+=437.55226853371124  f-=437.55226853298495
h=0.0001 i=5 f+=437.5522862405679  f-=437.5522862059402
h=0.001 i=1 f+=437.55249094536777  f-=437.55249081586726
h=0.001 i=5 f+=437.55425998165464  f-=437.55425980637756
repeat f0: 437.5522662871405  437.5522662871405

Great find! Look at this: - f(θhat) = 437.5522662871405 - f(θhat ± 1e-4 e_1) = 437.55226853... (about +2.2e-6 above f0) So f(θhat ± h) > f(θhat) consistently. That's expected (θhat is a minimum). But the gap isn't h²/2 * second derivative , let me see: (f+ + f- - 2 f0) at h=1e-4 for i=1: = 437.55226853371124 + 437.55226853298495 - 2 * 437.5522662871405 = 875.10453706669619 - 875.1045325742810 = 0.00045. Hmm, so Hessian ≈ 0.00045/(1e-4)^2 = 4.5e4 for i=1. So SE for i=1 would be sqrt(1/4.5e4) ≈ 4.7e-3. Reasonable! But the script used f0 and called `fd_hessian(f, ff.θ)` , let me check why. Oh!! I see. In my fd_hessian function, I reuse `f0` computed at the start. But when I compute f(θ±h), the returned value from the function IS consistent (the warmup from cache or fresh start produces consistent value). However, in fd_hessian, f0 was computed BEFORE the perturbations. If the cache is populated by solving at θhat with fresh η starts (zeros), then subsequent calls (at θhat±h) use the same "fresh start" logic. So there's no stale cache issue. Oh wait, `laplace_nll(θ, subs, spec)` without cache uses `η0 = zeros(2)` each time. So each call is deterministic. Fine. But in the debugging test above, I computed f0 = 437.5522662871405 exactly. And f(θhat ± 1e-4 e_1) = 437.55226853... with a gap of ~2.2e-6 from f0. BUT my earlier fd_hessian output showed diagonal 8.73e6 for h=0.01 , which would mean (f+ + f- - 2f0) = 873 for h=0.01! Let me reconcile. Oh I see , the earlier test used the warm-started laplace_nll with cache. In that case, f0 called with warm cache might give a DIFFERENT value than subsequent calls at perturbed θ (which also use warm cache but the cache might not be refreshed from the previous iteration). Actually, looking at my code more carefully: ```julia function laplace_nll(θ, subs, spec; etas_cache=nothing, return_etas=false) ... η0 = etas_cache === nothing ? zeros(2) : etas_cache[i] η̂ = optimise_eta(s, p; η0 = η0) ``` So `etas_cache` provides initial η values. The cache is READ-ONLY within laplace_nll. In `fd_hessian`, I pass the SAME `f` (closure over `etas_cache`) that's computed repeatedly. The cache stays constant throughout! It's initialized from the fit's final etas. So f0 = f(θhat) uses cache etas, which ARE the true minimizers, so optimise_eta returns them essentially unchanged (with tiny refinement noise). But when we compute f(θhat + 1e-4 e_1), the cache etas are close (but not exact) minimizers for the new θ. The inner optimizer refines them with tol=1e-8. Hmm, yet somehow we get a 873 discrepancy. Let me check the code again. Oh wait , the test just now that showed "f0=437.55" and "f(θhat+1e-4) = 437.5522685" WAS using `f = θ -> laplace_nll(θ, subs, spec)` without cache. So inner starts from zero every time. And the values are reasonable. But the earlier test using `fd_hessian(f, ff.θ; h=0.001)` was using WITHOUT cache too! Let me re-read... actually yes, it called `fd_hessian` with `f = θ -> laplace_nll(θ, subs, spec)`. So that should be the same behavior. Wait, in the earlier test, output was: ``` h=0.001 i=1 grad=6.475025315921812e-5 hess_diag=8.731057394963605e8 ``` hess_diag = 8.73e8, meaning (f+ + f- - 2f0) = 8.73e8 * (1e-3)^2 = 873. But in this test (without cache), (f+ + f- - 2f0) at h=1e-3 for i=1 is: 437.55249094536777 + 437.55249081586726 - 2*437.5522662871405 = 875.10498176123503 - 875.1045325742810 = 0.00044918694 ≈ 4.5e-4. So HUGE discrepancy! The earlier test must have had something very different. Let me read the first debug test more carefully: ``` # Try with no cache and tighter tolerance f = θ -> laplace_nll(θ, subs, spec_full) # no cache for h in (0.01, 0.02, 0.05, 0.1, 0.2) H = fd_hessian(f, ff.θ; h=h) ... ``` Ah yes, no cache. But the SEs scaled linearly. The diagonal was 8.73e6 for h=0.01 (per the other test). (f+ + f- - 2f0) = 8.73e6 * 1e-4 = 873. But the direct test with same f at h=1e-4 showed (f+ + f- - 2f0) = 4.5e-4 for i=1. At h= …[truncated]

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 

df = CSV.read(data_path(), DataFrame)
subs = load_subjects(df)
spec = ModelSpec("full", true, true, true)
ff = fit_model(subs, spec)
f = θ -> laplace_nll(θ, subs, spec)
f0 = f(ff.θ)
println("f0 = ", f0)
# directly call with the exact same steps as fd_hessian
h = 1e-3
hs = [max(h, h*abs(ff.θ[i])) for i in 1:length(ff.θ)]
println("hs = ", hs)
for i in 1:length(ff.θ)
    ep = copy(ff.θ); ep[i] += hs[i]
    em = copy(ff.θ); em[i] -= hs[i]
    fp = f(ep); fm = f(em)
    H_ii = (fp - 2f0 + fm) / hs[i]^2
    println("i=$i fp=$fp  fm=$fm  H_ii=$H_ii SE=$(sqrt(1/max(H_ii,0)))")
end
' 2>&1 &
BGPID=$!
sleep 150
kill $BGPID 2>/dev/null; wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (7.6s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.6s)
Fitting full model...
  -logL = 437.55226628753263  (8.0s)
Computing standard errors (FD Hessian)...
  (0.4 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 37.7 s.
f0 = 437.5522662871405
hs = [0.005918214786740397, 0.001, 0.001, 0.001, 0.001, 0.0015130012998702009, 0.0017598513227222105, 0.0010040144520417772]
i=1 fp=437.5601459624997  fm=437.56011947146317  H_ii=2.4928297729499932e7 SE=0.00020028742750612905
i=2 fp=437.5528701370231  fm=437.5528693593373  H_ii=8.731057394963605e8 SE=3.384282267818105e-5
i=3 fp=437.55246374696947  fm=437.55246363328183  H_ii=8.731049273802513e8 SE=3.384283841758088e-5
i=4 fp=437.5529807078902  fm=437.55298050610236  H_ii=8.731059612139925e8 SE=3.384281838113618e-5
i=5 fp=437.55425998165464  fm=437.55425980637756  H_ii=8.731085197880323e8 SE=3.3842768794276117e-5
i=6 fp=437.55229041864516  fm=437.5522901148859  H_ii=3.814061261126957e8 SE=5.120426868771563e-5
i=7 fp=437.5523538822562  fm=437.5523537306701  H_ii=2.819125253793177e8 SE=5.9558371449507696e-5
i=8 fp=437.5523415238996  fm=437.5523417234055  H_ii=8.661365970800985e8 SE=3.397870361983821e-5

OK so both at θhat and at θhat±1e-4 (or ±1e-3), f is ~437.55. But at θhat, f0 = 437.55226628. At θhat+1e-3, f+ ≈ 437.5528 (for i=2). The difference is ~5e-4. But previously at h=1e-4 for i=1, I got: f+ = 437.55226853371124 f- = 437.55226853298495 So (f+ + f- - 2f0) = 437.55226853371124 + 437.55226853298495 - 2*437.5522662871405 = 0.0004491... ≈ 4.5e-4. And now at h=1e-3 for i=2 (first "normal" h): f+ = 437.5528701370231 f- = 437.5528693593373 (f+ + f- - 2f0) = 437.5528701370231 + 437.5528693593373 - 2*437.5522662871405 = 875.1057394963604 - 875.104532574281 = 0.001207... Hmm expected (f+ - f0) ≈ h²/2 * H_true. If H_true is say 100, (f+ - f0) ≈ 0.5 * 1e-6 * 100 = 5e-5. Observed is ~6e-4 for i=2 with h=1e-3 (f+ - f0 = 0.00060). But the SUM is (f+ + f- - 2f0) ≈ 0.00121. Let me think: if f = f0 + a*δ + b*δ² where a = grad, b = H/2, then f(θ+h) + f(θ-h) - 2f0 = 2b*h² = H*h². So H = 0.00121 / 1e-6 = 1210. SE would be sqrt(1/1210) ≈ 0.029. But the output says H_ii = 8.73e8, SE = 3.4e-5. WHAT?! Let me recompute manually: fp = 437.5528701370231 fm = 437.5528693593373 2*f0 = 2 * 437.5522662871405 = 875.1045325742810 fp - 2f0 + fm = 437.5528701370231 + 437.5528693593373 - 875.1045325742810 = 875.1057394963604 - 875.1045325742810 = 0.001206922 Divide by hs[2]^2 = (1e-3)^2 = 1e-6: 0.00120692 / 1e-6 = 1206.92. NOT 8.73e8. So where is 8.73e8 coming from??? OH WAIT. There's a floating-point precision issue with large numbers and very close values. Let me check the actual calculation: (437.5528701370231 - 2 * 437.5522662871405 + 437.5528693593373) / 1e-6 In floating point, 437.55... and 437.55... are very close, and subtracting them gives loss of precision. Then you multiply by 1/h². So precision matters. Actually the values ARE to ~10 significant digits. f+ - f0 = 0.0006037... which has about 4 significant digits of the original. Still computable. Let me recompute manually in Julia... Wait, I wonder if H_ii calculation has a bug. Let me re-examine: ``` H[i,i] = (fdpm[i,1] - 2f0 + fdpm[i,2]) / hs[i]^2 ``` Julia evaluates 2f0 as 2*f0. For f0 = 437.55226628714..., 2*f0 = 875.1045325742... . Then `fdpm[i,1] - 2f0 + fdpm[i,2]` , this evaluates left to right: `fdpm[i,1] - 2f0` = 437.5528701370231 - 875.1045325742810 = -437.5516624372579 then + fdpm[i,2] = -437.5516624372579 + 437.5528693593373 = 0.00120692 Divide by 1e-6 = 1206.92. So it should give H_ii = 1207. But the output says H_ii = 8.73e8! Oh I see , I printed different values! The actual run produced different f+ and f- values than what I see in the test. Let me look again: Wait, the test I just ran: "i=2 fp=437.5528701370231 fm=437.5528693593373 H_ii=8.731057394963605e8" Hmm let me compute: 437.5528701370231 - 875.1045325742810 + 437.5528693593373 = -437.5516624372579 + 437.5528693593373 = 0.0012069220794 (roughly) / 1e-6 = 1206.9 That should give SE = sqrt(1/1206.9) = 0.0288. But output says H_ii = 8.73e8, SE = 3.4e-5. That's 8.73e8 = 1206.9 * 1e6 / 1e6 / ... Hmm. Wait let me check: maybe `H_ii` was not `(fp + fm - 2f0)/h²` but `(fp + fm - 2f0)/h^3` or something? Let me check: 0.00120692 / (1e-3)^3 = 1.20692e6. Not right either. 0.00120692 / (1e-3)^4 = 1.20692e9. Close! Hmm, 8.73e8 and 1.2e9 are in the same ballpark. Wait, what if the calculation is `(fp + fm - 2f0)` interpreted as `(fp + fm) - 2*f0` where `f0` is somehow wrong? Oh! Actually looking at my test code, I compute `f0 = f(ff.θ)` ONCE at the top. But `fp = f(ep)` and `fm = f(em)` are computed AFTER. In Julia, `f` is `θ -> laplace_nll(θ, subs, spec)` , no cache. But each call uses zeros(2) as starting point, so should be deterministic. Wait actually HOLD ON. Let me look at the `println`: ``` i=2 fp=437.5528701370231 fm=437.5528693593373 H_ii=8.731057394963605e8 SE=3.384282267818105e-5 ``` H_ii=8.731057394963605e8. That's 8.731...e8. If I compute (fp + fm - 2f0) that I expect ≈ 1.2e-3, divided by (1e-3)^2 = 1e-6, gives 1.2e3. Not 8.7e8. WAIT. 1.2e-3 / 1e-6 = 1.2 …[truncated]

bash

cd /app && julia --startup-file=no -e '
include("analysis.jl") 

df = CSV.read(data_path(), DataFrame)
subs = load_subjects(df)
spec = ModelSpec("full", true, true, true)
ff = fit_model(subs, spec)
f = θ -> laplace_nll(θ, subs, spec)
f0 = f(ff.θ)
# test the actual raw arithmetic
h = 1e-3
i = 2
ep = copy(ff.θ); ep[i] += h
em = copy(ff.θ); em[i] -= h
fp = f(ep); fm = f(em)
diff = fp + fm - 2*f0
println("f0 = ", repr(f0))
println("fp = ", repr(fp))
println("fm = ", repr(fm))
println("diff (fp+fm-2f0) = ", repr(diff))
println("diff / h^2 = ", repr(diff/h^2))

# Now run fd_hessian exactly
H = fd_hessian(f, ff.θ; h=1e-3)
println("H diag = ", [H[i,i] for i in 1:8])
' 2>&1 &
BGPID=$!
sleep 180
kill $BGPID 2>/dev/null; wait 2>/dev/null

output

┌ Info: LRT
│   LR2 = 51.959019134930486
│   pv2 = 5.667114691486915e-13
│   LR3 = 83.40909520552123
└   pv3 = 7.725829256376352e-19
Fitting base model...
  -logL = 505.2363234577585  (7.0s)
Fitting cl_wt model...
  -logL = 479.25681389029324  (5.9s)
Fitting full model...
  -logL = 437.55226628753263  (8.5s)
Computing standard errors (FD Hessian)...
  (0.4 s)
cor(obs, pop_pred) = 0.8149974182006159;  cor(obs, ind_pred) = 0.9710149607975146
Done in 39.5 s.
f0 = 437.5522662871405
fp = 437.5528701370231
fm = 437.5528693593373
diff (fp+fm-2f0) = 0.0012069220794046487
diff / h^2 = 1206.9220794046487
H diag = [2.4928297729499932e7, 8.731057394963605e8, 8.731049273802513e8, 8.731059612139925e8, 8.731085197880323e8, 3.814061261126957e8, 2.819125253793177e8, 8.661365970800985e8]

I see! The direct manual calculation gives diff/h^2 = 1207 for i=2, but `fd_hessian` gives H[2,2] = 8.73e8. These use the exact same h. So there must be a bug in `fd_hessian`. Let me re-read: ```julia function fd_hessian(f, θ::Vector{Float64}; h::Float64 = 5e-3) n = length(θ); H = zeros(n,n); f0 = f(θ) hs = [max(h, h*abs(θ[i])) for i in 1:n] fdpm = zeros(n, 2) for i in 1:n ep = copy(θ); ep[i] += hs[i]; fdpm[i,1] = f(ep) em = copy(θ); em[i] -= hs[i]; fdpm[i,2] = f(em) H[i,i] = (fdpm[i,1] - 2f0 + fdpm[i,2]) / hs[i]^2 end for i in 1:n, j in (i+1):n ... H[i,j] = ... H[j,i] = H[i,j] end ``` Wait, in the nested loop `for i in 1:n, j in (i+1):n`, the `i` here SHADOWS the outer `i`! But no, they're separate loops. And H[i,i] was set in the first loop. The second loop only sets H[i,j] for i<j. Hmm. BUT WAIT: `hs[i]^2` , when i=2, hs[2] = max(1e-3, 1e-3*|θ[2]|) = max(1e-3, 1e-3*0.612) = 1e-3. OK so hs[2] = 1e-3 = h. So that's correct. Let me trace manually. In fd_hessian with my f: - f0 = f(θ) = 437.5522662871405 - For i=2: hs[2] = 1e-3. ep = θ with θ[2] += 1e-3. fp = f(ep) = 437.5528701370231. - em = θ with θ[2] -= 1e-3. fm = f(em) = 437.5528693593373. - H[2,2] = (fp - 2*f0 + fm) / 1e-6 Let me compute this carefully in Julia: 437.5528701370231 - 2*437.5522662871405 + 437.5528693593373 = 437.5528701370231 + 437.5528693593373 - 2*437.5522662871405 Using double precision, 2*437.5522662871405 is 875.1045325742810. In Julia actually 2*437.5522662871405 might have a tiny FP variation: julia> 2 * 437.5522662871405 875.104532574281 Then (437.5528701370231 + 437.5528693593373) = 875.1057394963604 Subtract: 875.1057394963604 - 875.104532574281 = 0.0012069220794046... Divide by 1e-6 = 1206.922. But the code got 8.73e8. There MUST be something different. OH! I bet in fd_hessian, `2f0` is parsed as `2f0` which in Julia might be 2 * Float32(0)! Because `2f0` in Julia literal notation means Float32 zero! Yes! `1f0 === Float32(1)`. So `2f0` is Float32 constant `2.0f0 = 2.0f0` = 2.0 as Float32. But when used in `fdpm[i,1] - 2f0 + fdpm[i,2]`, it becomes `fdpm[i,1] - 2.0f0 + fdpm[i,2]` = `fdpm[i,1] - 2.0 + fdpm[i,2]` (since Float32(2) promotes). Wait, `2f0` in Julia: `f0` is a float literal suffix, so `2f0` is `2 * 10^0` as Float32 = `2.0f0`. Let me test.

bash

cd /app && julia --startup-file=no -e 'println(2f0); println(typeof(2f0)); f0 = 437.5522662871405; println(2f0); println(typeof(2f0))'

output

2.0
Float32
2.0
Float32

Found it! `2f0` is a Float32 literal, not `2 * f0`. The code `(fdpm[i,1] - 2f0 + fdpm[i,2])` is computing `fdpm[i,1] - 2.0f0 + fdpm[i,2]` = `fdpm[i,1] - 2.0 + fdpm[i,2]` = `437.55287 - 2.0 + 437.55287` = 873.105...! Yes! That explains the 873 anomaly exactly. Let me fix this by writing `2 * f0` explicitly.

bash

grep -n "2f0\|4hi\|4*hi" /app/analysis.jl

output

1:# Work only in this file.
7:# Outputs: write everything to /app/output/
19:    apgar_high::Float64
32:        apgar_high = (apg == ">= 5") ? 1.0 : 0.0
45:        push!(subs, SubjData(Int(sid), wt, apgar_high, dts, damts, sts, scs))
65:        for j in eachindex(dtimes)
120:    lCl = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high + η[1]
175:                     etas_cache::Union{Nothing,Vector{Vector{Float64}}} = nothing,
183:        η0 = etas_cache === nothing ? zeros(2) : etas_cache[i]
203:                   θ0 = nothing, verbose::Bool = false)
205:    if θ0 === nothing
222:        for i in eachindex(ηs); etas_cache[i] = ηs[i]; end
226:    # BFGS with finite-difference gradient is usually fast for this size.
248:        H[i,i] = (fdpm[i,1] - 2f0 + fdpm[i,2]) / hs[i]^2
273:        key = s.apgar_high == 1.0 ? ">= 5" : "< 5"
296:        lCl_pop = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high
318:    wts_hi = Float64[]; lcl_hi = Float64[]
322:        if s.apgar_high == 1.0
323:            push!(wts_hi, s.wt); push!(lcl_hi, lcl_i)
328:    !isempty(wts_hi) && scatter!(ax3, wts_hi, lcl_hi;
344:    hi = max(maximum(rows_op.conc_obs), maximum(rows_op.pred_pop),
346:    pad = 0.05 * (hi-lo) + 1e-3
350:                limits = ((lo-pad, hi+pad), (lo-pad, hi+pad)))
353:    lines!(ax4a, [lo-pad, hi+pad], [lo-pad, hi+pad];
359:                limits = ((lo-pad, hi+pad), (lo-pad, hi+pad)))
362:    lines!(ax4b, [lo-pad, hi+pad], [lo-pad, hi+pad];
443:    pv2 = ccdf(Chisq(df2), LR2)
444:    pv3 = ccdf(Chisq(df3), LR3)
489:        lCl_ind = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high + η[1]
491:        lCl_pop = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high
498:        for k in eachindex(s.samp_times)

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:         H[i,i] = (fdpm[i,1] - 2f0 + fdpm[i,2]) / hs[i]^2
new_str:         H[i,i] = (fdpm[i,1] - 2.0*f0 + fdpm[i,2]) / hs[i]^2

output

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

bash

grep -n "2f\|2f0\|2\*f0\|- 2\*" /app/analysis.jl | head

output

520:    aic = 2*k_pars - 2*logL
521:    bic = log(n_obs_total)*k_pars - 2*logL

bash

grep -n "f0\|2q_new\|q_new" /app/analysis.jl | head -20

output

152:        q_new = q
156:            q_new, _, _ = inner_all(η_new, s, p)
157:            if q_new <= q - 1e-10*step*dot(g, d) || step < 1e-6
163:        q_new2, g, H = inner_all(η, s, p)
165:            q = q_new2
168:        q = q_new2
242:    n = length(θ); H = zeros(n,n); f0 = f(θ)
248:        H[i,i] = (fdpm[i,1] - 2.0*f0 + fdpm[i,2]) / hs[i]^2

Now let me also make the outer optimization more thorough and add Richardson extrapolation for better Hessian accuracy:

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:     # BFGS with finite-difference gradient is usually fast for this size.
    res = optimize(f, θ0, NelderMead(),
                   Optim.Options(iterations = 800, g_tol = 1e-5,
                                 show_trace = verbose))
    θ1 = Optim.minimizer(res)
    res2 = optimize(f, θ1, BFGS(),
                    Optim.Options(iterations = 150, g_tol = 1e-5,
                                  show_trace = verbose))
    θhat = Optim.minimizer(res2)
new_str:     # BFGS with finite-difference gradient is usually fast for this size.
    res = optimize(f, θ0, NelderMead(),
                   Optim.Options(iterations = 1500, g_tol = 1e-6,
                                 show_trace = verbose))
    θ1 = Optim.minimizer(res)
    res2 = optimize(f, θ1, BFGS(),
                    Optim.Options(iterations = 200, g_tol = 1e-6,
                                  show_trace = verbose))
    θhat = Optim.minimizer(res2)
    # final polish with Nelder-Mead (helps after BFGS gets close)
    res3 = optimize(f, θhat, NelderMead(),
                    Optim.Options(iterations = 500, g_tol = 1e-7,
                                  show_trace = verbose))
    θhat = Optim.minimizer(res3)

output

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

bash

cd /app && time julia --startup-file=no analysis.jl 2>&1 | tail -30 &
BGPID=$!
for i in $(seq 1 27); do sleep 10; if ! kill -0 $BGPID 2>/dev/null; then break; fi; done
if kill -0 $BGPID 2>/dev/null; then kill $BGPID 2>/dev/null; echo "KILLED"; fi
wait 2>/dev/null

output

Fitting base model...
  -logL = 505.2363234576006  (7.5s)
Fitting cl_wt model...
  -logL = 479.25681388851996  (8.1s)
Fitting full model...
  -logL = 437.5522662870832  (10.7s)
┌ Info: LRT
│   LR2 = 51.95901913816124
│   pv2 = 5.667114682162393e-13
│   LR3 = 83.40909520287346
└   pv3 = 7.725829266604427e-19
Computing standard errors (FD Hessian)...
  (0.3 s)
cor(obs, pop_pred) = 0.8149974181480817;  cor(obs, ind_pred) = 0.9710149571062566
Done in 42.8 s.
[stderr]
real	1m7.106s
user	1m2.870s
sys	0m1.040s

bash

cat /app/output/model_summary.json

output

{
    "bic": 915.4519335095205,
    "logLik": -437.5522662870832,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -26.823471248604665,
            "df": 150,
            "std_error": 0.22063567912814386,
            "estimate": -5.918214795510131
        },
        {
            "term": "lCl.Wt",
            "t_value": 7.601516840189567,
            "df": 150,
            "std_error": 0.08051312414505597,
            "estimate": 0.6120218690449162
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -0.2936233941578891,
            "df": 150,
            "std_error": 0.15618441873650046,
            "estimate": -0.04585939914398827
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -6.986080831839407,
            "df": 150,
            "std_error": 0.068040108413713,
            "estimate": -0.47533369718531554
        },
        {
            "term": "lV.Wt",
            "t_value": 13.113176671497403,
            "df": 150,
            "std_error": 0.040688125211454186,
            "estimate": 0.5335505743298063
        }
    ],
    "aic": 891.1045325741665,
    "n_subjects": 59,
    "n_obs": 155,
    "random_effects_sd": {
        "lCl": 0.22024786800226548,
        "lV": 0.17207044662243948,
        "Residual": 2.7292162017471306
    }
}

Now the standard errors are reasonable. The parameter estimates match expected values: - lCl intercept ≈ -5.92, SE = 0.22, t = -27 - lCl.Wt ≈ 0.61, SE = 0.08, t = 7.6 (strong positive effect of weight on clearance) - lCl.ApgarInd>= 5 ≈ -0.046, SE = 0.16, t = -0.29 (weak effect of Apgar) - lV intercept ≈ -0.48, SE = 0.068, t = -7.0 - lV.Wt ≈ 0.53, SE = 0.04, t = 13.1 (strong positive effect of weight on volume) All positive SEs, t-values reasonable. Let me also check the plots exist and verify everything is good. The full analysis runs in ~1min which is well within a reasonable timeout. Let me check plots.

bash

ls -la /app/output/; echo "---"; head -3 /app/output/*.csv

output

total 583
drwxrws--- 2 h2tagent h2tagent   4096 May 31 10:51 .
drwxrws--- 3 h2tagent h2tagent   4096 May 31 10:50 ..
-rw-r--r-- 1 h2tagent h2tagent    336 May 31 10:51 lrt_chain.csv
-rw-r--r-- 1 h2tagent h2tagent   1369 May 31 10:51 model_summary.json
-rw-r--r-- 1 h2tagent h2tagent   7779 May 31 10:51 obs_vs_pred.csv
-rw-r--r-- 1 h2tagent h2tagent   2522 May 31 10:51 per_subject_params.csv
-rw-r--r-- 1 h2tagent h2tagent 159650 May 31 10:51 plot_conc_profile.png
-rw-r--r-- 1 h2tagent h2tagent  51256 May 31 10:51 plot_covariate_effect.png
-rw-r--r-- 1 h2tagent h2tagent  86380 May 31 10:51 plot_obs_vs_pred.png
-rw-r--r-- 1 h2tagent h2tagent 200127 May 31 10:51 plot_per_subject_fit.png
-rw-r--r-- 1 h2tagent h2tagent  66875 May 31 10:51 plot_residuals.png
-rw-r--r-- 1 h2tagent h2tagent  10189 May 31 10:51 residual_diagnostics.csv
---
==> /app/output/lrt_chain.csv <==
step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.2363234576006,1020.4726469152012,1035.6897724997973,,
2,cl_wt,6,-479.25681388851996,970.5136277770399,988.7741784785554,51.95901913816124,5.667114682162393e-13

==> /app/output/obs_vs_pred.csv <==
Subject,time,conc_obs,pred_pop,pred_ind
1,2.0,17.3,18.878293182228155,18.425115807062138
1,112.5,31.0,30.428298442362706,30.31508120510635

==> /app/output/per_subject_params.csv <==
Subject,Cl,V
1,0.005809672693432002,1.345173901932019
2,0.00552620430644722,1.2204301274435414

==> /app/output/residual_diagnostics.csv <==
Subject,time,fitted_ind,resid,std_resid
1,2.0,18.425115807062138,-1.1251158070621372,-0.4122486911597128
1,112.5,30.31508120510635,0.684918794893651,0.25095805691582607

Let me verify the plots visually:

str_replace_based_edit_tool

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

output

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…[truncated]

str_replace_based_edit_tool

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

output

<output_image>
…[truncated]

str_replace_based_edit_tool

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

output

<output_image>
…[truncated]

str_replace_based_edit_tool

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

output

<output_image>
…[truncated]

The concentration profile plot has repeated legend entries (all subjects are added to the legend even though I pass "" as label). But I passed `lab = drew[key] ? "" : ...`. Let me check , looks like passing `""` to `label` still creates a legend entry. Let me use `nothing` or a different approach. Also, the covariate effect plot may be fine but I should check. Let me see.

str_replace_based_edit_tool

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

output

<output_image>
…[truncated]

Let me fix the concentration profile plot legend to avoid duplicates:

str_replace_based_edit_tool

command: str_replace
path: /app/analysis.jl
old_str:     # 1. Concentration profile ------------------------------------------------
    fig1 = Figure(size = (1000, 620))
    ax = Axis(fig1[1,1], xlabel="Time (hours)", ylabel="Concentration (mg/L)",
              title="Phenobarbital serum concentration profiles by Apgar category")
    palette = Dict(">= 5" => :steelblue, "< 5" => :tomato)
    drew = Dict(">= 5" => false, "< 5" => false)
    for s in subs
        isempty(s.samp_times) && continue
        key = s.apgar_high == 1.0 ? ">= 5" : "< 5"
        lab = drew[key] ? "" : "ApgarInd $key"
        scatterlines!(ax, s.samp_times, s.samp_conc;
                      color=palette[key], markersize=6, label=lab)
        drew[key] = true
    end
    axislegend(ax, position=:rt)
    save(joinpath(out_dir, "plot_conc_profile.png"), fig1, px_per_unit=1)
new_str:     # 1. Concentration profile ------------------------------------------------
    fig1 = Figure(size = (1000, 620))
    ax = Axis(fig1[1,1], xlabel="Time (hours)", ylabel="Concentration (mg/L)",
              title="Phenobarbital serum concentration profiles by Apgar category")
    palette = Dict(">= 5" => :steelblue, "< 5" => :tomato)
    for s in subs
        isempty(s.samp_times) && continue
        key = s.apgar_high == 1.0 ? ">= 5" : "< 5"
        scatterlines!(ax, s.samp_times, s.samp_conc;
                      color=palette[key], markersize=6)
    end
    # Manual legend entries (one per category)
    leg_elements = [LineElement(color=palette[">= 5"]),
                    LineElement(color=palette["< 5"])]
    Legend(fig1[1,2], leg_elements, ["ApgarInd >= 5", "ApgarInd < 5"];
           tellwidth=true)
    save(joinpath(out_dir, "plot_conc_profile.png"), fig1, px_per_unit=1)

output

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

Now let me also double-check the random-effects variances don't hit pathological lower bounds. Let me re-run to verify the fix:

bash

cd /app && time julia --startup-file=no analysis.jl 2>&1 | tail -15 &
BGPID=$!
for i in $(seq 1 25); do sleep 10; if ! kill -0 $BGPID 2>/dev/null; then break; fi; done
if kill -0 $BGPID 2>/dev/null; then kill $BGPID 2>/dev/null; echo "KILLED"; fi
wait 2>/dev/null

output

Fitting base model...
  -logL = 505.2363234576006  (7.7s)
Fitting cl_wt model...
  -logL = 479.25681388851996  (8.0s)
Fitting full model...
  -logL = 437.5522662870832  (10.9s)
┌ Info: LRT
│   LR2 = 51.95901913816124
│   pv2 = 5.667114682162393e-13
│   LR3 = 83.40909520287346
└   pv3 = 7.725829266604427e-19
Computing standard errors (FD Hessian)...
  (0.3 s)
cor(obs, pop_pred) = 0.8149974181480817;  cor(obs, ind_pred) = 0.9710149571062566
Done in 41.9 s.
[stderr]
real	1m6.363s
user	1m1.920s
sys	0m1.270s

str_replace_based_edit_tool

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

output

<output_image>
…[truncated]

Now let me make sure all values are robust. Let me also run a quick sanity check on the outputs:

bash

cat /app/output/model_summary.json

output

{
    "bic": 915.4519335095205,
    "logLik": -437.5522662870832,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -26.823471248604665,
            "df": 150,
            "std_error": 0.22063567912814386,
            "estimate": -5.918214795510131
        },
        {
            "term": "lCl.Wt",
            "t_value": 7.601516840189567,
            "df": 150,
            "std_error": 0.08051312414505597,
            "estimate": 0.6120218690449162
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -0.2936233941578891,
            "df": 150,
            "std_error": 0.15618441873650046,
            "estimate": -0.04585939914398827
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -6.986080831839407,
            "df": 150,
            "std_error": 0.068040108413713,
            "estimate": -0.47533369718531554
        },
        {
            "term": "lV.Wt",
            "t_value": 13.113176671497403,
            "df": 150,
            "std_error": 0.040688125211454186,
            "estimate": 0.5335505743298063
        }
    ],
    "aic": 891.1045325741665,
    "n_subjects": 59,
    "n_obs": 155,
    "random_effects_sd": {
        "lCl": 0.22024786800226548,
        "lV": 0.17207044662243948,
        "Residual": 2.7292162017471306
    }
}

The results look great. But I'm a bit concerned that `lCl.ApgarInd>= 5` has a really small t-value (-0.29) while the LRT says the full model is strongly significant. The full model adds TWO params (Apgar on Cl, Wt on V), so the LR is for both jointly. Let me also verify the per-subject CSV has positive Cl and V values:

bash

cd /app && julia --startup-file=no -e '
using CSV, DataFrames
ps = CSV.read("/app/output/per_subject_params.csv", DataFrame)
op = CSV.read("/app/output/obs_vs_pred.csv", DataFrame)
rd = CSV.read("/app/output/residual_diagnostics.csv", DataFrame)
lrt = CSV.read("/app/output/lrt_chain.csv", DataFrame)
println("per_subject all positive: ", all(ps.Cl .> 0) && all(ps.V .> 0))
println("per_subject rows: ", nrow(ps), " subjects: ", length(unique(ps.Subject)))
println("obs_vs_pred rows: ", nrow(op))
println("residual_diagnostics rows: ", nrow(rd))
using Statistics
println("cor(obs, pop): ", cor(op.conc_obs, op.pred_pop))
println("cor(obs, ind): ", cor(op.conc_obs, op.pred_ind))
println("AIC descending: ", issorted(-lrt.AIC))
println(lrt)
' 2>&1 | tail -30

output

per_subject all positive: true
per_subject rows: 59 subjects: 59
obs_vs_pred rows: 155
residual_diagnostics rows: 155
cor(obs, pop): 0.8149974181480817
cor(obs, ind): 0.9710149571062566
AIC descending: true
3×8 DataFrame
 Row │ step   model_name  n_params  logLik    AIC       BIC       LR_stat       LR_pvalue
     │ Int64  String7     Int64     Float64   Float64   Float64   Float64?      Float64?
─────┼────────────────────────────────────────────────────────────────────────────────────────────
   1 │     1  base               5  -505.236  1020.47   1035.69   missing       missing
   2 │     2  cl_wt              6  -479.257   970.514   988.774       51.959         5.66711e-13
   3 │     3  full               8  -437.552   891.105   915.452       83.4091        7.72583e-19

All looks good. Let me also verify the plot sizes meet the 900x550 minimum:

bash

cd /app && for f in /app/output/*.png; do
  python3 -c "from PIL import Image; img=Image.open('$f'); print('$f', img.size)"
done 2>/dev/null || {
  # fallback with ImageMagick
  for f in /app/output/*.png; do identify "$f" | awk '{print $1, $3}'; done
}

output

/app/output/plot_conc_profile.png (1000, 620)
/app/output/plot_covariate_effect.png (1000, 620)
/app/output/plot_obs_vs_pred.png (1200, 620)
/app/output/plot_per_subject_fit.png (1200, 900)
/app/output/plot_residuals.png (1200, 620)

All plots meet the 900×550 minimum. Let me also check the final script for the sometimes-edge-case concerns mentioned in the task: 1. The held-out CSV might have different Apgar categories. Let me make sure I handle that:

bash

grep -n "ApgarInd\|apgar_high" /app/analysis.jl | head -20

output

19:    apgar_high::Float64
31:        apg = String(strip(String(first(rows.ApgarInd))))
32:        apgar_high = (apg == ">= 5") ? 1.0 : 0.0
45:        push!(subs, SubjData(Int(sid), wt, apgar_high, dts, damts, sts, scs))
92:    spec.clapgar && push!(names, "lCl.ApgarInd>= 5")
120:    lCl = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high + η[1]
277:        key = s.apgar_high == 1.0 ? ">= 5" : "< 5"
284:    Legend(fig1[1,2], leg_elements, ["ApgarInd >= 5", "ApgarInd < 5"];
302:        lCl_pop = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high
328:        if s.apgar_high == 1.0
335:        color=:steelblue, markersize=10, label="ApgarInd >= 5")
337:        color=:tomato, markersize=10, label="ApgarInd < 5")
495:        lCl_ind = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high + η[1]
497:        lCl_pop = p.lCl0 + p.lCl_wt*s.wt + p.lCl_apg*s.apgar_high

The parsing is robust , it checks for `">= 5"` after stripping whitespace. But I should handle if the comparison produces NaN or weird patterns. Also, the per-subject plot might have fewer than 9 subjects. Let me double-check my per-subject plot handles subject counts smaller than 9. Also what if a subject has no samples? Actually my code: ```julia ids_all = sort(unique(rows_op.Subject)) n_panels = min(9, length(ids_all)) ``` `rows_op` only has rows for non-missing conc, so subjects with no samples are excluded. Good. But the test says "at least 6 panels". If there are fewer than 6 subjects in the new data, my plot has fewer panels. Let me increase it to at least 9 by taking up to 9 subjects, but what if there are only 5? I need to guarantee at least 6 panels to meet requirement, but if the data has <6 subjects, I can't. Since Phenobarbital data has 59 subjects typically and perturbations won't drop below 6 likely, this should be fine. Let me also add a safety check for cases where p.ωCl could become very small, which would make inverse variance huge. Also I should make sure my predictions work correctly for subjects with no dose rows (edge case). The original spec doesn't preclude this but let me check. Let me also improve robustness of: - The FD Hessian should use a safer step size. - The inner optimization should handle pathological cases gracefully. Let me also review my Laplace's log|H| calculation , I should probably use slogdet to avoid under/overflow for small H. Actually, since H is 2×2, det is straightforward. I think the code is reasonably robust. Let me try it with a quick perturbation test , add some noise to the data and see if it still works.

bash

cd /app && julia --startup-file=no -e '
using CSV, DataFrames, Random
Random.seed!(42)
df = CSV.read("/app/Phenobarb.csv", DataFrame)
# Perturb: drop some subjects, add noise to conc
n_drop = 15
ids = unique(df.Subject)
keep = sort(sample_ids = setdiff(ids, rand(ids, n_drop)))
df2 = filter(r -> r.Subject in keep, df)
# perturb concentrations slightly
for i in 1:nrow(df2)
    if !ismissing(df2.conc[i])
        df2.conc[i] *= (1.0 + 0.1*randn())
    end
end
CSV.write("/tmp/Pheno_perturbed.csv", df2)
println("Perturbed saved: subjects=$(length(keep)) rows=$(nrow(df2))")
' 2>&1 | tail -5

# Now run analysis with perturbed data
ENV_SETUP="PHENOBARB_DATA_PATH=/tmp/Pheno_perturbed.csv PHENOBARB_OUTPUT_DIR=/tmp/out_test"
mkdir -p /tmp/out_test
cd /app && eval "env $ENV_SETUP time julia --startup-file=no analysis.jl 2>&1 | tail -15" &
BGPID=$!
for i in $(seq 1 25); do sleep 10; if ! kill -0 $BGPID 2>/dev/null; then break; fi; done
if kill -0 $BGPID 2>/dev/null; then kill $BGPID 2>/dev/null; echo "KILLED"; fi
wait 2>/dev/null

output

...

Stacktrace:
 [1] top-level scope
   @ none:8
env: ‘time’: No such file or directory

bash

cd /app && julia --startup-file=no -e '
using CSV, DataFrames, Random
Random.seed!(42)
df = CSV.read("/app/Phenobarb.csv", DataFrame)
ids = unique(df.Subject)
n_drop = 15
drop = rand(ids, n_drop)
keep = setdiff(ids, drop)
df2 = filter(r -> r.Subject in keep, df)
for i in 1:nrow(df2)
    if !ismissing(df2.conc[i])
        df2.conc[i] *= (1.0 + 0.1*randn())
    end
end
CSV.write("/tmp/Pheno_perturbed.csv", df2)
println("Perturbed saved: subjects=$(length(keep)) rows=$(nrow(df2))")
' 2>&1 | tail -3

mkdir -p /tmp/out_test
cd /app && PHENOBARB_DATA_PATH=/tmp/Pheno_perturbed.csv PHENOBARB_OUTPUT_DIR=/tmp/out_test time julia --startup-file=no analysis.jl 2>&1 | tail -15 &
BGPID=$!
for i in $(seq 1 25); do sleep 10; if ! kill -0 $BGPID 2>/dev/null; then break; fi; done
if kill -0 $BGPID 2>/dev/null; then kill $BGPID 2>/dev/null; echo "KILLED"; fi
wait 2>/dev/null

output

Perturbed saved: subjects=48 rows=612
bash: line 984: time: command not found

bash

cd /app && PHENOBARB_DATA_PATH=/tmp/Pheno_perturbed.csv PHENOBARB_OUTPUT_DIR=/tmp/out_test julia --startup-file=no analysis.jl 2>&1 | tail -15 &
BGPID=$!
for i in $(seq 1 25); do sleep 10; if ! kill -0 $BGPID 2>/dev/null; then break; fi; done
if kill -0 $BGPID 2>/dev/null; then kill $BGPID 2>/dev/null; echo "KILLED"; fi
wait 2>/dev/null

output

Fitting base model...
  -logL = 430.38657404403307  (6.4s)
Fitting cl_wt model...
  -logL = 408.17606687717796  (7.0s)
Fitting full model...
  -logL = 372.93900200844683  (9.2s)
┌ Info: LRT
│   LR2 = 44.42101433371022
│   pv2 = 2.6482907664916104e-11
│   LR3 = 70.47412973746225
└   pv3 = 4.974359502834519e-16
Computing standard errors (FD Hessian)...
  (0.3 s)
cor(obs, pop_pred) = 0.8065946475771608;  cor(obs, ind_pred) = 0.9584748183559252
Done in 37.2 s.

bash

cat /tmp/out_test/model_summary.json | head -30; echo ---; cat /tmp/out_test/lrt_chain.csv

output

{
    "bic": 784.6942461282506,
    "logLik": -372.93900200844683,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -21.538716718616254,
            "df": 123,
            "std_error": 0.2767562926472831,
            "estimate": -5.960975387424289
        },
        {
            "term": "lCl.Wt",
            "t_value": 6.681906213742532,
            "df": 123,
            "std_error": 0.09756647411869072,
            "estimate": 0.6519300296666295
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -0.264579272966913,
            "df": 123,
            "std_error": 0.1908539733100203,
            "estimate": -0.05049600550121179
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -6.431467192484635,
            "df": 123,
            "std_error": 0.07552887935645151,
---
step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-430.38657404403307,870.7731480880661,885.0332994076642,,
2,cl_wt,6,-408.17606687717796,828.3521337543559,845.4643153378736,44.42101433371022,2.6482907664916104e-11
3,full,8,-372.93900200844683,761.8780040168937,784.6942461282506,70.47412973746225,4.974359502834519e-16

The analysis robustly handles perturbed data too. All criteria met: - AIC strictly decreasing: 870.8 → 828.4 → 761.9 - LRT p-values well below 1e-6 - Correlation thresholds satisfied

bash

rm -rf /tmp/out_test /tmp/Pheno_perturbed.csv
ls /app/output/

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

All 10 required output files are present. Let me also do a final review of the analysis script to make sure it's clean:

bash

wc -l /app/analysis.jl; grep -n "^function\|^# ---" /app/analysis.jl

output

558 /app/analysis.jl
15:# --- subject data container ---------------------------------------------------
26:function load_subjects(df::DataFrame)
50:# --- predictions and analytic derivatives -------------------------------------
58:function pred_and_jac(stimes::Vector{Float64},
81:# --- model spec ---------------------------------------------------------------
89:function param_layout(spec::ModelSpec)
98:function unpack(θ::AbstractVector, spec::ModelSpec)
119:function inner_all(η::Vector{Float64}, s::SubjData, p)
141:function optimise_eta(s::SubjData, p; η0 = zeros(2), maxit = 40, tol = 1e-8)
173:# --- marginal -log likelihood via Laplace -------------------------------------
174:function laplace_nll(θ::AbstractVector, subs::Vector{SubjData}, spec::ModelSpec;
201:# --- Nelder-Mead wrapper that is simple and fast ------------------------------
202:function fit_model(subs::Vector{SubjData}, spec::ModelSpec;
245:# --- FD Hessian of marginal -logL --------------------------------------------
246:function fd_hessian(f, θ::Vector{Float64}; h::Float64 = 5e-3)
266:# --- plots --------------------------------------------------------------------
267:function make_plots(df::DataFrame, subs::Vector{SubjData}, per_subj::DataFrame,
396:# --- main ---------------------------------------------------------------------
397:function main()

The analysis is complete. Summary of what it does: 1. **Loads** the per-subject PK data from CSV with dose events and sample events. 2. **Models** each subject with a 1-compartment IV bolus superposition formula. 3. **Fits** three nested PK mixed models using Laplace-approximation marginal likelihood: - `base`: `lCl ~ 1`, `lV ~ 1` with random intercepts - `cl_wt`: adds `Wt` on `lCl` - `full`: adds `ApgarInd` on `lCl` and `Wt` on `lV` 4. **Optimization** uses Nelder-Mead → BFGS → Nelder-Mead refinement; inner random-effect optima solved by a 2-D Newton-Raphson with Gauss-Newton Hessian and Armijo-style step halving. 5. **Standard errors** computed from a finite-difference Hessian of the marginal likelihood at the final estimate. 6. **Outputs**: - `model_summary.json` with fixed effects (estimate/SE/t/df), RE SDs, logLik/AIC/BIC - `lrt_chain.csv` with step-wise LRT statistics and p-values - `per_subject_params.csv` with empirical-Bayes Cl and V per subject (positive) - `obs_vs_pred.csv` and `residual_diagnostics.csv` - 5 PNG diagnostic plots All quality thresholds are met: - AIC strictly decreases each step (1020 → 971 → 891) - LRT p-values ≪ 1e-6 for both steps (5.67e-13 and 7.73e-19) - `cor(obs, pred_pop)` = 0.815 > 0.55 - `cor(obs, pred_ind)` = 0.971 > 0.75 - All plots ≥ 900×550 px

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: 5  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).
----------------------------------------------------------------------
558 /app/analysis.jl
15:# --- subject data container ---------------------------------------------------
26:function load_subjects(df::DataFrame)
50:# --- predictions and analytic derivatives -------------------------------------
58:function pred_and_jac(stimes::Vector{Float64},
81:# --- model spec ---------------------------------------------------------------
89:function param_layout(spec::ModelSpec)
98:function unpack(θ::AbstractVector, spec::ModelSpec)
119:function inner_all(η::Vector{Float64}, s::SubjData, p)
141:function optimise_eta(s::SubjData, p; η0 = zeros(2), maxit = 40, tol = 1e-8)
173:# --- marginal -log likelihood via Laplace -------------------------------------
174:function laplace_nll(θ::AbstractVector, subs::Vector{SubjData}, spec::ModelSpec;
201:# --- Nelder-Mead wrapper that is simple and fast ------------------------------
202:function fit_model(subs::Vector{SubjData}, spec::ModelSpec;
245:# --- FD Hessian of marginal -logL --------------------------------------------
246:function fd_hessian(f, θ::Vector{Float64}; h::Float64 = 5e-3)
266:# --- plots --------------------------------------------------------------------
267:function make_plots(df::DataFrame, subs::Vector{SubjData}, per_subj::DataFrame,
396:# --- main ---------------------------------------------------------------------
397:function main()

Reproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_c24266ee3cdc4006. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_c24266ee3cdc4006 · verifier authoritative; classifier explanatory.