SyncValsverifier → artifact → classifier → verdict
SyncVals · Trajectory

neonatal-drug-exposure-nlme

claude-code claude-opus-4-8 ✓ resolved GOOD_SUCCESS ↑ 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
GOOD_SUCCESSLegitimate solve, implements the asked-for behavior; tests verify real functionality.
SubtypeLegitimate Solution - Hard Task Executed Well
EvidenceTest output shows 'pass' with reward=1.0. All 10 required outputs created successfully with correct structure. Model quality metrics achieved: cor(conc_obs, pred_ind)=0.971 > 0.75, cor(conc_obs, pred_pop)=0.815 > 0.55. LRT p-values both < 1e-6 (5.67e-13 and 7.73e-19). AIC strictly decreasing (1020.47 > 970.514 > 891.105). All pytest schema and invariant tests passed. LLM judge passed plot rubric (per rubric.json criteria: time axes in hours, concentration in mg/L, visible legends, 6+ facet panels, correlation lines, residual plots with reference lines). Agent trajectory shows exploratory data analysis (59 subjects, 155 obs identified), mathematical model design (one-compartment PK with superposition), and implementation of Laplace-approximated NLME with numerical optimization. No forbidden access patterns (test/solution references) detected in script scan. Solution works on both public and hidden data variants.
Root causeThe agent successfully implemented a sophisticated pharmacokinetic NLME model from scratch using Laplace approximation for mixed-effects estimation. The solution demonstrates deep mathematical understanding of population PK models, proper implementation of numerical optimization, and rigorous adherence to the exact output specification. All tests pass including both stringent pytest invariant checks and LLM-based plot quality evaluation.
RecommendationN/A - task is fine. This is a well-specified, hard task that the agent solved legitimately and thoroughly.
Trajectory
Tool-by-tool agent trajectory
127 tool calls · 3 tool types · 127 steps
Work only in `/app/analysis.jl`. The bundled inputs are: - `/app/Phenobarb.csv` - `/app/dataset_manifest.json` Do not read from `/tests` or `/solution`. ## Background `Phenobarb.csv` is a real neonatal pharmacokinetics study of preterm infants given intravenous phenobarbital. Each baby contributes a small number of serum concentration measurements interleaved with dose events. A neonatology analytics team wants a population PK fit that estimates clearance and volume of distribution at the population level and per subject, tests whether birth weight and Apgar category shift those parameters, and produces diagnostic plots for the clinical report. Your `analysis.jl` will be executed on a held-out perturbation of `Phenobarb.csv` with a different number of subjects and rows. Derive all counts from the CSV at runtime , do not hardcode subject or row counts. ## Input semantics `Phenobarb.csv` has exactly these columns: - `Subject` , integer subject identifier - `Wt` , birth weight in kg - `Apgar` , Apgar score at 5 minutes, integer 1 through 10 - `ApgarInd` , two-level factor, either `< 5` (asphyxiated) or `>= 5` (normal) - `time` , time in hours since first event for that subject - `dose` , dose in mg at this event row, missing for sample rows - `conc` , serum concentration in mg/L at this event row, missing for dose rows A row is a dose event when `dose` is non-missing; a sample event when `conc` is non-missing. Do not drop dose rows. Use `dataset_manifest.json` as the contract source for required output filenames and exact column order for every output CSV. ## Required modelling Fit a one-compartment open PK model with first-order elimination at the population level. Model clearance and volume on the log scale (`lCl`, `lV`). Each subject has random intercepts on `lCl` and `lV` with a diagonal (no correlation) random-effect covariance structure. Do the covariate build-up in this exact sequence: 1. **Base model** (`base`): `lCl ~ 1`, `lV ~ 1` 2. **cl_wt model** (`cl_wt`): add birth weight as fixed effect on `lCl` 3. **Full model** (`full`): keep weight on `lCl`, add `ApgarInd` on `lCl`, add weight on `lV` Each step must yield a strictly lower AIC than the step before it. The likelihood-ratio p-value for both step 1→2 and step 2→3 must be below 1e-6. ## Required output files All files go into `/app/output/`. Use exact filenames from `dataset_manifest.json`. ### Tables 1. **`model_summary.json`** , JSON for the final (full) model with exactly: - `n_obs` , integer, count of non-missing `conc` rows - `n_subjects` , integer, count of distinct Subject values - `fixed_effects` , array of objects with fields `term`, `estimate`, `std_error`, `t_value`, `df`. Terms in this exact order: `lCl.(Intercept)`, `lCl.Wt`, `lCl.ApgarInd>= 5`, `lV.(Intercept)`, `lV.Wt` - `random_effects_sd` , object with positive numeric fields `lCl`, `lV`, `Residual` - `logLik`, `aic`, `bic` , numeric scalars for the final model 2. **`lrt_chain.csv`** , columns (in order): `step, model_name, n_params, logLik, AIC, BIC, LR_stat, LR_pvalue` - `step`: 1, 2, 3; `model_name`: `base`, `cl_wt`, `full` - `LR_stat` and `LR_pvalue` are empty/missing for step 1 3. **`per_subject_params.csv`** , columns: `Subject, Cl, V` - Empirical-Bayes estimates in native units (not log scale), all positive - Sorted by integer `Subject` ascending 4. **`obs_vs_pred.csv`** , columns: `Subject, time, conc_obs, pred_pop, pred_ind` - One row per non-missing concentration observation - `pred_pop`: population prediction (zero random effects) - `pred_ind`: individual prediction (subject empirical-Bayes estimates) - `cor(conc_obs, pred_ind)` must exceed 0.75; `cor(conc_obs, pred_pop)` must exceed 0.55 - Sorted by Subject then time 5. **`residual_diagnostics.csv`** , columns: `Subject, time, fitted_ind, resid, std_resid` - `resid = conc_obs - fitted_ind` - `std_resid = resid / σ` where `σ` is the estimated residual SD …[truncated]
Let me start by exploring the task and understanding what's needed.
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 -30 /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
---
745 /app/Phenobarb.csv
bash
julia --version; julia -e 'using Pkg; Pkg.status()' 2>&1 | head -40
output
julia version 1.10.4
Status `/usr/local/share/julia/environments/v1.10/Project.toml`
  [336ed68f] CSV v0.10.16
  [13f3f980] CairoMakie v0.15.10
  [a93c6f00] DataFrames v1.8.2
  [31c24e10] Distributions v0.25.125
  [0f8b85d8] JSON3 v1.14.3
  [429524aa] Optim v2.1.0
  [2913bbd2] StatsBase v0.34.11
  [10745b16] Statistics v1.10.0
Now I understand the setup. Let me design the approach: 1. **Data model**: One-compartment PK with first-order elimination, superposition of doses. - For each subject i, Cl_i = exp(β_lCl^T x_i + b_lCl_i), V_i = exp(β_lV^T x_i + b_lV_i) - Concentration at time t: C(t) = Σ_doses (dose/V) * exp(-Cl/V * (t - t_dose)) - Random effects b ~ N(0, diag(σ_lCl², σ_lV²)) - Residual: conc_obs = C(t) + ε, ε ~ N(0, σ²) 2. **Fitting**: Use Laplace approximation for mixed-effects NLME: - For each subject, find mode of b|data and use Laplace approximation - Maximize over fixed effects + variance components Let me write this carefully. Given the complexity, I'll implement a Laplace-approximated NLME fit. Actually, thinking about this more carefully , Laplace for a 2D random-effects per subject is tractable. Let me code it step by step. For each subject i with vector of observations y_i and fixed effect predictors X_i (same across time for each subject): - η_Cl_i = X_Cl_i * β_Cl + b_lCl_i - η_V_i = X_V_i * β_V + b_lV_i - Cl_i = exp(η_Cl_i), V_i = exp(η_V_i) - f_ij(b_i) = Σ over doses k with t_dose_k ≤ t_ij: (dose_k / V_i) * exp(-(Cl_i/V_i) * (t_ij - t_dose_k)) - Conditional likelihood: -0.5 * Σ (y_ij - f_ij(b_i))² / σ² - 0.5 * nobs_i * log(2πσ²) - Random effect prior: -0.5 * b_i' * Σ^{-1} * b_i - 0.5 * log((2π)² * |Σ|) Marginal likelihood via Laplace: - For each subject, minimize negative joint log density (NLL + prior) over b_i to get b_i^* - Laplace: marginal ≈ joint at mode * (2π)^(d/2) / sqrt(|H|) where H is Hessian of negative log joint So per-subject marginal log-likelihood = -NLL(b_i^*, θ) - 0.5 * b_i^{*T} Σ^{-1} b_i^* - 0.5 * log|Σ| - 0.5 * log|H| + d/2 * log(1) (since (2π)^{d/2} from Laplace cancels with (2π)^{d/2} normalizing constant of Σ) Wait, let me redo. The integrand is: p(y_i | b_i, θ) * p(b_i | θ) where p(b_i | θ) = N(0, Σ) = (2π)^(-d/2) |Σ|^(-1/2) exp(-0.5 b_i' Σ^{-1} b_i) Let g(b) = -log[p(y|b) p(b)] = NLL_lik + 0.5 b' Σ^{-1} b + 0.5 log|Σ| + d/2 log(2π) + 0.5 * nobs * log(2π σ²) + 0.5 * Σ (y-f)²/σ² Actually let me use simpler forms. Let - ℓ(b) = log p(y|b,θ) + log p(b|θ) Laplace: log marginal ≈ ℓ(b*) + d/2 * log(2π) - 0.5 * log det(-∇² ℓ(b*)) where -∇²ℓ(b*) = H is the Hessian of -ℓ. OK let's code this. Implementation plan: 1. Load CSV 2. For each subject, get (times, doses at each dose row, concentrations at sample rows) 3. Define function that computes per-subject marginal loglik via Laplace 4. Sum across subjects for total marginal loglik 5. Optimize over θ = (β_Cl, β_V, log(σ_lCl), log(σ_lV), log(σ)) 6. Fit 3 nested models 7. Compute outputs Let me also compute the EBE (empirical Bayes estimates) at the final model , these are just the b* for each subject at the MLE of θ. Standard errors: Use Hessian at MLE , we only need SEs for fixed effects. t_value = estimate / se. df = n_obs - n_params (approximate). Let me write this now. For predictions: - pred_pop: set b = 0, compute C(t) - pred_ind: use b*_i, compute C(t) For residuals: resid = conc_obs - pred_ind; std_resid = resid / σ_res. Let me code carefully, making sure I handle the ApgarInd binary covariate correctly (`>= 5` coded as 0 or 1). Let me use R convention: levels sorted, first level is reference. `< 5` < `>= 5` alphabetically (well, "<" is 60 and ">" is 62, so `< 5` comes first), so `< 5` is reference, `>= 5` is the indicator. Actually, the fixed_effects specification has "lCl.ApgarInd>= 5" , so that indicates `>= 5` is the non-reference level (indicator). Good. Let me put it all together. I'll start writing the script.
bash
awk -F, 'NR>1 {print $1}' /app/Phenobarb.csv | sort -u | wc -l
output
59
bash
awk -F, 'NR>1 && $7!="" {n++} END{print n}' /app/Phenobarb.csv
output
155
59 subjects, 155 non-missing conc observations. Good. Let me write a Julia script using NLME via Laplace approximation.
str_replace_based_edit_tool
command: create
path: /app/analysis.jl
file_text: #!/usr/bin/env julia
# One-compartment population PK fit for Phenobarb (Laplace-approx NLME).
# Writes all outputs into /app/output/.

using CSV, DataFrames, Statistics, LinearAlgebra, JSON3, Distributions, Optim
using CairoMakie

# -------------------- Load data --------------------
const CSV_PATH = "/app/Phenobarb.csv"
const OUT_DIR  = "/app/output"
isdir(OUT_DIR) || mkpath(OUT_DIR)

df_all = CSV.read(CSV_PATH, DataFrame)

# Normalise columns / types
df_all.Subject = Int.(df_all.Subject)
df_all.Wt      = Float64.(df_all.Wt)
sort!(df_all, [:Subject, :time])

subjects = sort(unique(df_all.Subject))
n_subjects = length(subjects)
n_obs = count(!ismissing, df_all.conc)

# Build per-subject arrays
struct SubjData
    id::Int
    wt::Float64
    apgar5::Int   # 1 if ApgarInd == ">= 5"
    dose_times::Vector{Float64}
    dose_amts::Vector{Float64}
    obs_times::Vector{Float64}
    obs_conc::Vector{Float64}
end

subj_data = SubjData[]
for s in subjects
    rows = df_all[df_all.Subject .== s, :]
    wt   = rows.Wt[1]
    ap5  = rows.ApgarInd[1] == ">= 5" ? 1 : 0
    dose_rows = .!ismissing.(rows.dose)
    obs_rows  = .!ismissing.(rows.conc)
    dt = Float64.(rows.time[dose_rows])
    da = Float64.(rows.dose[dose_rows])
    ot = Float64.(rows.time[obs_rows])
    oc = Float64.(rows.conc[obs_rows])
    push!(subj_data, SubjData(s, wt, ap5, dt, da, ot, oc))
end

# -------------------- PK prediction --------------------
# One-compartment, IV bolus, superposition:
#   C(t) = sum_{k: t_k <= t} (dose_k / V) * exp(-(Cl/V) * (t - t_k))
@inline function conc_at(t::Float64, Cl::Float64, V::Float64,
                         dtimes::Vector{Float64}, damts::Vector{Float64})
    k = Cl / V
    s = 0.0
    @inbounds for i in eachindex(dtimes)
        tk = dtimes[i]
        if tk <= t
            s += (damts[i] / V) * exp(-k * (t - tk))
        end
    end
    return s
end

predict_subject(Cl, V, sd::SubjData) =
    [conc_at(t, Cl, V, sd.dose_times, sd.dose_amts) for t in sd.obs_times]

# -------------------- Model design --------------------
# X_Cl and X_V design row per subject (same across time).
# Three specs:
#   :base   X_Cl = [1],         X_V = [1]
#   :cl_wt  X_Cl = [1, Wt],     X_V = [1]
#   :full   X_Cl = [1, Wt, ap5], X_V = [1, Wt]
function design(sd::SubjData, spec::Symbol)
    if spec == :base
        return [1.0], [1.0]
    elseif spec == :cl_wt
        return [1.0, sd.wt], [1.0]
    elseif spec == :full
        return [1.0, sd.wt, Float64(sd.apgar5)], [1.0, sd.wt]
    end
end

nfix(spec::Symbol) =
    spec == :base ? (1, 1) : spec == :cl_wt ? (2, 1) : (3, 2)

# parameter packing: θ = [β_Cl; β_V; log σ_lCl; log σ_lV; log σ_res]
function unpack(θ, spec)
    pCl, pV = nfix(spec)
    βCl = θ[1:pCl]
    βV  = θ[pCl+1:pCl+pV]
    lsCl = θ[pCl+pV+1]
    lsV  = θ[pCl+pV+2]
    lsR  = θ[pCl+pV+3]
    return βCl, βV, exp(lsCl), exp(lsV), exp(lsR)
end
nparams(spec) = sum(nfix(spec)) + 3

# -------------------- Laplace approx NLL for one subject --------------------
# b = [b_lCl, b_lV]
# log p(y_i | b_i, θ) = -n_i/2 log(2πσ²) - 0.5/σ² * sum (y - f(b))²
# log p(b_i | θ)     = -log(2π σ_lCl σ_lV) - 0.5*(b1²/σ_lCl² + b2²/σ_lV²)
# Laplace: log p(y_i) ≈ log p(y_i|b*) + log p(b*|θ) + log(2π) - 0.5 log det H
function subj_neg_loglik(b::AbstractVector, sd::SubjData, XCl, XV,
                         βCl, βV, σCl, σV, σR)
    ηCl = dot(XCl, βCl) + b[1]
    ηV  = dot(XV, βV)  + b[2]
    Cl = exp(ηCl); V = exp(ηV)
    ŷ = predict_subject(Cl, V, sd)
    r = sd.obs_conc .- ŷ
    n = length(r)
    # conditional -log p(y|b)
    nll_y = 0.5 * n * log(2π * σR^2) + 0.5 * sum(abs2, r) / σR^2
    # prior -log p(b)
    nll_b = log(2π * σCl * σV) + 0.5*(b[1]^2 / σCl^2 + b[2]^2 / σV^2)
    return nll_y + nll_b
end

# Numerical Hessian (2x2)
function num_hessian(f, b; h=1e-4)
    H = zeros(2,2)
    f0 = f(b)
    for i in 1:2, j in i:2
        bpp = copy(b); bpp[i]+=h; bpp[j]+=h
        bpm = copy(b); bpm[i]+=h; bpm[j]-=
…[truncated]
output
Existing file was successfully overwritten at /app/analysis.jl
bash
cd /app && timeout 280 julia analysis.jl 2>&1 | tail -80
output
[stderr]
Terminated
Took too long. I need to speed up. The bottleneck is numerical Hessian on the full Laplace marginal loglik (each function eval re-optimizes b for every subject). Let me speed things up significantly: 1. Use gradient-based optimization (autodiff finite diff) for outer loop , but that's slow 2. More importantly: cache inner optima between outer steps. With NelderMead inner, it's pretty slow. 3. Use BFGS with proper starting b=0 and only do a few iterations. Since problem is 2D, BFGS converges in <20 iterations easily. Skip the NelderMead warmup. 4. Use analytical gradient for inner problem? Too complex. Use finite differences , already fine. 5. Parallelize: 59 subjects in parallel , but not crucial if we speed up other things. Let me also: - Replace the 2*optimize scheme inside Laplace with a single BFGS call from zeros(2) - Reduce iterations in outer NelderMead Additionally, the outer Hessian is computing 4 * n² * n_subj * inner_solves. With n=8 outer params, that's 4*8*8*59 = 15k inner solves, each running optimize(). That's too much. I'll cut the outer Hessian to use a larger h with fewer points AND precompute inner modes once for the MLE and approximate SEs differently , but we still need outer Hessian. Actually the bottleneck is really the inner optimization. Let me make it fast: use Newton's method in 2D with numerical gradient and Hessian, warm-start from current fit. Let me simplify things , implement a fast Newton-Raphson for the inner problem (2D) with analytic-ish derivatives via autodiff finite diff. Then wrap the whole thing around a caching layer. Actually, a much simpler speed boost: cache the current b*_i and warm-start from previous call's value. Since outer optimization takes small steps, inner modes barely change. Let me implement that with a mutable global cache, and use LBFGS for inner with finite-diff autodiff. Also, drastically reduce outer optimization's NelderMead iterations , use just one run with lighter tolerance. Let me rewrite for speed.
Too slow. Let me optimize the inner loop significantly by caching warm-starts for the inner modes and using a fast Newton step in 2D.
str_replace_based_edit_tool
command: create
path: /app/analysis.jl
file_text: #!/usr/bin/env julia
# One-compartment population PK fit for Phenobarb (Laplace-approx NLME).
# Writes all outputs into /app/output/.

using CSV, DataFrames, Statistics, LinearAlgebra, JSON3, Distributions, Optim
using CairoMakie

# -------------------- Load data --------------------
const CSV_PATH = "/app/Phenobarb.csv"
const OUT_DIR  = "/app/output"
isdir(OUT_DIR) || mkpath(OUT_DIR)

df_all = CSV.read(CSV_PATH, DataFrame)
df_all.Subject = Int.(df_all.Subject)
df_all.Wt      = Float64.(df_all.Wt)
sort!(df_all, [:Subject, :time])

subjects  = sort(unique(df_all.Subject))
n_subjects = length(subjects)
n_obs = count(!ismissing, df_all.conc)

# -------------------- Per-subject data --------------------
struct SubjData
    id::Int
    wt::Float64
    apgar5::Int                           # 1 if ApgarInd == ">= 5" else 0
    dose_times::Vector{Float64}
    dose_amts::Vector{Float64}
    obs_times::Vector{Float64}
    obs_conc::Vector{Float64}
end

subj_data = SubjData[]
for s in subjects
    rows = df_all[df_all.Subject .== s, :]
    ap5  = rows.ApgarInd[1] == ">= 5" ? 1 : 0
    drw = .!ismissing.(rows.dose)
    orw = .!ismissing.(rows.conc)
    push!(subj_data, SubjData(
        s, rows.Wt[1], ap5,
        Float64.(rows.time[drw]), Float64.(rows.dose[drw]),
        Float64.(rows.time[orw]), Float64.(rows.conc[orw]),
    ))
end

# -------------------- PK prediction --------------------
@inline function conc_at(t, Cl, V, dtimes, damts)
    k = Cl / V
    s = 0.0
    @inbounds for i in eachindex(dtimes)
        tk = dtimes[i]
        if tk <= t
            s += (damts[i] / V) * exp(-k * (t - tk))
        end
    end
    return s
end

# -------------------- Design --------------------
function design(sd::SubjData, spec::Symbol)
    if spec == :base
        return [1.0], [1.0]
    elseif spec == :cl_wt
        return [1.0, sd.wt], [1.0]
    else  # :full
        return [1.0, sd.wt, Float64(sd.apgar5)], [1.0, sd.wt]
    end
end

nfix(spec) = spec == :base ? (1,1) : spec == :cl_wt ? (2,1) : (3,2)
nparams(spec) = sum(nfix(spec)) + 3

function unpack(θ, spec)
    pCl, pV = nfix(spec)
    βCl = θ[1:pCl]
    βV  = θ[pCl+1:pCl+pV]
    σCl = exp(θ[pCl+pV+1])
    σV  = exp(θ[pCl+pV+2])
    σR  = exp(θ[pCl+pV+3])
    return βCl, βV, σCl, σV, σR
end

# -------------------- Joint neg-log-density for one subject --------------------
@inline function nll_joint(b1, b2, sd::SubjData, XCl, XV, βCl, βV, σCl, σV, σR)
    ηCl = 0.0; @inbounds for i in eachindex(XCl); ηCl += XCl[i]*βCl[i]; end
    ηV  = 0.0; @inbounds for i in eachindex(XV);  ηV  += XV[i]*βV[i];   end
    Cl = exp(ηCl + b1); V = exp(ηV + b2)
    n = length(sd.obs_times)
    rss = 0.0
    @inbounds for j in 1:n
        ŷ = conc_at(sd.obs_times[j], Cl, V, sd.dose_times, sd.dose_amts)
        r = sd.obs_conc[j] - ŷ
        rss += r*r
    end
    val_y = 0.5*n*log(2π*σR^2) + 0.5*rss/σR^2
    val_b = log(2π*σCl*σV) + 0.5*(b1*b1/σCl^2 + b2*b2/σV^2)
    return val_y + val_b
end

# Gradient and Hessian of nll_joint wrt (b1,b2) via central differences.
function grad_hess(sd, XCl, XV, βCl, βV, σCl, σV, σR, b1, b2; h=1e-4)
    f = (x,y) -> nll_joint(x, y, sd, XCl, XV, βCl, βV, σCl, σV, σR)
    f0 = f(b1, b2)
    fpp = f(b1+h, b2+h); fpm = f(b1+h, b2-h); fmp = f(b1-h, b2+h); fmm = f(b1-h, b2-h)
    fp0 = f(b1+h, b2);   fm0 = f(b1-h, b2);   f0p = f(b1, b2+h); f0m = f(b1, b2-h)
    g1 = (fp0 - fm0)/(2h)
    g2 = (f0p - f0m)/(2h)
    H11 = (fp0 - 2f0 + fm0)/(h*h)
    H22 = (f0p - 2f0 + f0m)/(h*h)
    H12 = (fpp - fpm - fmp + fmm)/(4h*h)
    return f0, (g1,g2), (H11, H22, H12)
end

# Find mode of nll_joint via damped Newton starting from b0 (warm-start).
function find_mode(sd, XCl, XV, βCl, βV, σCl, σV, σR, b0; tol=1e-8, maxit=30)
    b1, b2 = b0[1], b0[2]
    local fval, g, H
    for it in 1:maxit
        fval, g, H = grad_hess(sd, XCl, XV, βCl, βV, σCl, σV, σR, b1, b2)
        # Solve H * Δ = -g  (2x2)
        H11, H22, H12 = H
        det = H11*H22 - H1
…[truncated]
output
Existing file was successfully overwritten at /app/analysis.jl
bash
cd /app && timeout 280 julia analysis.jl 2>&1 | tail -60
output
[stderr]
Terminated
Still too slow. The Newton iteration per subject is probably stuck running many iterations, and even then my test isn't terminating. Let me add timing and trace to debug. Actually I bet the issue is my Newton step isn't converging fast enough because I'm doing central differences for gradient AND re-computing for Hessian at each step. That's 9 function evals per Newton iteration, maybe 20-30 iterations... = 270 per subject per outer step. 59 subjects = 16k PK function evals per outer step. NM probably does thousands of outer steps. Let me profile a single evaluation first.
bash
cd /app && timeout 60 julia -e '
include("analysis.jl")
' 2>&1 | tail -20 &
pid=$!
sleep 50 && kill -9 $pid 2>/dev/null
wait 2>/dev/null
output
<system>Tool ran without output or errors</system>
bash
cd /app && timeout 90 julia -e '
using CSV, DataFrames, Statistics, LinearAlgebra, JSON3, Distributions, Optim

df_all = CSV.read("/app/Phenobarb.csv", DataFrame)
df_all.Subject = Int.(df_all.Subject)
df_all.Wt      = Float64.(df_all.Wt)
sort!(df_all, [:Subject, :time])
subjects  = sort(unique(df_all.Subject))
n_subjects = length(subjects); n_obs = count(!ismissing, df_all.conc)
println(n_subjects, " subjects, ", n_obs, " obs")

# Simpler: include analysis.jl functions inline minimal
include("analysis.jl")
' 2>&1 | head -40 &
pid=$!
sleep 85 && kill -9 $pid 2>/dev/null
wait 2>/dev/null
echo "done"
output
done
Problem , the script is hanging (no output). Could be package precompilation , let me do a quick test just to measure startup overhead.
bash
cd /app && time julia -e 'using CSV, DataFrames, JSON3, Distributions, Optim, CairoMakie; println("ok")' 2>&1 | tail -10
output
[stderr]
Shell command timed out.
Tool interaction exceeded 300 seconds.
bash
restart: true
output
<system>tool has been restarted.</system>
bash
ls /app/output/ 2>&1
output
<system>Tool ran without output or errors</system>
bash
timeout 240 julia --startup-file=no -e 'println("hello")' 2>&1 | tail -5
output
hello
bash
timeout 200 julia --startup-file=no -e 'using CSV; using DataFrames; println("data ok")' 2>&1 | tail -5
output
data ok
bash
timeout 200 julia --startup-file=no -e 'using CairoMakie; println("makie ok")' 2>&1 | tail -5
output
[stderr]
Terminated
CairoMakie is slow to load (first time). Let me precompile it so that subsequent loads are fast.
bash
timeout 290 julia --startup-file=no -e '
using Pkg
Pkg.precompile()
' 2>&1 | tail -10
output
[stderr]
Terminated
bash
ls ~/.julia/compiled/v1.10 2>&1 | head -20
ls /root/.julia/compiled/v1.10 2>&1 | head -20
output
ls: cannot access '/home/h2tagent/.julia/compiled/v1.10': No such file or directory
ls: cannot access '/root/.julia/compiled/v1.10': Permission denied
bash
whoami
env | grep -i julia
echo "depot"; echo $JULIA_DEPOT_PATH
julia --startup-file=no -e 'println(DEPOT_PATH)'
output
h2tagent
JULIA_SYSTEM_DEPOT=/usr/local/share/julia
JULIA_VERSION=1.10.4
JULIA_DEPOT_PATH=/tmp/julia-depot:/usr/local/share/julia
depot
/tmp/julia-depot:/usr/local/share/julia
["/tmp/julia-depot", "/usr/local/share/julia"]
bash
ls /tmp/julia-depot/compiled/v1.10 2>&1 | head
ls /usr/local/share/julia/compiled/v1.10 2>&1 | head
output
ADTypes
ADTypesChainRulesCoreExt
ADTypesConstructionBaseExt
AbstractFFTs
AbstractFFTsChainRulesCoreExt
AbstractTrees
Adapt
AdaptSparseArraysExt
AdaptStaticArraysExt
AdaptivePredicates
ADTypes
ADTypesChainRulesCoreExt
ADTypesConstructionBaseExt
AbstractFFTs
AbstractFFTsChainRulesCoreExt
AbstractTrees
Adapt
AdaptSparseArraysExt
AdaptStaticArraysExt
AdaptivePredicates
bash
ls /usr/local/share/julia/compiled/v1.10/CairoMakie/ 2>&1 | head
output
9mSey_NWwp1.ji
9mSey_NWwp1.so
bash
timeout 290 julia --startup-file=no -e '
t0 = time()
using CairoMakie
println("makie: ", round(time()-t0, digits=1), "s")
' 2>&1 | tail -5
output
┌ Warning: attempting to remove probably stale pidfile
│   path = "/tmp/julia-depot/compiled/v1.10/CairoMakie/9mSey_MJWkB.ji.pidfile"
└ @ FileWatching.Pidfile /usr/local/share/julia/stdlib/v1.10/FileWatching/src/pidfile.jl:244
makie: 77.8s
bash
timeout 60 julia --startup-file=no -e '
t0 = time()
using CairoMakie
println("makie: ", round(time()-t0, digits=1), "s")
' 2>&1 | tail -5
output
makie: 6.1s
bash
timeout 60 julia --startup-file=no -e '
t0 = time()
using CSV, DataFrames, JSON3, Distributions, Optim, CairoMakie, Statistics, LinearAlgebra
println("all: ", round(time()-t0, digits=1), "s")
' 2>&1 | tail -5
output
all: 7.5s
Good, cached. Now test the actual analysis script:
bash
cd /app && timeout 290 julia --startup-file=no analysis.jl 2>&1 | tail -60
output
Fitting base model ...
ERROR: LoadError: DomainError with -1.4021438438481158e17:
log was called with a negative real argument but will only return a complex result if called with a complex argument. Try log(Complex(x)).
Stacktrace:
  [1] throw_complex_domainerror(f::Symbol, x::Float64)
    @ Base.Math ./math.jl:33
  [2] _log(x::Float64, base::Val{:ℯ}, func::Symbol)
    @ Base.Math ./special/log.jl:301
  [3] log(x::Float64)
    @ Base.Math ./special/log.jl:267
  [4] laplace_neg_marginal(θ::Vector{Float64}, spec::Symbol; capture::Bool)
    @ Main /app/analysis.jl:175
  [5] laplace_neg_marginal
    @ /app/analysis.jl:160 [inlined]
  [6] (::var"#10#12"{Symbol})(θ::Vector{Float64})
    @ Main /app/analysis.jl:198
  [7] value(obj::NonDifferentiable{Float64, Vector{Float64}}, x::Vector{Float64})
    @ NLSolversBase /usr/local/share/julia/packages/NLSolversBase/gOqwS/src/interface.jl:24
  [8] update_state!(f::NonDifferentiable{Float64, Vector{Float64}}, state::Optim.NelderMeadState{Vector{Float64}, Float64, Vector{Float64}}, method::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/solvers/zeroth_order/nelder_mead.jl:229
  [9] optimize(d::NonDifferentiable{Float64, Vector{Float64}}, initial_x::Vector{Float64}, method::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters}, options::Optim.Options{Float64, Nothing}, state::Optim.NelderMeadState{Vector{Float64}, Float64, Vector{Float64}})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:88
 [10] optimize
    @ /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/optimize.jl:54 [inlined]
 [11] optimize(f::Function, x0::Vector{Float64}, method::NelderMead{Optim.AffineSimplexer, Optim.AdaptiveParameters}, options::Optim.Options{Float64, Nothing}; inplace::Bool, autodiff::ADTypes.AutoFiniteDiff{Val{:central}, Val{:central}, Val{:hcentral}, Nothing, Nothing, Bool})
    @ Optim /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/interface.jl:225
 [12] optimize
    @ /usr/local/share/julia/packages/Optim/lukVW/src/multivariate/optimize/interface.jl:216 [inlined]
 [13] fit_model(spec::Symbol; init::Nothing, verbose::Bool)
    @ Main /app/analysis.jl:199
 [14] fit_model(spec::Symbol)
    @ Main /app/analysis.jl:185
 [15] top-level scope
    @ /app/analysis.jl:211
in expression starting at /app/analysis.jl:211
The inner Newton is producing a negative Hessian determinant leading to log(negative). I need to guard against that more robustly. The issue is some step in outer optim leads to extreme parameters, so the inner mode-finding fails. Let me make the Laplace more robust: if the detected mode has negative or near-zero Hessian, fall back to returning a large but finite penalty.
str_replace_based_edit_tool
command: str_replace
path: /app/analysis.jl
old_str:     total = 0.0
    for (i, sd) in enumerate(subj_data)
        XCl, XV = design(sd, spec)
        b0 = bstar_all[i]
        (b1, b2), (H11, H22, H12), det, fmin =
            find_mode(sd, XCl, XV, βCl, βV, σCl, σV, σR, b0)
        bstar_all[i] = [b1, b2]
        # -log p(y_i) ≈ fmin + 0.5 log det H - log(2π)
        total += fmin + 0.5*log(det) - log(2π)
    end
new_str:     total = 0.0
    for (i, sd) in enumerate(subj_data)
        XCl, XV = design(sd, spec)
        b0 = bstar_all[i]
        (b1, b2), (H11, H22, H12), det, fmin =
            find_mode(sd, XCl, XV, βCl, βV, σCl, σV, σR, b0)
        bstar_all[i] = [b1, b2]
        # Guard: if determinant is not positive or non-finite, return Inf
        if !(isfinite(det) && det > 0) || !isfinite(fmin)
            return Inf
        end
        total += fmin + 0.5*log(det) - log(2π)
        if !isfinite(total)
            return Inf
        end
    end
output
The file /app/analysis.jl has been edited successfully.
Also, let me add some parameter bounds in unpack to prevent runaway values:
str_replace_based_edit_tool
command: str_replace
path: /app/analysis.jl
old_str: function laplace_neg_marginal(θ, spec; capture=false)
    βCl, βV, σCl, σV, σR = unpack(θ, spec)
    if !(σCl > 0 && σV > 0 && σR > 0) || any(!isfinite, θ)
        return Inf
    end
new_str: function laplace_neg_marginal(θ, spec; capture=false)
    if any(!isfinite, θ) || any(abs.(θ) .> 50)
        return Inf
    end
    βCl, βV, σCl, σV, σR = unpack(θ, spec)
    if !(σCl > 0 && σV > 0 && σR > 0)
        return Inf
    end
output
The file /app/analysis.jl has been edited successfully.
bash
cd /app && timeout 290 julia --startup-file=no analysis.jl 2>&1 | tail -40
output
Computing fixed-effect SEs ...
ERROR: LoadError: -Inf not allowed to be written in JSON spec
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] #write#94
    @ /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:283 [inlined]
  [3] write(::StructTypes.NumberType, buf::Vector{UInt8}, pos::Int64, len::Int64, x::Float64)
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:282
  [4] write(::StructTypes.DictType, buf::Vector{UInt8}, pos::Int64, len::Int64, x::Dict{String, Any}; kw::@Kwargs{})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:157
  [5] write(::StructTypes.DictType, buf::Vector{UInt8}, pos::Int64, len::Int64, x::Dict{String, Any})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:147
  [6] write(::StructTypes.ArrayType, buf::Vector{UInt8}, pos::Int64, len::Int64, x::Vector{Dict{String, Any}}; kw::@Kwargs{})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:187
  [7] write(::StructTypes.ArrayType, buf::Vector{UInt8}, pos::Int64, len::Int64, x::Vector{Dict{String, Any}})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:181
  [8] write(::StructTypes.DictType, buf::Vector{UInt8}, pos::Int64, len::Int64, x::Dict{String, Any}; kw::@Kwargs{})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:157
  [9] write
    @ /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:147 [inlined]
 [10] write(obj::Dict{String, Any}; kw::@Kwargs{})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:40
 [11] write
    @ /usr/local/share/julia/packages/JSON3/rT1w2/src/write.jl:37 [inlined]
 [12] pretty(out::IOStream, x::Dict{String, Any}, ac::JSON3.AlignmentContext; kw::@Kwargs{})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/pretty.jl:54
 [13] pretty
    @ /usr/local/share/julia/packages/JSON3/rT1w2/src/pretty.jl:54 [inlined]
 [14] pretty(out::IOStream, x::Dict{String, Any})
    @ JSON3 /usr/local/share/julia/packages/JSON3/rT1w2/src/pretty.jl:54
 [15] (::var"#20#21")(io::IOStream)
    @ Main /app/analysis.jl:350
 [16] open(::var"#20#21", ::String, ::Vararg{String}; kwargs::@Kwargs{})
    @ Base ./io.jl:396
 [17] open(::Function, ::String, ::String)
    @ Base ./io.jl:393
 [18] top-level scope
    @ /app/analysis.jl:349
in expression starting at /app/analysis.jl:349
Models fit but SEs produced -Inf t_values or similar. Some SE is 0 probably, making t = est/0 = Inf. Let me check: the outer Hessian might have an ill-conditioned entry because σ params were identified around the boundary... Actually the issue is that when fitting with 5×5 Hessian on fixed effects only, one column might be ill-conditioned. Or more likely, one of the diag entries of Cfe is 0 or negative. Let me inspect what is happening. Let me see how fast it ran to this point first:
bash
cd /app && timeout 290 julia --startup-file=no analysis.jl 2>&1 | grep -E "logLik|wall|cor|step|model_name|param|LRT" | head -30
output
logLik=-634.245530355901
  logLik=-641.5371467766723
  logLik=-634.670649409434  total wall=208.8s
 Row │ step   model_name  n_params  logLik    AIC      BIC      LR_stat       LR_pvalue
cor(obs,ind)=-0.11872422707873961  cor(obs,pop)=-0.11872422502696935
Uh oh. Several problems: 1. Base model logLik=-634.25 while cl_wt logLik=-641.54 → cl_wt is WORSE than base? That's bad , must not have converged properly 2. Final model cor(obs, ind) is NEGATIVE and very low → predictions are broken Something is really wrong with the optimizer , it's not finding good modes. Looking at base model first , `log Cl = -3` means Cl=0.05 L/h. For a baby with Wt=1.4kg and dose=25mg, concentration at 2h should be ~17.3 mg/L. Let me check: V ≈ 1.2 L roughly. So C(2) = (25/1.2)*exp(-0.05/1.2 * 2) = 20.83*exp(-0.083) ≈ 19.1 mg/L. Not too bad. But the next dose at 12.5h is just 3.5mg. So initial estimate at 2h (only 1 dose) should work. The issue is my fit isn't converging. Actually the problem is fit_clwt.logLik < fit_base.logLik. That's impossible for nested models with one more parameter! The optimizer is struggling. Let me check the NM optimization. The cache of bstar is likely corrupted between successive outer steps. Also: `BSTAR_CACHE[spec] = [zeros(2) for _ in 1:length(subj_data)]` is reset at start of each fit. But between NM evaluations, the bstar ref may update in-place from previous θ , which is fine as warm-start. The real issue is likely just poor optimization. Let me use a proper robust optimizer strategy and better starting points. Also, the starting σR = log(2.0) gives σR=2 mg/L, but the observed concs are 15-35 mg/L. σR probably should be larger initially. Let me also verify the PK model. In R/nlme, the typical Phenobarb model is: conc(t_ij) = Σ_{k: t_k <= t_ij} (dose_k / V_i) * exp(-Cl_i/V_i * (t_ij - t_k)) That's what I have. Good. Let me use better starting values. From the data: first obs = 17.3 mg/L after 25mg dose = V ≈ 25/17.3 ≈ 1.45 L. For infant Wt=1.4kg. So V/kg ≈ 1. So log(V) ≈ 0 (for intercept, assuming per-kg scaling not included). Actually V/Wt ≈ 1 L/kg, so if we model log(V) = β0 + β1*Wt, probably β0 should be ~0 with modest β1, OR just β0 ~ log(avg V) = log(1 L/kg * 1.4 kg) = log(1.4) ≈ 0.35. For Cl: typical half-life ~100h, so Cl/V ~ 0.007/h, so Cl ~ 0.007 * 1.45 = 0.010 L/h. log(Cl) ~ -4.6. My starting is -3.0. Not terrible. Let me also ditch cached `BSTAR_CACHE` approach and instead RESET it cleanly to zero at each outer eval. The issue is that as NM moves θ around and some mode-finds don't converge, stale modes can poison the next eval. Actually for NM, warm-start is generally good since θ changes slowly. But the main problem is: NelderMead on 5-8 parameters is unreliable. Let me switch to BFGS with finite-diff gradient for the outer loop, with bounds. That's much more reliable. Also, let me not hardcode the starting σ's , use log(σ_initial) that's reasonable. Let me rewrite to use a more robust approach: 1. Outer optimization: Nelder-Mead followed by BFGS with autodiff finite 2. Better starting point derived from data 3. Don't cache across outer optimizer: reset BSTAR per call but use zeros as initial , actually caching helps speed. Let me instead cache per outer-call and share across inner. 4. Allow the optimizer more time (iterations) Wait , the walltime is already 208s for just three fits! That's a big problem because adding SE computation plus plots will blow the 300s limit. I need to make it FASTER. Main slowdown: each Laplace evaluation is O(n_subj × Newton_iters × 9 PK_evals). Let me write an analytic inner gradient/Hessian , can be done since the PK model is a closed-form sum of exponentials. Actually let me just make the inner mode-finding simpler and faster, and use a smaller starting point. Better approach: use BFGS with finite-diff autodiff for outer, MUCH faster than NM. Also, reduce the inner Newton max iterations. Let me also prune tolerances: we don't need superb accuracy. Let me think about the total structure. With ~8 params, BFGS with finite diff will do ~8*3 function evals per iteration. If each eval takes 200ms (for 59 subjects × Newton) and BFGS needs 50 iterations, that's 8*3*50*0.2 = 240s for one fit. 3 fits = 720s. Too slo …[truncated]
bash
cd /app && timeout 60 julia --startup-file=no -e '
include("analysis.jl")
' 2>&1 | tail -5 &
pid=$!
# kill after 30 seconds, we only want to see how much initial loading takes
sleep 30 && echo "TIME30" && ps aux | grep julia
wait $pid 2>/dev/null
output
TIME30
h2tagent  2233  3.7 16.5 2377872 1907820 ?     Sl   10:19   0:25 /usr/local/bin/julia -C native -J/usr/local/lib/julia/sys.so -g1 --startup-file=no -O2 --output-o /tmp/julia-depot/compiled/v1.10/CairoMakie/jl_Tu73pu --output-ji /tmp/julia-depot/compiled/v1.10/CairoMakie/jl_wK9jSK --output-incremental=yes --startup-file=no --history-file=no --warn-overwrite=yes --color=auto -
h2tagent  2384  0.0  0.0  11136  3012 ?        S    10:30   0:00 timeout 60 julia --startup-file=no -e  include("analysis.jl") 
h2tagent  2386 94.4 11.2 1735076 1295772 ?     Rl   10:30   0:28 julia --startup-file=no -e  include("analysis.jl") 
h2tagent  2390 50.0  0.0  11960  5176 ?        S    10:30   0:00 grep julia
Fitting base model ...
bash
pkill -9 -f "include" 2>/dev/null; pkill -9 -f "analysis" 2>/dev/null; pkill -9 -f "jl_" 2>/dev/null; sleep 2; ps aux | grep julia | head
output
h2tagent  2402  0.0  0.0  11960  5636 ?        S    10:31   0:00 grep julia
OK, processes are clear. Let me rewrite analysis.jl with a MUCH faster inner loop using analytic derivatives, and better overall structure. Actually, the issue with the previous cl_wt < base logLik is likely that my optimizer ran out of iterations. Since NM converged at a suboptimal point and didn't find the true minimum, the chain of fits produced nonsense modes. Let me implement: 1. Analytic gradient/Hessian for the inner mode-find (fast Newton) 2. BFGS outer with finite-diff (avoids NM convergence issues) 3. Proper data-driven initial values 4. Total wall budget: target < 180s so we have room for SEs + plots For the PK model C(t) = Σ_k (D_k/V) * exp(-k*(t - t_k)) where k = Cl/V, t_k ≤ t: d C / d Cl = Σ_k (D_k/V) * exp(-k(t-t_k)) * (-(t-t_k)/V) d C / d V = Σ_k -(D_k/V²) * exp(-k(t-t_k)) + Σ_k (D_k/V) * exp(-k(t-t_k)) * (Cl/V²)(t-t_k) = Σ_k (D_k/V²) * exp(-k(t-t_k)) * [-1 + (Cl/V)(t-t_k)] = Σ_k (D_k/V²) * exp(-k(t-t_k)) * [k(t-t_k) - 1] Now re-parameterize η_Cl = log(Cl), η_V = log(V): dCl/dη_Cl = Cl; dV/dη_V = V dC/dη_Cl = (dC/dCl)*Cl = -(Cl/V)*(t-t_k) * [D_k/V * exp(-k(t-t_k))] summed = -Σ_k (D_k/V) * k*(t-t_k) * exp(-k(t-t_k)) dC/dη_V = (dC/dV)*V = Σ_k (D_k/V) * exp(-k(t-t_k)) * [k(t-t_k) - 1] Good. Now for NLL_y = sum (y_j - C_j)² / (2σ²): ∂NLL_y/∂η_Cl = (1/σ²) Σ_j (C_j - y_j) * dC_j/dη_Cl And b1 = η_Cl - Xβ, so ∂NLL_y/∂b1 = ∂NLL_y/∂η_Cl. For NLL_b = 0.5 * (b1²/σ_Cl² + b2²/σ_V²): ∂NLL_b/∂b1 = b1/σ_Cl² ∂NLL_b/∂b2 = b2/σ_V² For Hessian, I can use Gauss-Newton approximation: drop second derivatives of C(t) terms. The GN Hessian for nonlinear LS is: H_GN(b) = (1/σ²) * J'J + prior Hessian where J_jk = dC_j/db_k. This approximation is positive definite always (plus prior), great for Newton. Using GN will be much more robust. Let me rewrite. Actually full Newton with finite-diff gradient is also fine. Let me just use GN-Newton for speed and robustness.
str_replace_based_edit_tool
command: create
path: /app/analysis.jl
file_text: #!/usr/bin/env julia
# One-compartment population PK fit for Phenobarb (Laplace-approx NLME).
# Writes all outputs into /app/output/.

using CSV, DataFrames, Statistics, LinearAlgebra, JSON3, Distributions, Optim
using CairoMakie

const CSV_PATH = "/app/Phenobarb.csv"
const OUT_DIR  = "/app/output"
isdir(OUT_DIR) || mkpath(OUT_DIR)

# -------------------- Load data --------------------
df_all = CSV.read(CSV_PATH, DataFrame)
df_all.Subject = Int.(df_all.Subject)
df_all.Wt      = Float64.(df_all.Wt)
sort!(df_all, [:Subject, :time])

subjects  = sort(unique(df_all.Subject))
n_subjects = length(subjects)
n_obs = count(!ismissing, df_all.conc)

struct SubjData
    id::Int
    wt::Float64
    apgar5::Int
    dose_times::Vector{Float64}
    dose_amts::Vector{Float64}
    obs_times::Vector{Float64}
    obs_conc::Vector{Float64}
end
subj_data = SubjData[]
for s in subjects
    rs = df_all[df_all.Subject .== s, :]
    ap5 = rs.ApgarInd[1] == ">= 5" ? 1 : 0
    drw = .!ismissing.(rs.dose); orw = .!ismissing.(rs.conc)
    push!(subj_data, SubjData(
        s, rs.Wt[1], ap5,
        Float64.(rs.time[drw]), Float64.(rs.dose[drw]),
        Float64.(rs.time[orw]), Float64.(rs.conc[orw])))
end

# -------------------- PK prediction and derivatives --------------------
# Returns C(t) and dC/dη_Cl, dC/dη_V where η_Cl = log(Cl), η_V = log(V).
@inline function conc_and_grad(t, Cl, V, dtimes, damts)
    k = Cl / V
    C = 0.0; g_eta_Cl = 0.0; g_eta_V = 0.0
    @inbounds for i in eachindex(dtimes)
        tk = dtimes[i]
        if tk <= t
            dt = t - tk
            e  = exp(-k*dt)
            Di_over_V = damts[i]/V
            term = Di_over_V * e
            C += term
            # dC/dη_Cl = - Σ (D/V) * k*dt * e
            g_eta_Cl += -term * k * dt
            # dC/dη_V  = Σ (D/V) * e * (k*dt - 1)
            g_eta_V  += term * (k*dt - 1.0)
        end
    end
    return C, g_eta_Cl, g_eta_V
end

@inline function conc_only(t, Cl, V, dtimes, damts)
    k = Cl / V
    C = 0.0
    @inbounds for i in eachindex(dtimes)
        tk = dtimes[i]
        if tk <= t
            C += (damts[i]/V) * exp(-k*(t - tk))
        end
    end
    return C
end

# -------------------- Design --------------------
function design(sd::SubjData, spec::Symbol)
    if spec == :base
        return [1.0], [1.0]
    elseif spec == :cl_wt
        return [1.0, sd.wt], [1.0]
    else
        return [1.0, sd.wt, Float64(sd.apgar5)], [1.0, sd.wt]
    end
end

nfix(spec) = spec == :base ? (1,1) : spec == :cl_wt ? (2,1) : (3,2)
nparams(spec) = sum(nfix(spec)) + 3

function unpack(θ, spec)
    pCl, pV = nfix(spec)
    βCl = @view θ[1:pCl]
    βV  = @view θ[pCl+1:pCl+pV]
    σCl = exp(θ[pCl+pV+1])
    σV  = exp(θ[pCl+pV+2])
    σR  = exp(θ[pCl+pV+3])
    return βCl, βV, σCl, σV, σR
end

# -------------------- Inner: mode-find with Gauss-Newton --------------------
# For given subject, compute gradient & Gauss-Newton Hessian of
# g(b) = 0.5 * rss/σ² + 0.5 * (b1²/σCl² + b2²/σV²)  [+ constants].
# Use full Hessian at mode for Laplace (analytic gradient + finite diff Hessian).
function inner_g_and_gradH(b1, b2, sd, XCl, XV, βCl, βV, σCl, σV, σR)
    ηCl0 = 0.0; @inbounds for i in eachindex(XCl); ηCl0 += XCl[i]*βCl[i]; end
    ηV0  = 0.0; @inbounds for i in eachindex(XV);  ηV0  += XV[i]*βV[i];   end
    Cl = exp(ηCl0 + b1); V = exp(ηV0 + b2)
    n = length(sd.obs_times)
    rss = 0.0; g1 = 0.0; g2 = 0.0
    H11 = 0.0; H22 = 0.0; H12 = 0.0
    σR2 = σR*σR
    @inbounds for j in 1:n
        C, dC1, dC2 = conc_and_grad(sd.obs_times[j], Cl, V, sd.dose_times, sd.dose_amts)
        r = C - sd.obs_conc[j]   # sign: d/db 0.5(r)² where r = C - y
        rss += r*r
        g1 += r * dC1 / σR2
        g2 += r * dC2 / σR2
        H11 += dC1*dC1 / σR2
        H22 += dC2*dC2 / σR2
        H12 += dC1*dC2 / σR2
    end
    nll_y = 0.5*n*log(2π*σR2) + 0.5*rss/σR2
    nll_b = log(2π*σCl*σV) + 0.5*(b1*b1/σCl^2 + b2*b2/σV^2)
    # add prior grad/hess
 
…[truncated]
output
Existing file was successfully overwritten at /app/analysis.jl
bash
cd /app && timeout 290 julia --startup-file=no analysis.jl 2>&1 | tail -50
output
Fitting base model ...
ERROR: LoadError: TypeError: in keyword argument autodiff, expected ADTypes.AbstractADType, got a value of type Symbol
Stacktrace:
 [1] fit_model(spec::Symbol; init::Nothing)
   @ Main /app/analysis.jl:220
 [2] fit_model(spec::Symbol)
   @ Main /app/analysis.jl:201
 [3] top-level scope
   @ /app/analysis.jl:235
in expression starting at /app/analysis.jl:235
bash
timeout 60 julia --startup-file=no -e 'using Optim; @show typeof(Optim.Options(g_tol=1e-6)); using Pkg; Pkg.status("Optim")' 2>&1 | tail -5
output
typeof(Optim.Options(g_tol = 1.0e-6)) = Optim.Options{Float64, Nothing}
Status `/usr/local/share/julia/environments/v1.10/Project.toml`
  [429524aa] Optim v2.1.0
Optim 2.x uses `ADTypes`. I should just remove the autodiff kwarg and use BFGS with numerical gradient via finite differences manually, or switch the BFGS polish to not use autodiff. Simplest: just skip BFGS polish and rely on two rounds of NelderMead. Or use `Optim.BFGS()` without autodiff , but then we need to provide gradient. Actually, `optimize(f, x0, BFGS())` with no gradient uses finite differences by default in older Optim versions but maybe not 2.x. Let me just provide my own gradient via finite differences wrapper. Actually the simplest: use `Optim.NelderMead()` for both passes. Or use `SimulatedAnnealing` , no. Let me write an explicit finite-diff gradient and pass it to BFGS. Actually for Optim 2.x, `autodiff=ADTypes.AutoFiniteDifferences()` or similar. Let me just use `FiniteDiff` alternative. Actually the simplest workaround: use `GradientDescent()` with numerical finite-difference gradient wrapper. Or just use NelderMead. Given 8 params, NM is slow but works. Let me swap to using BFGS with NLSolversBase's finite-diff , or just wrap manually:
bash
timeout 60 julia --startup-file=no -e '
using Optim
# test simple BFGS with numerical gradient via OnceDifferentiable
using Optim: OnceDifferentiable
f(x) = sum(abs2, x .- 1)
od = OnceDifferentiable(f, zeros(3); autodiff=:finite)
r = optimize(od, zeros(3), BFGS())
@show Optim.minimum(r), Optim.minimizer(r)
' 2>&1 | tail -5
output
ERROR: TypeError: in keyword argument autodiff, expected ADTypes.AbstractADType, got a value of type Symbol
Stacktrace:
 [1] top-level scope
   @ none:6
bash
timeout 60 julia --startup-file=no -e '
using Optim, ADTypes
f(x) = sum(abs2, x .- 1)
od = Optim.OnceDifferentiable(f, zeros(3); autodiff=AutoFiniteDiff())
r = optimize(od, zeros(3), BFGS())
@show Optim.minimum(r)
' 2>&1 | tail -5
output
@ ./essentials.jl:926 [inlined]
 [5] invoke_in_world
   @ ./essentials.jl:923 [inlined]
 [6] require(into::Module, mod::Symbol)
   @ Base ./loading.jl:1746
bash
timeout 60 julia --startup-file=no -e '
using Pkg
Pkg.status()
' 2>&1 | grep -iE "adtypes|finitediff"
output
<system>Tool ran without output or errors</system>
bash
ls /usr/local/share/julia/compiled/v1.10 | grep -iE "adtypes|finite|forward|diffres"
output
ADTypes
ADTypesChainRulesCoreExt
ADTypesConstructionBaseExt
DifferentiationInterfaceFiniteDiffExt
FiniteDiff
FiniteDiffSparseArraysExt
FiniteDiffStaticArraysExt
ADTypes and FiniteDiff are available but not in the project. Let me just implement my own numerical gradient for BFGS using Optim's function-only interface: Actually `Optim.optimize(f, g!, x0, BFGS(), opts)` with user-supplied gradient works. Let me write a simple finite-diff gradient function and pass to BFGS.
str_replace_based_edit_tool
command: str_replace
path: /app/analysis.jl
old_str:     # Nelder-Mead first (robust to bad starts), then BFGS polish with finite diff
    r1 = optimize(f, θ0, NelderMead(),
                  Optim.Options(g_tol=1e-6, iterations=2500))
    θ1 = Optim.minimizer(r1)
    r2 = optimize(f, θ1, BFGS(),
                  Optim.Options(g_tol=1e-6, iterations=300);
                  autodiff=:finite)
    if Optim.minimum(r2) < Optim.minimum(r1)
        θhat = Optim.minimizer(r2); nll = Optim.minimum(r2)
    else
        θhat = θ1; nll = Optim.minimum(r1)
    end
new_str:     # Nelder-Mead first (robust to bad starts), then BFGS polish with manual FD gradient
    r1 = optimize(f, θ0, NelderMead(),
                  Optim.Options(g_tol=1e-6, iterations=2500))
    θ1 = Optim.minimizer(r1)
    function g!(G, θ)
        h = 1e-4
        for k in eachindex(θ)
            xp = copy(θ); xm = copy(θ); xp[k]+=h; xm[k]-=h
            G[k] = (f(xp) - f(xm)) / (2h)
        end
        return G
    end
    r2 = optimize(f, g!, θ1, BFGS(),
                  Optim.Options(g_tol=1e-6, iterations=200))
    if Optim.minimum(r2) < Optim.minimum(r1)
        θhat = Optim.minimizer(r2); nll = Optim.minimum(r2)
    else
        θhat = θ1; nll = Optim.minimum(r1)
    end
output
The file /app/analysis.jl has been edited successfully.
bash
cd /app && timeout 290 julia --startup-file=no analysis.jl 2>&1 | tail -30
output
Fitting base model ...
  logLik=-505.236  AIC=1020.473  t=3.1s
Fitting cl_wt model ...
  logLik=-479.257  AIC=970.514  t=3.3s
Fitting full model ...
  logLik=-437.552  AIC=891.105  t=3.6s
3×8 DataFrame
 Row │ step   model_name  n_params  logLik    AIC       BIC       LR_stat       LR_pvalue
     │ Int64  String      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
cor(obs,ind)=0.971  cor(obs,pop)=0.815
σCl=0.22  σV=0.172  σR=2.729
Computing fixed-effect SEs ...
Done. Elapsed=17.1s
Excellent! All fits work, correlations pass (ind=0.97, pop=0.82), AIC strictly decreases, p-values are well below 1e-6. And the runtime is only 17 seconds. Let me verify output files:
bash
ls -la /app/output/
output
total 1267
drwxrws--- 2 h2tagent h2tagent   4096 May 31 10:34 .
drwxrws--- 3 h2tagent h2tagent   4096 May 31 10:33 ..
-rw-r--r-- 1 h2tagent h2tagent    335 May 31 10:34 lrt_chain.csv
-rw-r--r-- 1 h2tagent h2tagent   1368 May 31 10:34 model_summary.json
-rw-r--r-- 1 h2tagent h2tagent   7773 May 31 10:34 obs_vs_pred.csv
-rw-r--r-- 1 h2tagent h2tagent   2526 May 31 10:34 per_subject_params.csv
-rw-r--r-- 1 h2tagent h2tagent 388740 May 31 10:34 plot_conc_profile.png
-rw-r--r-- 1 h2tagent h2tagent 103424 May 31 10:34 plot_covariate_effect.png
-rw-r--r-- 1 h2tagent h2tagent 146059 May 31 10:34 plot_obs_vs_pred.png
-rw-r--r-- 1 h2tagent h2tagent 483933 May 31 10:34 plot_per_subject_fit.png
-rw-r--r-- 1 h2tagent h2tagent 142549 May 31 10:34 plot_residuals.png
-rw-r--r-- 1 h2tagent h2tagent  10198 May 31 10:34 residual_diagnostics.csv
bash
cat /app/output/model_summary.json
output
{
    "bic": 915.4519335098474,
    "logLik": -437.5522662872467,
    "fixed_effects": [
        {
            "term": "lCl.(Intercept)",
            "t_value": -26.965998453090428,
            "df": 150,
            "std_error": 0.2194694899901729,
            "estimate": -5.918213927575548
        },
        {
            "term": "lCl.Wt",
            "t_value": 7.630161381609899,
            "df": 150,
            "std_error": 0.0802108292564257,
            "estimate": 0.6120215717792848
        },
        {
            "term": "lCl.ApgarInd>= 5",
            "t_value": -0.29400387365924685,
            "df": 150,
            "std_error": 0.15598318273305325,
            "estimate": -0.04585965994921581
        },
        {
            "term": "lV.(Intercept)",
            "t_value": -6.9951282763566125,
            "df": 150,
            "std_error": 0.06795213761795175,
            "estimate": -0.4753339192902102
        },
        {
            "term": "lV.Wt",
            "t_value": 13.118668423969625,
            "df": 150,
            "std_error": 0.04067109741100981,
            "estimate": 0.5335506413740072
        }
    ],
    "aic": 891.1045325744934,
    "n_subjects": 59,
    "n_obs": 155,
    "random_effects_sd": {
        "lCl": 0.22024683354338667,
        "lV": 0.1720704285516958,
        "Residual": 2.7292185981002457
    }
}
bash
cat /app/output/lrt_chain.csv
echo
head -5 /app/output/per_subject_params.csv
echo
head -5 /app/output/obs_vs_pred.csv
echo
head -5 /app/output/residual_diagnostics.csv
output
step,model_name,n_params,logLik,AIC,BIC,LR_stat,LR_pvalue
1,base,5,-505.2363234556618,1020.4726469113236,1035.68977249592,,
2,cl_wt,6,-479.25681388969383,970.5136277793877,988.7741784809032,51.959019131935975,5.667114700129609e-13
3,full,8,-437.5522662872467,891.1045325744934,915.4519335098474,83.40909520489424,7.725829258798329e-19

Subject,Cl,V
1,0.005809675648222586,1.3451737186489632
2,0.005526210377524698,1.2204298293240206
3,0.008028365470257839,1.6621760967513357
4,0.004107324099606106,0.9114791760919537

Subject,time,conc_obs,pred_pop,pred_ind
1,2.0,17.3,18.87829554764221,18.42511821489749
1,112.5,31.0,30.428299131416264,30.315079241534495
2,2.0,9.7,10.737684916440829,12.179947046279677
2,63.5,24.6,19.740856782942384,22.512718073121572

Subject,time,fitted_ind,resid,std_resid
1,2.0,18.42511821489749,-1.1251182148974905,-0.41224921143387444
1,112.5,30.315079241534495,0.6849207584655055,0.25095855602855155
2,2.0,12.179947046279677,-2.479947046279678,-0.9086655968143846
2,63.5,22.512718073121572,2.087281926878429,0.7647910388458236
All outputs look correct. Let me quickly verify the plots look reasonable:
str_replace_based_edit_tool
command: view
path: /app/output/plot_conc_profile.png
output
<system>Image resized from 2000x1240 to 1400x868 to fit display limits</system>
<output_image>
…[truncated]
str_replace_based_edit_tool
command: view
path: /app/output/plot_per_subject_fit.png
output
<system>Image resized from 2400x1800 to 1270x952 to fit display limits</system>
<output_image>
…[truncated]
str_replace_based_edit_tool
command: view
path: /app/output/plot_obs_vs_pred.png
output
<system>Image resized from 2400x1240 to 1518x784 to fit display limits</system>
<output_image>
…[truncated]
str_replace_based_edit_tool
command: view
path: /app/output/plot_covariate_effect.png
output
<system>Image resized from 2000x1240 to 1400x868 to fit display limits</system>
<output_image>
…[truncated]
str_replace_based_edit_tool
command: view
path: /app/output/plot_residuals.png
output
<system>Image resized from 2400x1240 to 1518x784 to fit display limits</system>
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…[truncated]
All plots look great. Let me double-check the final model quality , the structure matches expected Phenobarb results well. The LRT chain has p-values well below 1e-6, AIC strictly decreases, and cor(obs, pred_ind)=0.97 and cor(obs, pred_pop)=0.82 both pass the thresholds. Let me also verify the script handles edge cases and works with a perturbation. Let me also confirm all per-subject Cl, V are positive:
bash
awk -F, 'NR>1 && ($2<=0 || $3<=0) {bad++} END{print "bad:",bad+0}' /app/output/per_subject_params.csv
output
bad: 0
Let me also confirm that the run is robust to perturbed inputs by simulating a quick perturbation test:
bash
cp /app/Phenobarb.csv /tmp/Phenobarb_orig.csv
# Create a perturbed test: drop a few subjects, perturb Wt slightly
python3 -c "
import csv, random
random.seed(42)
rows = list(csv.DictReader(open('/app/Phenobarb.csv')))
drop_ids = set(random.sample([str(i) for i in range(1, 60)], 5))
out = [r for r in rows if r['Subject'] not in drop_ids]
# perturb conc slightly
for r in out:
    if r['conc']:
        r['conc'] = f\"{float(r['conc']) * (1 + random.gauss(0, 0.02)):.3f}\"
with open('/app/Phenobarb.csv','w') as f:
    w = csv.DictWriter(f, fieldnames=rows[0].keys(), quoting=csv.QUOTE_NONNUMERIC)
    w.writeheader(); w.writerows(out)
print('rows:', len(out))
"
cd /app && timeout 290 julia --startup-file=no analysis.jl 2>&1 | tail -15
# restore
cp /tmp/Phenobarb_orig.csv /app/Phenobarb.csv
output
rows: 674
Fitting cl_wt model ...
  logLik=-419.278  AIC=850.555  t=3.4s
Fitting full model ...
  logLik=-381.651  AIC=779.303  t=3.7s
3×8 DataFrame
 Row │ step   model_name  n_params  logLik    AIC      BIC      LR_stat       LR_pvalue
     │ Int64  String      Int64     Float64   Float64  Float64  Float64?      Float64?
─────┼──────────────────────────────────────────────────────────────────────────────────────────
   1 │     1  base               5  -447.828  905.656  920.256  missing       missing
   2 │     2  cl_wt              6  -419.278  850.555  868.075       57.101         4.13987e-14
   3 │     3  full               8  -381.651  779.303  802.662       75.2525        4.56171e-17
cor(obs,ind)=0.967  cor(obs,pop)=0.835
σCl=0.106  σV=0.184  σR=2.776
Computing fixed-effect SEs ...
Done. Elapsed=18.6s
The perturbed version works great too: all correlations pass, AIC strictly decreases, p-values < 1e-6.
bash
# Final clean run on original data
cd /app && rm -f output/*.png output/*.json output/*.csv
timeout 290 julia --startup-file=no analysis.jl 2>&1 | tail -15
echo "---"
ls /app/output/
output
Fitting cl_wt model ...
  logLik=-479.257  AIC=970.514  t=3.4s
Fitting full model ...
  logLik=-437.552  AIC=891.105  t=3.6s
3×8 DataFrame
 Row │ step   model_name  n_params  logLik    AIC       BIC       LR_stat       LR_pvalue
     │ Int64  String      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
cor(obs,ind)=0.971  cor(obs,pop)=0.815
σCl=0.22  σV=0.172  σR=2.729
Computing fixed-effect SEs ...
Done. Elapsed=17.4s
---
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, and the key metrics satisfy the spec: - **LRT p-values**: 5.67e-13 (step 1→2) and 7.73e-19 (step 2→3), both below 1e-6 - **AIC monotonically decreasing**: 1020.5 → 970.5 → 891.1 - **Correlations**: cor(obs, pred_ind)=0.971 (>0.75 ✓), cor(obs, pred_pop)=0.815 (>0.55 ✓) - **Runtime**: ~17s well under 300s - **All Cl, V positive** in per_subject_params.csv The analysis script: 1. Loads Phenobarb.csv and derives all counts at runtime 2. Fits three nested one-compartment NLME models (base → cl_wt → full) using Laplace-approximated marginal likelihood with analytic Gauss-Newton inner mode finding and NM+BFGS outer optimization 3. Produces all 10 required outputs with proper column orders and exact filenames from the manifest 4. Robust to perturbed input data (tested with 54 subjects & ±2% concentration noise)
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: 8  status: completed  raw_score: 1.0
# reward rule: binary: score 1.0 == 1.0
# => reward = 1.0  (PASS)
#
# 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).
----------------------------------------------------------------------
Fitting cl_wt model ...
  logLik=-479.257  AIC=970.514  t=3.4s
Fitting full model ...
  logLik=-437.552  AIC=891.105  t=3.6s
3×8 DataFrame
 Row │ step   model_name  n_params  logLik    AIC       BIC       LR_stat       LR_pvalue
     │ Int64  String      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
cor(obs,ind)=0.971  cor(obs,pop)=0.815
σCl=0.22  σV=0.172  σR=2.729
Computing fixed-effect SEs ...
Done. Elapsed=17.4s
---
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

Reproduce this trial: git checkout 2f94510 && PYTHONPATH=src python3 scripts/build_site.py , then open trial/trial_06e311a48b2a4944. Re-running the agent live requires EVAL_PLATFORM_ENABLE_OAUTH_SMOKE=1 and is non-deterministic.

Trial trial_06e311a48b2a4944 · verifier authoritative; classifier explanatory.