| |
| """Full parameter reporting and estimator-bias check for the reference study. |
| |
| Replays capacity_simulation.py with the same seed and the same sequence of |
| random draws, but records all four fitted parameters in every bootstrap |
| replicate. The published midpoint intervals are reproduced exactly as a check. |
| A separate Monte Carlo of the direct logistic control estimates the fitter's |
| systematic bias at this design. All inputs are synthetic constructions. |
| """ |
| from __future__ import annotations |
| import json |
| from pathlib import Path |
| import numpy as np |
| import capacity_simulation as S |
|
|
| ATTAINABLE_MAX = 0.95 |
|
|
|
|
| def bootstrap_all(rng, values, repetitions=400): |
| """Same draws as S.bootstrap_midpoint, but keeps every parameter.""" |
| draws = [] |
| for _ in range(repetitions): |
| means = np.array([rng.choice(values[int(n)], size=len(values[int(n)]), replace=True).mean() |
| for n in S.TEAM_SIZES]) |
| draws.append(S.fit_curve(S.TEAM_SIZES, means)) |
| return np.array(draws) |
|
|
|
|
| def summarize(theta, draws): |
| ceil_draws = draws[:, 0] + draws[:, 1] |
| q = lambda v: [float(x) for x in np.quantile(v, [0.025, 0.975])] |
| return { |
| "floor": float(theta[0]), "floor_ci": q(draws[:, 0]), |
| "ceiling": float(theta[0] + theta[1]), "ceiling_ci": q(ceil_draws), |
| "midpoint": float(theta[2]), "midpoint_ci": q(draws[:, 2]), |
| "tau": float(theta[3]), "tau_ci": q(draws[:, 3]), |
| "corr_midpoint_tau": float(np.corrcoef(draws[:, 2], draws[:, 3])[0, 1]), |
| "corr_midpoint_ceiling": float(np.corrcoef(draws[:, 2], ceil_draws)[0, 1]), |
| "ceiling_above_attainable": bool(theta[0] + theta[1] > ATTAINABLE_MAX), |
| } |
|
|
|
|
| def main(): |
| rng = np.random.default_rng(S.SEED) |
| out = {} |
| |
| truth = np.array([0.15, 0.80, 4.35, 0.90]) |
| values, means = {}, [] |
| for n in S.TEAM_SIZES.astype(int): |
| p = float(S.logistic(np.array([n]), *truth)[0]) |
| sc = rng.binomial(1, p, size=S.SESSIONS_PER_SIZE).astype(float) |
| values[n] = sc; means.append(float(sc.mean())) |
| theta = S.fit_curve(S.TEAM_SIZES, np.array(means)) |
| out["direct_control"] = summarize(theta, bootstrap_all(rng, values)) |
| |
| for cond in S.CONDITIONS: |
| values, means = {}, [] |
| for n in S.TEAM_SIZES.astype(int): |
| sc = np.array([S.simulate_session(rng, n, cond) for _ in range(S.SESSIONS_PER_SIZE)]) |
| sc = sc[np.isfinite(sc)]; values[n] = sc; means.append(float(sc.mean())) |
| theta = S.fit_curve(S.TEAM_SIZES, np.array(means)) |
| out[cond] = summarize(theta, bootstrap_all(rng, values)) |
|
|
| |
| pub = json.loads(Path("simulation_summary.json").read_text()) |
| checks = {"direct_control": pub["direct_logistic_control"]["midpoint_ci"]} |
| checks.update({c: pub[c]["midpoint_ci"] for c in S.CONDITIONS}) |
| out["reproduces_published_midpoint_ci"] = all( |
| np.allclose(out[k]["midpoint_ci"], v, atol=1e-9) for k, v in checks.items()) |
|
|
| |
| mc = np.random.default_rng(S.SEED + 1) |
| fitted = [] |
| for _ in range(500): |
| m = [mc.binomial(1, float(S.logistic(np.array([n]), *truth)[0]), size=S.SESSIONS_PER_SIZE).mean() |
| for n in S.TEAM_SIZES.astype(int)] |
| fitted.append(S.fit_curve(S.TEAM_SIZES, np.array(m))[2]) |
| fitted = np.array(fitted) |
| bias = float(fitted.mean() - truth[2]) |
| n0 = pub["design"]["predicted_midpoint"] |
| add = out["additive"] |
| out["estimator_bias"] = { |
| "replicates": 500, "true_midpoint": float(truth[2]), |
| "mean_fitted": float(fitted.mean()), "bias": bias, |
| "sd_fitted": float(fitted.std(ddof=1)), |
| "mc_se_of_bias": float(fitted.std(ddof=1) / np.sqrt(len(fitted))), |
| } |
| out["additive_gap"] = { |
| "n0": n0, "raw_gap": add["midpoint"] - n0, |
| "raw_gap_ci": [add["midpoint_ci"][0] - n0, add["midpoint_ci"][1] - n0], |
| "bias_corrected_gap": add["midpoint"] - bias - n0, |
| "bias_corrected_gap_ci": [add["midpoint_ci"][0] - bias - n0, add["midpoint_ci"][1] - bias - n0], |
| "gap_in_tau_units": (add["midpoint"] - bias - n0) / add["tau"], |
| } |
| Path("capacity_parameters.json").write_text(json.dumps(out, indent=2) + "\n") |
|
|
| print(f"reproduces published midpoint CIs exactly: {out['reproduces_published_midpoint_ci']}\n") |
| print(f"{'condition':15}{'floor':>20}{'ceiling':>20}{'midpoint':>20}{'tau':>20}{'r(mid,tau)':>11}") |
| for k in ["direct_control", *S.CONDITIONS]: |
| r = out[k]; f = lambda a, b: f"{r[a]:.2f} [{r[b][0]:.2f},{r[b][1]:.2f}]" |
| flag = " ceiling>.95" if r["ceiling_above_attainable"] else "" |
| print(f"{k:15}{f('floor','floor_ci'):>20}{f('ceiling','ceiling_ci'):>20}" |
| f"{f('midpoint','midpoint_ci'):>20}{f('tau','tau_ci'):>20}{r['corr_midpoint_tau']:>11.2f}{flag}") |
| b = out["estimator_bias"]; g = out["additive_gap"] |
| print(f"\nfitter bias over 500 replicates: {b['bias']:+.3f} (MC s.e. {b['mc_se_of_bias']:.3f}; " |
| f"single-replicate SD {b['sd_fitted']:.3f})") |
| print(f"additive gap raw {g['raw_gap']:+.3f} [{g['raw_gap_ci'][0]:+.3f},{g['raw_gap_ci'][1]:+.3f}]; " |
| f"bias-corrected {g['bias_corrected_gap']:+.3f} [{g['bias_corrected_gap_ci'][0]:+.3f}," |
| f"{g['bias_corrected_gap_ci'][1]:+.3f}] = {g['gap_in_tau_units']:+.2f} tau") |
|
|
|
|
| if __name__ == "__main__": |
| main() |
|
|
