"""F2-conf-03: Monte Carlo coverage of OLS CIs under heteroskedasticity.
Run from workspace root: ~/wp29/venv/bin/python out/analysis.py"""
import json, os
import numpy as np, pandas as pd
from scipy import stats

SEED = 20261030
ALPHA, BETA, N, R = 1.0, 0.5, 30, 2000

d = pd.read_csv("data/design.csv")
issues = []
n_rows = len(d)
if d[["x", "sigma"]].isna().any().any():
    issues.append({"issue": "missing values", "handling": "none dropped; would fail"})
if (d["sigma"] <= 0).any():
    issues.append({"issue": "non-positive sigma", "handling": "flagged"})
if n_rows != N:
    issues.append({"issue": f"expected {N} rows, got {n_rows}", "handling": "flagged"})
x = d["x"].to_numpy(float); sig = d["sigma"].to_numpy(float)
n = len(x)

X = np.column_stack([np.ones(n), x])
XtXi = np.linalg.inv(X.T @ X)
A = XtXi @ X.T                      # beta_hat = A y
a = A[1]                            # weights for slope
sd_exact = float(np.sqrt(np.sum(a**2 * sig**2)))  # Var = sum w_i^2 sigma_i^2
sd_naive_formula = float(np.sqrt(np.mean(sig**2) * XtXi[1, 1]))  # for reference only

tcrit = stats.t.ppf(0.975, n - 2)
rng = np.random.default_rng(SEED)
eps = rng.standard_normal((R, n))
Y = ALPHA + BETA * x + sig * eps     # R x n
B = Y @ A.T                          # R x 2
resid = Y - B @ X.T
s2 = (resid**2).sum(1) / (n - 2)
se_conv = np.sqrt(s2 * XtXi[1, 1])
hc0 = (resid**2) @ (a**2)            # slope element of sandwich
se_hc1 = np.sqrt(hc0 * n / (n - 2))
bh = B[:, 1]
cov_conv = float(np.mean(np.abs(bh - BETA) <= tcrit * se_conv))
cov_hc1 = float(np.mean(np.abs(bh - BETA) <= tcrit * se_hc1))
mcse_conv = float(np.sqrt(cov_conv * (1 - cov_conv) / R))
mcse_hc1 = float(np.sqrt(cov_hc1 * (1 - cov_hc1) / R))
mcse_nominal = float(np.sqrt(0.95 * 0.05 / R))
# Decision rule: binomial MC SE at R (evaluated at the estimated coverage)
undercovers = bool(cov_conv < 0.95 - 3 * mcse_conv)

res = {
    "task_id": "F2-conf-03",
    "coverage_conventional": cov_conv,
    "coverage_hc1": cov_hc1,
    "sd_beta_exact": sd_exact,
    "sd_beta_mc": float(np.std(bh, ddof=1)),
    "mean_se_conventional": float(se_conv.mean()),
    "conventional_ci_undercovers": undercovers,
    "n_replications": R,
    "n_obs_per_replication": n,
    "feasibility": "complete",
    "feasibility_reason": None,
    "data_issues": issues,
    "n_input_rows": {"design.csv": n_rows},
    "random_seed": SEED,
}
os.makedirs("out", exist_ok=True)
with open("out/results.json", "w") as f:
    json.dump(res, f, indent=2)
extra = {"mcse_coverage_conventional": mcse_conv, "mcse_coverage_hc1": mcse_hc1,
         "mcse_at_nominal_0.95": mcse_nominal,
         "undercovers_using_nominal_mcse": bool(cov_conv < 0.95 - 3 * mcse_nominal),
         "t_crit": float(tcrit), "mean_se_hc1": float(se_hc1.mean()),
         "homoskedastic_formula_sd_with_mean_sigma2": sd_naive_formula,
         "mean_beta_hat": float(bh.mean())}
with open("out/diagnostics.json", "w") as f:
    json.dump(extra, f, indent=2)
print(json.dumps(res, indent=2)); print(json.dumps(extra, indent=2))