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| import numpy as np
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| import matplotlib.pyplot as plt
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| from scipy.stats import chi2
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|
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| from .likelihood import relative_likelihood
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| def confidence_regions(
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| *,
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| data,
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| mean_ci,
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| sigma_ci,
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| probs,
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| eps_mu,
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| eps_sigma,
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| add_ci_box,
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| ):
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| """
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| Likelihood-based confidence regions for (μ, σ).
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| """
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| probs = probs[::-1]
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| levels = np.exp(-0.5 * chi2.ppf(probs, 2))
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|
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| mu_grid = np.linspace(
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| mean_ci[0] - eps_mu[0],
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| mean_ci[1] + eps_mu[1],
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| 200,
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| )
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| sigma_grid = np.linspace(
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| sigma_ci[0] - eps_sigma[0],
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| sigma_ci[1] + eps_sigma[1],
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| 200,
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| )
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| MU, SIGMA = np.meshgrid(mu_grid, sigma_grid)
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| sigma_hat = np.std(data, ddof=0)
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| mu_hat = np.mean(data)
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|
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| Z = relative_likelihood(
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| data=data,
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| mu=MU,
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| sigma=SIGMA,
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| sigma_hat=sigma_hat,
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| )
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| fig, ax = plt.subplots(figsize=(8, 6))
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| contour = ax.contour(
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| MU,
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| SIGMA,
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| Z,
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| levels=levels,
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| cmap="plasma",
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| )
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| ax.scatter(mu_hat, sigma_hat, c="black", s=60, label="MLE", zorder=5)
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|
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| if add_ci_box:
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| x = [
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| mean_ci[0],
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| mean_ci[1],
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| mean_ci[1],
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| mean_ci[0],
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| mean_ci[0],
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| ]
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| y = [
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| sigma_ci[0],
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| sigma_ci[0],
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| sigma_ci[1],
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| sigma_ci[1],
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| sigma_ci[0],
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| ]
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| ax.plot(x, y, "r--", label="CI box")
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| handles, _ = contour.legend_elements()
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| labels = [f"{100*p:.1f}%" for p in probs]
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| ax.legend(
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| handles + [ax.collections[-1]],
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| labels + ["MLE"],
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| loc="upper right",
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| frameon=True,
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| )
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| ax.set_title(r"Confidence Regions for $(\mu, \sigma)$")
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| ax.set_xlabel(r"$\mu$")
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| ax.set_ylabel(r"$\sigma$")
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| ax.grid(True, linestyle="--", alpha=0.6)
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| plt.tight_layout()
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| return fig
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|
