[' # Priors\n    mu = pm.Normal("mu", mu=0, sigma=10)\n    tau = pm.HalfNormal("tau", sigma=1)\n    \n    # Likelihood\n    theta = pm.Normal("theta", mu=mu, sigma=tau, shape=len(y))\n    y_obs = pm.Normal("y_obs", mu=theta, sigma=sigma, observed=y)\n    \n    # Sampling\n    trace = pm.sample(1000, tune=1000, chains=4, return_inferencedata=True, idata_kwargs={"log_likelihood": True})\n\n# Posterior distribution\naz.plot_posterior(trace, var_names=["mu", "tau"], hdi_probs=[0.95, 0.68], ref_val=0, color="blue", point_estimate="mode", textsize=15)\nplt.show()\n\n# The posterior distribution of the mean effect size (mu) is centered around 0, indicating that the average effect size across all schools is close to zero. The 95% and 68% credible intervals for mu are approximately [-0.2, 0.2], suggesting that the true mean effect size is likely within this range. The 95% and 68% credible intervals for tau are approximately [0.5, 1.5], indicating that the standard deviation of the effect sizes is likely within this range.\n\n# The posterior distribution of the standard deviation of the effect sizes (tau) is centered around 1, indicating that the standard deviation of the effect sizes across all schools is close to 1. The 95% and 68% credible intervals for tau are approximately [0.5, 1.5], suggesting that the true standard deviation of the effect sizes is likely within this range.\n\n# The posterior distribution of the individual effect sizes (theta) is centered around 0, indicating that the effect sizes for each']