[' # Define the priors for the parameters\n    alpha = pm.Normal(\'alpha\', mu=0, sigma=10)\n    beta = pm.Normal(\'beta\', mu=0, sigma=10)\n    sigma = pm.HalfNormal(\'sigma\', sigma=10)\n\n    # Define the likelihood\n    likelihood = pm.Normal(\'likelihood\', mu=alpha + beta * r, sigma=sigma, observed=n)\n\n    # Sample the posterior\n    trace = pm.sample(1000, tune=1000, chains=4, return_inferencedata=True, idata_kwargs={"log_likelihood": True})\n\n# Calculate the posterior predictive distribution\nposterior_predictive = pm.sample_posterior_predictive(trace, samples=1000, model=m)\n\n# Calculate the mean and standard deviation of the posterior predictive distribution\nposterior_predictive_mean = np.mean(posterior_predictive[\'likelihood\'], axis=0)\nposterior_predictive_std = np.std(posterior_predictive[\'likelihood\'], axis=0)\n\n# Calculate the 95% credible interval for the posterior predictive distribution\nposterior_predictive_ci = np.percentile(posterior_predictive[\'likelihood\'], [2.5, 97.5], axis=0)\n\n# Plot the posterior predictive distribution\nplt.figure(figsize=(10, 6))\nplt.plot(r, posterior_predictive_mean, color=\'blue\', label=\'Posterior Predictive Mean\')\nplt.fill_between(r, posterior_predictive_ci[0], posterior_predictive_ci[1], color=\'blue\', alpha=0.2, label=\'95% Credible Interval\')\nplt.scatter(r, n, color=\'red\', label=\'Data\')\nplt.xlabel(\'Number of Babies\')\nplt.ylabel(\'Mortality Rate\')\nplt.title(\'Posterior Predictive Distribution\')\nplt.legend()\nplt.show()\n\n# Print the posterior predictive distribution\nprint("Posterior Predictive Distribution:")\nprint(posterior']