[' # Define the GP model\n    gp = pm.gp.Latent(cov_func=pm.gp.cov.ExpQuad(1, ls=1.0), mean_func=pm.gp.mean.Zero())\n    \n    # Define the likelihood\n    y_obs = pm.Poisson(\'y_obs\', mu=gp.predict(x), observed=y)\n    \n    # Sample the posterior\n    trace = pm.sample(1000, tune=1000, chains=4, return_inferencedata=True, idata_kwargs={"log_likelihood": True})\n\n# Posterior predictive checks\ny_pred = trace.posterior_predictive["y_obs"]\n\n# Plotting the data and posterior predictive samples\nplt.figure(figsize=(10, 6))\nplt.scatter(x, y, label=\'Observed data\', color=\'blue\')\nplt.plot(x, y_pred.mean(axis=0), label=\'Posterior predictive mean\', color=\'red\', alpha=0.5)\nplt.fill_between(x, y_pred.min(axis=0), y_pred.max(axis=0), color=\'red\', alpha=0.2, label=\'Posterior predictive interval\')\nplt.xlabel(\'x\')\nplt.ylabel(\'y\')\nplt.legend()\nplt.title(\'Posterior Predictive Check\')\nplt.show()']