O que é Posterior predictive distribution, credible interval?

The posterior predictive distribution of new data $\tilde x$ is $p(\tilde x \mid x) = \int p(\tilde x \mid \theta)\,p(\theta \mid x)\,d\theta$. A $(1 - \alpha)$ credible interval is an interval to which the posterior gives probability $1 - \alpha$, usually between its $\alpha/2$ and $1 - \alpha/2$ quantiles.