Posterior predictive probability
= Posterior predictive probability
{title2=$\mathbb P(Y_{\rm new}=1\mid\mathcal D)$}
A posterior predictive probability averages a future-event probability over the <Bayesian posterior>. For a <Bernoulli distribution> with unknown parameter $p$, it is $\mathbb E[p\mid\mathcal D]$. Under <Beta-binomial conjugacy> with posterior $\operatorname{Beta}(a,b)$, the predictive success probability is $a/(a+b)$.