Predictive variance
= Predictive variance
{title2=$\operatorname{Var}(Y_*\mid\mathcal D)$}
The <variance> of a <predictive distribution> quantifies spread of a future quantity conditional on the observed data and model assumptions. For a noisy future observation $Y_*=f_*+\epsilon_*$ with fresh independent noise of <variance> $\sigma^2$, it is $\operatorname{Var}(f_*\mid\mathcal D)+\sigma^2$. It should therefore be distinguished from the latent-function <posterior variance>.