This is an old version, view current version.

27.1 Posterior predictive distribution

Given a full Bayesian model p(y,θ), the posterior predictive density for new data ˜y given observed data y is p(˜yy)=p(˜yθ)p(θy)dθ. The product under the integral reduces to the joint posterior density p(˜y,θy), so that the integral is simply marginalizing out the parameters θ, leaving the predictive density p(˜yy) of future observations given past observations.