On Bayesian prediction: foundations and recent results for recursive predictive algorithms

The talk moves from fundamental properties of the predictive distributions for exchangeable sequences, that will be briefly reviewed. We then illustrate some implications in Bayesian learning - from predictive characterizations, to simulating from the prior and posterior distributions, and to explicit the statistical model underlying some recursive algorithms for approximate online prediction in Bayesian nonparametric mixture models. If time permits, we will also discuss a predictive interpretation of the (lack of) frequentist coverage of Bayesian credible intervals.