Bayesian prediction with multiple-samples information

The prediction of future outcomes of a random phenomenon is typically based on a certain number of "analogous" observations from the past. When observations are generated by multiple samples, a natural notion of analogy is partial exchangeability and the problem of prediction can be effectively addressed in a Bayesian nonparametric setting. Instead of confining ourselves to the prediction of a single future experimental outcome, as in most treatments of the subject, we aim at predicting features of an unobserved additional sample of any size. We first provide a structural property of prediction rules induced by partially exchangeable arrays, without assuming any specific nonparametric prior. Then we focus on a general class of hierarchical random probability measures and devise a simulation algorithm to forecast the outcome of m future observations, for any m larger than or equal to 1. The theoretical result and the algorithm are illustrated by means of a real dataset, which also highlights the "borrowing strength" behavior across samples induced by the hierarchical specification.