Bayesian prediction with multiple-samples information.

Federico Camerlenghi, Antonio Lijoi, Igor Prünster

Abstract: 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 ≥ 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. Previous article in issue Next article in issue AMS 2010 subject classifications 62F15 60G57 62G05