Bayesian prediction with multiple-samples information

Federico Camerlenghi, Antonio Lijoi and Igor Prünster

Journal of Multivariate Analysis, 2017, vol. 156, issue C, 18-28

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.

Keywords: Bayesian nonparametrics; Hierarchical processes; Partial exchangeability; Prediction; Pitman–Yor process; Species sampling models (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.jmva.2017.01.010

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