Bayesian prediction with multiple-samples information

JOURNAL OF MULTIVARIATE ANALYSIS

卷:156

Article

Camerlenghi, Federico^1,4,5  Lijoi, Antonio^2,3  Prunster, Igor^2,3 

[1] Univ Bologna, Dipartimento Sci Stat, Via Belle Arti 41, I-40126 Bologna, Italy

[2] Univ Bocconi, Dipartimento Sci Decis, BIDSA, Via Rontgen 1, I-20136 Milan, Italy

[3] Univ Bocconi, IGIER, Via Rontgen 1, I-20136 Milan, Italy

[4] Bocconi Univ, BIDSA, Milan, Italy

[5] Coll Carlo Alberto, Moncalieri, Italy

关键词: Bayesian nonparametrics;    Hierarchical processes;    Partial exchangeability;    Prediction;    Pitman-Yor process;    Species sampling models;   

DOI  :  10.1016/j.jmva.2017.01.010

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free