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Bayesian prediction with multiple-samples information

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  • Camerlenghi, Federico
  • Lijoi, Antonio
  • Prünster, Igor

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.

Suggested Citation

  • Camerlenghi, Federico & Lijoi, Antonio & Prünster, Igor, 2017. "Bayesian prediction with multiple-samples information," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 18-28.
  • Handle: RePEc:eee:jmvana:v:156:y:2017:i:c:p:18-28
    DOI: 10.1016/j.jmva.2017.01.010
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    References listed on IDEAS

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    Cited by:

    1. Riva Palacio, Alan & Leisen, Fabrizio, 2018. "Integrability conditions for compound random measures," Statistics & Probability Letters, Elsevier, vol. 135(C), pages 32-37.

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