A Unified Approach to Hierarchical Random Measures

Marta Catalano, Claudio Del Sole, Antonio Lijoi and Igor Prünster ()
Additional contact information
Marta Catalano: Luiss University
Claudio Del Sole: Bocconi University
Antonio Lijoi: Bocconi University
Igor Prünster: Bocconi University

Sankhya A: The Indian Journal of Statistics, 2024, vol. 86, issue 1, No 14, 255-287

Abstract: Abstract Hierarchical models enjoy great popularity due to their ability to handle heterogeneous groups of observations by leveraging on their underlying common structure. In a Bayesian nonparametric framework, the hierarchy is introduced at the level of group-specific random measures, and then translated to the observations’ level via suitable transformations. In this work, we propose a new strategy to derive closed-form expressions for the marginal and posterior distributions of each group. Indeed, by directly inserting a suitable set of latent variables into the generative model for the data, we unravel a common core shared by the different hierarchical constructions proposed in the Bayesian nonparametric literature. Specifically, we identify a key identity that underlies these models and highlight its role in the derivation of quantities of interest.

Keywords: Completely random measure; dependence structure; hierarchical process; mixture hazard; normalized random measure; partial exchangeability; 62F15; 62G05; 60G57 (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-023-00330-w

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