Latent Nested Nonparametric Priors (with Discussion).

Journal Article (Journal Article)

Discrete random structures are important tools in Bayesian nonparametrics and the resulting models have proven effective in density estimation, clustering, topic modeling and prediction, among others. In this paper, we consider nested processes and study the dependence structures they induce. Dependence ranges between homogeneity, corresponding to full exchangeability, and maximum heterogeneity, corresponding to (unconditional) independence across samples. The popular nested Dirichlet process is shown to degenerate to the fully exchangeable case when there are ties across samples at the observed or latent level. To overcome this drawback, inherent to nesting general discrete random measures, we introduce a novel class of latent nested processes. These are obtained by adding common and group-specific completely random measures and, then, normalizing to yield dependent random probability measures. We provide results on the partition distributions induced by latent nested processes, and develop a Markov Chain Monte Carlo sampler for Bayesian inferences. A test for distributional homogeneity across groups is obtained as a by-product. The results and their inferential implications are showcased on synthetic and real data.

Full Text

Duke Authors

Cited Authors

  • Camerlenghi, F; Dunson, DB; Lijoi, A; Prünster, I; Rodríguez, A

Published Date

  • December 2019

Published In

Volume / Issue

  • 14 / 4

Start / End Page

  • 1303 - 1356

PubMed ID

  • 35978607

Pubmed Central ID

  • PMC9381042

Electronic International Standard Serial Number (EISSN)

  • 1931-6690

International Standard Serial Number (ISSN)

  • 1936-0975

Digital Object Identifier (DOI)

  • 10.1214/19-ba1169


  • eng