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Heavy-Tailed NGG-Mixture Models

Lookup NU author(s): Dr Vianey Palacios RamirezORCiD

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Abstract

Heavy tails are often found in practice, and yet they are an Achilles heel of a variety of mainstream random probability measures such as the Dirichlet process (DP). The first contribution of this paper focuses on characterizing the tails of the so-called normalized generalized gamma (NGG) process. We show that the right tail of an NGG process is heavy-tailed provided that the centering distribution is itself heavy-tailed; the DP is the only member of the NGG class that fails to obey this convenient property. A second contribution of the paper rests on the development of two classes of heavy-tailed mixture models and the assessment of their relative merits. Multivariate extensions of the proposed heavy-tailed mixtures are devised here, along with a predictor-dependent version, to learn about the effect of covariates on a multivariate heavy-tailed response. The simulation study suggests that the proposed method performs well in various scenarios, and we showcase the application of the proposed methods in a neuroscience dataset.

Publication metadata

Author(s): Palacios Ramírez Vianey, de Carvalho Miguel, Gutiérrez Luis

Publication type: Article

Publication status: Published

Journal: Bayesian Analysis

Year: 2025

Volume: 20

Issue: 4

Pages: 1315-1343

Print publication date: 01/12/2025

Online publication date: 20/03/2024

Acceptance date: 01/01/2024

ISSN (print): 1936-0975

ISSN (electronic): 1931-6690

Publisher: International Society for Bayesian Analysis (ISBA)

URL: https://doi.org/10.1214/24-BA1420

DOI: 10.1214/24-BA1420

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