Heavy-Tailed NGG Mixture Models

TL;DR

This paper characterizes the heavy-tail properties of normalized generalized gamma (NGG) processes, develops heavy-tailed mixture models, and demonstrates their effectiveness through simulations and a neuroscience application.

Contribution

It provides a detailed analysis of the tail behavior of NGG processes and introduces new heavy-tailed mixture models with multivariate and predictor-dependent extensions.

Findings

NGG processes are heavy-tailed if the centering distribution is heavy-tailed

Proposed mixture models perform well in various simulated scenarios

Application to neuroscience data demonstrates practical utility

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.