Bayesian Nonparametric Quasi Likelihood

• 成果类型: Article; Early Access
• 署名作者: Linero, Antonio R.
• 署名单位: University of Texas System; University of Texas Austin
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2025.2594185
• 发表日期: 2026-02-11
• 关键词: Bayesian additive regression trees; Decision tree ensembles; Markov Chain Monte Carlo; Nonparametric Regression; Robust Statistics; regression; distributions; dispersion; rates

摘要

A recent trend in Bayesian research has been revisiting generalizations of the likelihood that enable Bayesian inference without requiring the specification of a data generating mechanism. This article focuses on a Bayesian nonparametric extension of Wedderburn's quasi-likelihood, using Bayesian additive regression trees to model the mean function. Here, the analyst posits only a structural relationship between the mean and variance of the outcome. We show that this approach provides a unified, computationally efficient, framework for extending Bayesian decision tree ensembles to many new settings, including simplex-valued and heavily heteroscedastic data. We also introduce Bayesian strategies for inferring the dispersion parameter of the quasi-likelihood, a task which is complicated by the fact that the quasi-likelihood itself does not contain information about this parameter; despite these challenges, we are able to inject updates for the dispersion parameter into a Markov chain Monte Carlo inference scheme in a way that, in the parametric setting, leads to a Bernstein-von Mises result for the stationary distribution of the resulting Markov chain. We illustrate the utility of our approach on a variety of both synthetic and non-synthetic datasets. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.