Nonparametric Predictive Inference for Discrete Data via Metropolis-Adjusted Dirichlet Sequences

• 成果类型: Article; Early Access
• 署名作者: Agnoletto, Davide; Rigon, Tommaso; Dunson, David B.
• 署名单位: Duke University; University of Milano-Bicocca
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459; 1537-274X
• DOI: 10.1080/01621459.2026.2662438
• 发表日期: 2026-07-31
• 关键词: Count data; Martingale posterior; nonparametric Bayes; predictive inference; smoothing; mixtures; models; priors

摘要

This article is motivated by challenges in conducting Bayesian inferences on unknown discrete distributions, with a particular focus on count data. To avoid the computational disadvantages of traditional mixture models, we develop a novel Bayesian predictive approach. In particular, our Metropolis-adjusted Dirichlet (mad) sequence model characterizes the predictive measure as a mixture of a base measure and Metropolis-Hastings kernels centered on previous data points. The resulting mad sequence is asymptotically exchangeable and the posterior on the data generator takes the form of a martingale posterior. This structure leads to straightforward algorithms for inference on count distributions, with easy extensions to multivariate, regression, and binary data cases. We obtain a useful asymptotic Gaussian approximation and illustrate the methodology on a variety of applications. for this article are available online, including a standardized description of the materials available for reproducing the work.