Ultimate Polya Gamma Samplers - Efficient MCMC for Possibly Imbalanced Binary and Categorical Data

• 成果类型: Article
• 署名作者: Zens, Gregor; Fruhwirth-Schnatter, Sylvia; Wagner, Helga
• 署名单位: International Institute for Applied Systems Analysis (IIASA); Johannes Kepler University Linz
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2259030
• 发表日期: 2024
• 页码: 2548-2559
• 关键词: multinomial probit model; bayesian-analysis; parameter expansion; regression; mixture; experts

摘要

Modeling binary and categorical data is one of the most commonly encountered tasks of applied statisticians and econometricians. While Bayesian methods in this context have been available for decades now, they often require a high level of familiarity with Bayesian statistics or suffer from issues such as low sampling efficiency. To contribute to the accessibility of Bayesian models for binary and categorical data, we introduce novel latent variable representations based on Polya-Gamma random variables for a range of commonly encountered logistic regression models. From these latent variable representations, new Gibbs sampling algorithms for binary, binomial, and multinomial logit models are derived. All models allow for a conditionally Gaussian likelihood representation, rendering extensions to more complex modeling frameworks such as state space models straightforward. However, sampling efficiency may still be an issue in these data augmentation based estimation frameworks. To counteract this, novel marginal data augmentation strategies are developed and discussed in detail. The merits of our approach are illustrated through extensive simulations and real data applications. Supplementary materials for this article are available online.