Bayesian inference for generalized linear models via quasi-posteriors

• 成果类型: Article
• 署名作者: Agnoletto, D.; Rigon, T.; Dunson, D. B.
• 署名单位: Duke University; University of Milano-Bicocca
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asaf022
• 发表日期: 2025
• 关键词: likelihood functions

摘要

Generalized linear models are routinely used for modelling relationships between a response variable and a set of covariates. The simple form of a generalized linear model comes with easy interpretability, but also leads to concerns about model misspecification impacting inferential conclusions. A popular semiparametric solution adopted in the frequentist literature is quasilikelihood, which improves robustness by only requiring correct specification of the first two moments. We develop a robust approach to Bayesian inference in generalized linear models through quasi-posterior distributions. We show that quasi-posteriors provide a coherent generalized Bayes inference method, while also approximating so-called coarsened posteriors. In so doing, we obtain new insights into the choice of coarsening parameter. Asymptotically, the quasi-posterior converges in total variation to a normal distribution and has important connections with the loss-likelihood bootstrap posterior. We demonstrate that it is also well calibrated in terms of frequentist coverage. Moreover, the loss-scale parameter has a clear interpretation as a dispersion, and this leads to a consolidated method-of-moments estimator.