Bayesian inference for generalized linear models via quasi-posteriors.

IF 2.4 2区 数学 Q2 BIOLOGY
Biometrika Pub Date : 2025-03-27 eCollection Date: 2025-01-01 DOI:10.1093/biomet/asaf022
D Agnoletto, T Rigon, D B Dunson
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引用次数: 0

Abstract

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.

广义线性模型的准后验贝叶斯推理。
广义线性模型通常用于模拟响应变量和一组协变量之间的关系。广义线性模型的简单形式易于解释,但也会导致对模型错误说明影响推断结论的担忧。在频率学文献中采用的一种流行的半参数解是拟似然,它通过只要求前两个矩的正确规范来提高鲁棒性。我们通过拟后验分布发展了广义线性模型中贝叶斯推理的鲁棒方法。我们证明了准后验提供了一种连贯的广义贝叶斯推理方法,同时也近似于所谓的粗后验。在此基础上,对粗化参数的选择有了新的认识。渐近地,准后验在总方差上收敛于正态分布,并与损失似然自举后验有重要联系。我们证明它在频率覆盖方面也得到了很好的校准。此外,损失尺度参数有一个清晰的解释为色散,这导致了一个统一的矩量估计方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Biometrika
Biometrika 生物-生物学
CiteScore
5.50
自引率
3.70%
发文量
56
审稿时长
6-12 weeks
期刊介绍: Biometrika is primarily a journal of statistics in which emphasis is placed on papers containing original theoretical contributions of direct or potential value in applications. From time to time, papers in bordering fields are also published.
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