A general framework for cutting feedback within modularized Bayesian inference

• 成果类型: Article
• 署名作者: Liu, Yang; Goudie, Robert J. B.
• 署名单位: University of Cambridge; MRC Biostatistics Unit
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1093/jrsssb/qkaf012
• 发表日期: 2025
• 页码: 1171-1199
• 关键词: models; likelihood

摘要

Standard Bayesian inference enables building models that combine information from various sources, but this inference may not be reliable if components of the model are misspecified. Cut inference, a particular type of modularized Bayesian inference, is an alternative that splits a model into modules and cuts the feedback from any suspect module. Previous studies have focused on a two module case, but a more general definition of a 'module' remains unclear. We present a formal definition of a 'module' and discuss its properties. We formulate methods for identifying modules; determining the order of modules; and building the cut distribution that should be used for cut inference within an arbitrary directed acyclic graph structure. We justify the cut distribution by showing that it not only cuts the feedback but also is the best approximation to the joint distribution satisfying this condition in Kullback-Leibler divergence. We also extend cut inference for the two module case to a general multiple-module case via a sequential splitting technique and demonstrate this via illustrative applications.