Pathwise concentration bounds for Bayesian beliefs

• 成果类型: Article
• 署名作者: Fudenberg, Drew; Lanzani, Giacomo; Strack, Philipp
• 署名单位: Massachusetts Institute of Technology (MIT); Yale University
• 刊物名称: THEORETICAL ECONOMICS
• ISSN/ISSBN: 1933-6837
• DOI: 10.3982/TE5206
• 发表日期: 2023-11-01
• 页码: 1585-1622
• 关键词: Misspecified learning; Bayesian consistency; C11; D81

摘要

We show that Bayesian posteriors concentrate on the outcome distributions that approximately minimize the Kullback-Leibler divergence from the empirical distribution, uniformly over sample paths, even when the prior does not have full support. This generalizes Diaconis and Freedman's (1990) uniform convergence result to, e.g., priors that have finite support, are constrained by independence assumptions, or have a parametric form that cannot match some probability distributions. The concentration result lets us provide a rate of convergence for Berk's (1966) result on the limiting behavior of posterior beliefs when the prior is misspecified. We provide a bound on approximation errors in anticipated-utility models, and extend our analysis to outcomes that are perceived to follow a Markov process.