Dissertation Defense: Xinyu Zhang, Statistics PhD Candidate
Title: Bayesian Restricted Likelihood, Generalized Bayes and Model Misspecification
Abstract: Model misspecification poses a significant challenge in Bayesian inference, requiring modifications to the traditional process of updating from prior to posterior distributions. Various methods have been proposed to account for model imperfections, among which Bayesian restricted likelihood (BRL) and generalized Bayes (GB) are two prominent approaches. BRL focuses on aspects of the model that are believed to be well-specified, deriving the posterior by conditioning on an insufficient statistic—such as Huber’s M-estimator—to capture those reliable aspects. In contrast, GB shifts the inferential focus to a specific target by replacing the likelihood function with the exponentiated negative loss, altering the standard Bayesian update to emphasize robustness in estimation.