Title: Bayesian estimates from loss functions
Authors: Yu Luo - Imperial College London (United Kingdom) [presenting]
Abstract: In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, but in general, such a model is not robust to model misspecification. An alternative that has gained attention in the frequentist domain is to utilize decision theory, and draw inference via loss functions without direct reference to a probability model for the observable quantities. Recently, there has been much research on Bayesian inference via loss functions, with a predominant focus on Gibbs posteriors. We will introduce another perspective to generate Bayesian estimates from loss functions via the Bayesian decision theory and non-parametric Bayesian inference. In particular, this updating framework generalizes the Bayesian bootstrap approach through Bayesian predictive inference instead of standard prior-to-posterior inference. Examples are drawn from causal inference.