Focused Bayesian Prediction

TL;DR

This paper introduces a Bayesian prediction method that improves accuracy by focusing on predictive performance rather than true data model specification, demonstrated through simulations and real data.

Contribution

It presents a novel Bayesian prediction approach that updates priors based on predictive accuracy measures, enhancing predictive performance without requiring true model correctness.

Findings

Notable gains in predictive accuracy over likelihood-based methods

Effective in simulation experiments and empirical data

Posterior concentrates on models with highest predictive accuracy

Abstract

We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After observing data, we update the prior to a posterior over these models, via a criterion that captures a user-specified measure of predictive accuracy. Under regularity, this update yields posterior concentration onto the element of the predictive class that maximizes the expectation of the accuracy measure. In a series of simulation experiments and empirical examples we find notable gains in predictive accuracy relative to conventional likelihood-based prediction.