Introducing prior information in Weighted Likelihood Bootstrap with applications to model misspecification

TL;DR

This paper introduces Posterior Bootstrap, an extension of Weighted Likelihood Bootstrap that incorporates prior information and addresses model misspecification in Bayesian inference, with applications to hierarchical models and improved robustness.

Contribution

It presents new algorithms for integrating prior knowledge into Weighted Likelihood Bootstrap and extends the methodology to hierarchical models, enhancing robustness against model misspecification.

Findings

Reduces impact of model misspecification compared to traditional Bayesian methods

Provides theoretical insights via Edgeworth expansions

Experimental results confirm improved inference accuracy

Abstract

We propose Posterior Bootstrap, a set of algorithms extending Weighted Likelihood Bootstrap, to properly incorporate prior information and address the problem of model misspecification in Bayesian inference. We consider two approaches to incorporating prior knowledge: the first is based on penalization of the Weighted Likelihood Bootstrap objective function, and the second uses pseudo-samples from the prior predictive distribution. We also propose methodology for hierarchical models, which was not previously known for methods based on Weighted Likelihood Bootstrap. Edgeworth expansions guide the development of our methodology and allow us to provide greater insight on properties of Weighted Likelihood Bootstrap than were previously known. Our experiments confirm the theoretical results and show a reduction in the impact of model misspecification against Bayesian inference in the misspecified setting.