Inverse Probability Weighting in a Post-Bayesian World

2026-06-26

AI Summary

This study addresses the challenge of accurate parameter estimation in Bayesian inference when selection bias and systematic bias are present. The authors propose a generalized Bayesian approach that, for the first time, integrates inverse probability weighting (IPW) into the Bayesian framework. By interpreting IPW as a reweighting of the Kullback–Leibler divergence between the model and the true data-generating mechanism, they construct a posterior distribution that simultaneously inherits the bias-correction properties of frequentist IPW and maintains Bayesian coherence. Theoretical analysis establishes favorable asymptotic convergence properties of the proposed posterior. Empirical validation on both simulated data and a large-scale prostate cancer registry dataset—used to predict mortality based on PSA levels—demonstrates the method’s effectiveness, substantially extending the applicability of Bayesian inference to settings with biased observations.

Abstract

We present a justification of the use of Inverse Probability Weighting (IPW) in a post-Bayesian framework, in which the bias-correction provided by IPW in a frequentist context is reframed as a reweighting of the Kullback-Leibler (KL) divergence between the statistical model and the true data-generating parameter value. We provide a coherent argument in support of this approach, including theoretical results concerning convergence and properties of the generalised belief posteriors. We present examples demonstrating the utility of post-Bayesian IPW in practice: these include two simulated examples of inference under selection bias in the observed data, and a large-scale real-data example concerning systematic biases present in registry data when using prostate-specific antigen (PSA) to predict prostate cancer mortality. The empirical and theoretical results together show the utility of IPW to address classes of problems previously intractable within a Bayesian approach.

Problem

• selection bias
• systematic bias
• Bayesian inference
• inverse probability weighting
• KL divergence

Innovation

• Inverse Probability Weighting
• Post-Bayesian
• KL divergence
• Selection bias
• Generalised belief posterior