Sets of Priors Reflecting Prior-Data Conflict and Agreement

TL;DR

This paper introduces a novel method for generating sets of priors in Bayesian analysis that adaptively reflect prior-data conflict or agreement, enhancing the robustness and informativeness of posterior inferences.

Contribution

It proposes a new approach to create prior sets that are sensitive to prior-data conflict and agreement, improving imprecise Bayesian modeling.

Findings

Prior-data conflict increases posterior imprecision

Strong prior-data agreement decreases posterior imprecision

Method enhances robustness of Bayesian inference

Abstract

In Bayesian statistics, the choice of prior distribution is often debatable, especially if prior knowledge is limited or data are scarce. In imprecise probability, sets of priors are used to accurately model and reflect prior knowledge. This has the advantage that prior-data conflict sensitivity can be modelled: Ranges of posterior inferences should be larger when prior and data are in conflict. We propose a new method for generating prior sets which, in addition to prior-data conflict sensitivity, allows to reflect strong prior-data agreement by decreased posterior imprecision.