Bayesian Selective Inference: Non-informative Priors

TL;DR

This paper examines Bayesian inference for selected parameters, critiques existing approaches, and introduces two non-informative priors that enable well-calibrated inference both Bayesianly and frequentistically.

Contribution

It proposes novel non-informative priors for Bayesian selective inference, addressing gaps in existing methods and enabling better calibration.

Findings

Proposed priors perform well in empirical tests

New priors facilitate both Bayesian and frequentist inference

Analysis clarifies correct Bayesian approach under selection

Abstract

We discuss Bayesian inference for parameters selected using the data. First, we provide a critical analysis of the existing positions in the literature regarding the correct Bayesian approach under selection. Second, we propose two types of non-informative priors for selection models. These priors may be employed to produce a posterior distribution in the absence of prior information as well as to provide well-calibrated frequentist inference for the selected parameter. We test the proposed priors empirically in several scenarios.