50 shades of Bayesian testing of hypotheses

TL;DR

This paper discusses Bayesian methods for hypothesis testing and model selection, highlighting challenges like prior specification, calibration, and computation, and proposing solutions to improve their practical application.

Contribution

It introduces novel Bayesian testing techniques that address prior and calibration issues, enhancing the reliability of Bayesian hypothesis testing.

Findings

Bayesian tests can be calibrated more effectively.

New methods improve computational efficiency.

Proposed approaches outperform traditional Bayesian tests.

Abstract

Hypothesis testing and model choice are quintessential questions for statistical inference and while the Bayesian paradigm seems ideally suited for answering these questions, it faces difficulties of its own ranging from prior modelling to calibration, to numerical implementation. This c