On Bayes factor functions

TL;DR

This paper introduces Bayes factor functions based on common test statistics using inverse-moment priors, compares them to local priors, and applies them to psychological experiments, enhancing Bayesian hypothesis testing.

Contribution

It develops a new class of Bayes factor functions with inverse-moment priors for standardized effects, offering a novel approach to Bayesian hypothesis testing with practical applications.

Findings

Bayes factor functions with inverse-moment priors perform well in simulations.

Comparison shows differences between local and non-local prior-based Bayes factors.

Application to psychology experiments demonstrates practical utility.

Abstract

We describe Bayes factors functions based on the sampling distributions of \emph{z}, \emph{t}, $\chi^2$, and \emph{F} statistics, using a class of inverse-moment prior distributions to define alternative hypotheses. These non-local alternative prior distributions are centered on standardized effects, which serve as indices for the Bayes factor function. We compare the conclusions drawn from resulting Bayes factor functions to those drawn from Bayes factors defined using local alternative prior specifications and examine their frequentist operating characteristics. Finally, an application of Bayes factor functions to replicated experimental designs in psychology is provided.