How to Guide Decisions with Bayes Factors

TL;DR

This paper explains how to use Bayes factors within Bayesian decision theory to guide decisions, especially when prior information is scarce or ambiguous, providing practical step-by-step guidance.

Contribution

It introduces a robust, interval-valued loss function framework for applying Bayes factors in decision-making, relaxing prior distribution restrictions and offering practical guidance.

Findings

Framework for hypothesis-based Bayesian decision-making with robust loss functions

Method to derive optimal decisions from Bayes factors

Guidelines for applying the approach in practical research settings

Abstract

Some scientific research questions ask to guide decisions and others do not. By their nature frequentist hypothesis-tests yield a dichotomous test decision as result, rendering them rather inappropriate for latter types of research questions. Bayes factors, however, are argued to be both able to refrain from making decisions and to be employed in guiding decisions. This paper elaborates on how to use a Bayes factor for guiding a decision. In this regard, its embedding within the framework of Bayesian decision theory is delineated, in which a (hypothesis-based) loss function needs to be specified. Typically, such a specification is difficult for an applied scientist as relevant information might be scarce, vague, partial, and ambiguous. To tackle this issue, a robust, interval-valued specification of this loss function shall be allowed, such that the essential but partial information can be included into the analysis as is. Further, the restriction of the prior distributions to be proper distributions (which is necessary to calculate Bayes factors) can be alleviated if a decision is of interest. Both the resulting framework of hypothesis-based Bayesian decision theory with robust loss function and how to derive optimal decisions from already existing Bayes factors are depicted by user-friendly and straightforward step-by-step guides.