Bayes Factor–Based Test Statistics
This chapter provides a basic introduction to the Bayesian view of statistical testing strategies with a focus on Bayes factor— type principles. Alternatively, one can provide testing procedures substituting the unknown alternative parameter with variables that do not depend on the observed data. Such approaches can be extended to provide test procedures within a Bayes factor–type framework. The chapter explores topics regarding the use of representative values instead of unknown parameters, as well as Bayes factor principles. Under Bayes factor type of statistical decision-making mechanisms, external information is incorporated into the evaluation of evidence about a hypothesis, and functions that represent possible parameter values under the alternative hypothesis are considered. The Bayes factor, as the centerpiece in Bayesian evaluation of evidence, closely presents human considerations of decision-making mechanisms based on formal statistical tests. Bayes factors involve computation of integrals usually solved via numerical integration.