This chapter systematically explores Bayesian hypothesis testing, and describes the

Bayes Factor as the evidence of the quality of one model specification over another. We

start with a general discussion of the state of hypothesis testing in the social and behavioral

sciences and outline where Bayesian posterior descriptions can replace a number of prob-

lematic practices. The emphasis will be mainly on using Bayesian tools for determining

the strength of evidence, rather than the details of the many differences between Bayesian

and non-Bayesian approaches. For a very clear, and succinct, discussion of the historical

developments in this regard, see Marden (2000).