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In statistics, there are a variety of methods for performing model selectionthat all stem from slightly different paradigms of statistical inference. Thereasons for choosing one particular method over another seem to be basedentirely on philosophical preferences. In the case of non-nested modelselection, two of the prevailing techniques are the Bayes Factor and thelikelihood ratio. This article focuses on reconciling the likelihood ratio andthe Bayes Factor for comparing a pair of non-nested models under two differentproblem frameworks typical in forensic science, the common-source and thespecific-source problem. We show that the Bayes Factor can be expressed as theexpected value of the corresponding likelihood ratio function with respect tothe posterior distribution for the parameters given the entire set of datawhere the set(s) of unknown-source observations has been generated according tothe second model. This expression leads to a number of useful theoretic andpractical results relating the two statistical approaches. This relationship isquite meaningful in many scientific applications where there is a generalconfusion between the various statistical methods, and particularly in the caseof forensic science.

Reconciling the Bayes Factor and Likelihood Ratio for Two Non-Nested Model Selection Problems