Bayes factor ($B_{01}$)

A Bayes factor compares two models through the ratio of their model evidences, $B_{01}=p(D\mid M_0)/p(D\mid M_1)$.

For suitable nested models whose common nuisance parameters have matching priors, the Savage-Dickey density ratio expresses a Bayes factor as posterior density divided by prior density at the nested parameter value.