Equal likelihoods preserve model odds
= Equal likelihoods preserve model odds
{title2=$P(D\mid H_1)=P(D\mid H_2)\Rightarrow O_{12}(D)=O_{12}$}
For two models with finite positive <prior odds>, a sequence of data with identical conditional <likelihoods> under both models has <Bayes factor> one. The <posterior odds> therefore equal the <prior odds>. This requires equality of the <probability> model for all the data considered, not merely that both models fit a selected data set.