where all quantities in ( pare computed using the first columns of figure shows the resulting posterior density ( ythe figure also shows the posterior density  ( )where ( = [ln( ( ln( ( ( :exp is derived from the bic approximation ( in both casesthere is clear maximum at suggesting that third-degree polynomial is the most appropriate model for the data figure posterior probabilities for each polynomial model of degree suppose that we wish to compare two modelssay model and model instead of computing the posterior ( texplicitlywe can compare the posterior odds ratiog( tg( ( ( tg( ( { bayes factor this gives rise to the bayes factor bi whose value signifies the strength of the evidence in favor of model over model in particular bi means that the evidence in favor for model is larger example (savage-dickey ratiosuppose that we have two models model has likelihood ( unp )depending on two parameters model has the same functional form for the likelihood but now is fixed to some (knownn that isg( up ( un we also assume that the prior information on bayes factor