Posterior odds

Topic: Model selection for stochastic models · more questions on this topic
BIC and AIC by hand ›

Two models have prior probabilities \mathbb{P}(M_1)=0.25 and \mathbb{P}(M_2)=0.75, and the data give Bayes factor B_{12}=6. Find the posterior odds and the posterior probability of M_1.

Worked answer (click to show)

Bayes factors multiply odds. Convert the prior to odds first and convert back only after applying the evidence factor. The prior odds are 0.25/0.75=1/3, so the posterior odds are

B_{12}\times\frac{\mathbb{P}(M_1)}{\mathbb{P}(M_2)}=6\times\frac13=2.

The posterior probability of M_1 is 2/(1+2)=2/3\approx 0.667.