C8. Evidence and model odds

Topic: Bayesian hypotheses and model comparison · more questions on this topic
‹ Question 18

What are marginal likelihoods and Bayes factors? How does a Bayes factor update model odds?

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Definitions/notation. For model M_j with a proper parameter prior, its marginal likelihood is m_j(x)=\int p(x\mid\theta_j,M_j)p(\theta_j\mid M_j)\,d\theta_j, and BF_{12}=m_1(x)/m_2(x) is the Bayes factor for M_1 against M_2. Posterior model odds equal BF_{12} times prior model odds; the Bayes factor alone is not a posterior model probability.