Ononot — In a Bayesian analysis with data D and prior \pi(\theta), th

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Inferential Statisticshard

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In a Bayesian analysis with data $D$ and prior $\pi(\theta)$ , the marginal likelihood is $p(D) = \int L(D|\theta)\pi(\theta) d\theta$ . If the posterior is $\pi(\theta|D) = \frac{L(D|\theta)\pi(\theta)}{p(D)}$ , what role does the marginal likelihood play in model selection?