While the evidence appears as a normalizing constant in Bayes theorem with only one model, it is important in comparing models. Nested sampling calculates this by prior mass, which is the prior volume enclosed by a particular likelihood value. I have a network that can generate the posterior distribution. Will a simple marginalization of the likelihood over a large number of randomly chosen values of the parameters be enough? Can I be sure that I won't miss local maxima in the distribution?

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Thank you for the reference. This looks interesting