If sample size (n) was so large enough, Bayesian information criterion (BIC), an evaluation criteria of model estimated by maximum likelihood method, would be approximated with Laplace method by integrating marginal likelihood corresponding to posterior probability of model. θ is a parameter of p-dimension and f(xn|θ) is probability distribution function, respectively.
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Probability density function, expected value and variance of each probability distribution
How to calculate Akaike information criterion with probability distribution function?
