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Laplace Approximation

An approach to approximating the integral of a function ∫ f(x)dx by fitting a multivariate normal density at the maximum x̂ of f(x) and computing the volume under the density. The covariance matrix of the fitted multivariate normal distribution is deter- mined by the Hessian matrix of log f(x) at the maximum x̂. The term is also used for approximating the posterior distribution with a multivariate normal centered at the maximum a posteriori estimate.

Laplace Approximation

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