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In mathematics, Laplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form
where is a twice-differentiable function, M is a large number, and the endpoints a and b could possibly be infinite. This technique was originally presented in Laplace (1774).
In Bayesian statistics, Laplace's approximation can refer to either approximating the posterior normalizing constant with Laplace's method[1] or approximating the posterior distribution with a Gaussian centered at the maximum a posteriori estimate.[2] Laplace approximations are used in the integrated nested Laplace approximations method for fast approximate Bayesian inference.
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