Laplace Approximation

Posted 2012.10.19 19:26
Laplace's method
From Wikipedia, the free encyclopedia

In mathematicsLaplace's method, named after Pierre-Simon Laplace, is a technique used to approximate integrals of the form

 \int_a^b\! e^{M f(x)} \, dx

where ƒ(x) is some twice-differentiable functionM is a large number, and the integral endpoints aand b could possibly be infinite. This technique was originally presented in Laplace (1774, pp. 366–367).

\int_a^b\! e^{M f(x)}\, dx\approx \sqrt{\frac{2\pi}{M|f''(x_0)|}}e^{M f(x_0)}  \mbox { as } M\to\infty. \,


 

 관련 논문과 발표 자료 

1. accurate approximations for posterior moments and marginal de

2. fully exponential laplace approximations to Expectations and

3. Laplace’s Method Approximations for Probabilistic Inference i

4. fully exponential laplace approximations using asymptotic mod

Laplace Approximation.pptx


 정리한 것 SCAN 











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