Laplace Approximation of High Dimensional Integrals
- 1 November 1995
- journal article
- research article
- Published by Oxford University Press (OUP) in Journal of the Royal Statistical Society Series B: Statistical Methodology
- Vol. 57 (4) , 749-760
- https://doi.org/10.1111/j.2517-6161.1995.tb02060.x
Abstract
It is shown that the usual Laplace approximation is not a valid asymptotic approximation when the dimension of the integral is comparable with the limiting parameter n. The formal Laplace expansion for multidimensional integrals is given and used to construct asymptotic approximations for high dimensional integrals. One example is considered in which the dimension of the integral is O(n1/2) and the relative error of the unmodified Laplace approximation is O(1). Nevertheless, it is possible to construct a valid asymptotic expansion by regrouping terms in the formal expansion according to asymptotic order in n.This publication has 8 references indexed in Scilit:
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