Error bounds for multidimensional Laplace approximation

@article{Mcclure1983ErrorBF,
  title={Error bounds for multidimensional Laplace approximation},
  author={J. P. Mcclure and R. Wong},
  journal={Journal of Approximation Theory},
  year={1983},
  volume={37},
  pages={372-390}
}
Abstract A numerical estimate is obtained for the error associated with the Laplace approximation of the double integral I ( λ ) = ∝∝ D g ( x , y ) e − λf ( x , y ) dx dy , where D is a domain in R 2 , λ is a large positive parameter, f ( x , y ) and g ( x , y ) are real-valued and sufficiently smooth, and ∝( x , y ) has an absolute minimum in D . The use of the estimate is illustrated by applying it to two realistic examples. The method used here applies also to higher dimensional integrals. 
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