Laplace expansion for posterior densities of nonlinear functions of parameters

Wing Hung Wong, Bing Li

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20 Scopus citations

Abstract

SUMMARY: An asymptotic expansion for marginal posterior densities of nonlinear functions of parameters is derived. The density in question is proportional to an integral over a lower dimensional manifold with the integrand including an appropriate change-in-volume term, Laplace's method is applied to obtain the expansion. Avoiding the difficult step of the explicit parameterization of the manifold, we carry out the expansion via an implicit and local parameterization, and the derivatives required can be evaluated recursively. An example indicates a considerable improvement by including the term of order O(n-1).

Original languageEnglish (US)
Pages (from-to)393-398
Number of pages6
JournalBiometrika
Volume79
Issue number2
DOIs
StatePublished - Jun 1 1992

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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