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Laplace Approximations for Natural Exponential Families with Cuts

Author

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  • M. Efstathiou
  • E. Gutiérrez‐Peña
  • A. F. M. Smith

Abstract

Standard and fully exponential form Laplace approximations to marginal densities are described and conditions under which these give exact answers are investigated. A general result is obtained and is subsequently applied in the case of natural exponential families with cuts, in order to derive the marginal posterior density of the mean parameter corresponding to the cut, the canonical parameter corresponding to the complement of the cut and transformations of these. Important cases of families for which a cut exists and the approximations are exact are presented as examples

Suggested Citation

  • M. Efstathiou & E. Gutiérrez‐Peña & A. F. M. Smith, 1998. "Laplace Approximations for Natural Exponential Families with Cuts," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 25(1), pages 77-92, March.
    • Handle: RePEc:bla:scjsta:v:25:y:1998:i:1:p:77-92
    DOI: 10.1111/1467-9469.00090
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