If you need an accessible version of this item please contact JSTOR User Support

An Application of the Laplace Method to Finite Mixture Distributions

Sybil L. Crawford
Journal of the American Statistical Association
Vol. 89, No. 425 (Mar., 1994), pp. 259-267
DOI: 10.2307/2291222
Stable URL: http://www.jstor.org/stable/2291222
Page Count: 9
  • Download PDF
  • Cite this Item

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If you need an accessible version of this item please contact JSTOR User Support
An Application of the Laplace Method to Finite Mixture Distributions
Preview not available

Abstract

An exact Bayesian analysis of finite mixture distributions is often computationally infeasible, because the number of terms in the posterior density grows exponentially with the sample size. A modification of the Laplace method is presented and applied to estimation of posterior functions in a Bayesian analysis of finite mixture distributions. The procedure, which involves computations similar to those required in maximum likelihood estimation, is shown to have high asymptotic accuracy for finite mixtures of certain exponential-family densities. For these mixture densities, the posterior density is also shown to be asymptotically normal. An approximation of the posterior density of the number of components is presented. The method is applied to Duncan's barley data and to a distribution of lake chemistry data for north-central Wisconsin.

Page Thumbnails

  • Thumbnail: Page 
259
    259
  • Thumbnail: Page 
260
    260
  • Thumbnail: Page 
261
    261
  • Thumbnail: Page 
262
    262
  • Thumbnail: Page 
263
    263
  • Thumbnail: Page 
264
    264
  • Thumbnail: Page 
265
    265
  • Thumbnail: Page 
266
    266
  • Thumbnail: Page 
267
    267