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Article
The modes of posterior distributions for mixed linear models
Proyecciones
  • Alicia L. Carriquiry, Iowa State University
  • Wolfgang Kliemann, Iowa State University
Document Type
Article
Publication Version
Published Version
Publication Date
1-1-2007
DOI
10.4067/S0716-09172007000300006
Abstract
Mixed linear models, also known as two-level hierarchical models, are commonly used in many applications. In this paper, we consider the marginal distribution that arises within a Bayesian framework, when the components of variance are integrated out of the joint posterior distribution. We provide analytical tools for describing the surface of the distribution of interest. The main theorem and its proof show how to determine the number of local maxima, and their approximate location and relative size. This information can be used by practitioners to assess the performance of Laplace-type integral approximations, to compute possibly disconnected highest posterior density regions, and to custom-design numerical algorithms.
Comments

This article is from Proyecciones 26 (2007): 281, doi:10.4067/S0716-09172007000300006. Posted with permission.

Rights
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright Owner
Alicia L. Carriquiry and Wolfgang Kliemann
Language
en
File Format
application/pdf
Citation Information
Alicia L. Carriquiry and Wolfgang Kliemann. "The modes of posterior distributions for mixed linear models" Proyecciones Vol. 26 Iss. 3 (2007) p. 281 - 308
Available at: http://works.bepress.com/alicia_carriquiry/27/