Document Type

Article

Publication Version

Published Version

Publication Date

2007

Journal or Book Title

Proyecciones

Volume

26

Issue

3

First Page

281

Last Page

308

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

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