Journal or Book Title
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.
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.
Alicia L. Carriquiry and Wolfgang Kliemann
Carriquiry, Alicia L. and Kliemann, Wolfgang, "The modes of posterior distributions for mixed linear models" (2007). Statistics Publications. 22.