The modes of posterior distributions for mixed linear models

  • Alicia L. Carriquiry Iowa State University.
  • Wolfgang Kliemann Iowa State University.
Palabras clave: Posterior modes, Mixed linear models, Poly-t distributions.


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.

Biografía del autor

Alicia L. Carriquiry, Iowa State University.
Department of Statistics, Iowa State University, U. S. A.Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago Chile. 
Wolfgang Kliemann, Iowa State University.
Department of Mathematics, Iowa State University, U. S. A.  Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago Chile.


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Cómo citar
Carriquiry, A., & Kliemann, W. (2017). The modes of posterior distributions for mixed linear models. Proyecciones. Journal of Mathematics, 26(3), 281-308.

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