THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS

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 a...

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Detalles Bibliográficos
Autores principales:	CARRIQUIRY,ALICIA L, KLIEMANN,WOLFGANG
Lenguaje:	English
Publicado:	Universidad Católica del Norte, Departamento de Matemáticas 2007
Materias:	Posterior modes mixed linear models poly-t distributions
Acceso en línea:	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000300006
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spelling	oai:scielo:S0716-091720070003000062008-01-28THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELSCARRIQUIRY,ALICIA LKLIEMANN,WOLFGANG 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.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.26 n.3 20072007-12-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000300006en10.4067/S0716-09172007000300006
institution	Scielo Chile
collection	Scielo Chile
language	English
topic	Posterior modes mixed linear models poly-t distributions
spellingShingle	Posterior modes mixed linear models poly-t distributions CARRIQUIRY,ALICIA L KLIEMANN,WOLFGANG THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS
description	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.
author	CARRIQUIRY,ALICIA L KLIEMANN,WOLFGANG
author_facet	CARRIQUIRY,ALICIA L KLIEMANN,WOLFGANG
author_sort	CARRIQUIRY,ALICIA L
title	THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS
title_short	THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS
title_full	THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS
title_fullStr	THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS
title_full_unstemmed	THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS
title_sort	modes of posterior distributions for mixed linear models
publisher	Universidad Católica del Norte, Departamento de Matemáticas
publishDate	2007
url	http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172007000300006
work_keys_str_mv	AT carriquiryalicial themodesofposteriordistributionsformixedlinearmodels AT kliemannwolfgang themodesofposteriordistributionsformixedlinearmodels AT carriquiryalicial modesofposteriordistributionsformixedlinearmodels AT kliemannwolfgang modesofposteriordistributionsformixedlinearmodels
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THE MODES OF POSTERIOR DISTRIBUTIONS FOR MIXED LINEAR MODELS

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