Posterior Distributions for Multivariate Normal Parameters

Geisser, Seymour; Cornfield, Jerome

doi:10.1111/j.2517-6161.1963.tb00518.x

Cited by 96 publications

(71 citation statements)

References 7 publications

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“…Note that for k = 1, it is equal to the independence-Jeffreys prior. Furthermore, Geisser and Cornfield [13] used that prior distribution over the mean vector and the covariance matrix of a multivariate normal distribution and showed that it yields a posterior distribution of the mean vector which reduces to the Fisher-Cornish fiducial density.…”

Section: General Casementioning

confidence: 99%

The multivariate Behrens–Fisher distribution

Girón

Castillo

2010

Journal of Multivariate Analysis

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a b s t r a c tThe main purpose of this paper is the study of the multivariate Behrens-Fisher distribution. It is defined as the convolution of two independent multivariate Student t distributions. Some representations of this distribution as the mixture of known distributions are shown. An important result presented in the paper is the elliptical condition of this distribution in the special case of proportional scale matrices of the Student t distributions in the defining convolution. For the bivariate Behrens-Fisher problem, the authors propose a non-informative prior distribution leading to highest posterior density (H.P.D.) regions for the difference of the mean vectors whose coverage probability matches the frequentist coverage probability more accurately than that obtained using the independence-Jeffreys prior distribution, even with small samples.

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Section: General Casementioning

confidence: 99%

The multivariate Behrens–Fisher distribution

Girón

Castillo

2010

Journal of Multivariate Analysis

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“…The use of conjugate priors is quite common in Bayesian statistics. Several authors (Geisser and Cornfield, 1963;Stone, 1964;Dickey, 1967;Logan and Gupta, 1993, to mention a few) have considered conjugate priors in the context of unknown covariance matrix. However, almost all have used an inverted Wishart density as the prior for the covariance matrix for a sole reason of mathematical tractability.…”

Section: Application To Bayesian Analysis Of the Multivariate Linear mentioning

confidence: 99%

On the matrix-variate generalized hyperbolic distribution and its Bayesian applications

Thabane

Haq

2004

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In the first part of the paper, we introduce the matrix-variate generalized hyperbolic distribution by mixing the matrix normal distribution with the matrix generalized inverse Gaussian density. The p-dimensional generalized hyperbolic distribution of [Barndorff-Nielsen, O. (1978). Hyperbolic distributions and distributions on hyperbolae. Scand. J. Stat., 5, 151-157], the matrix-T distribution and many well-known distributions are shown to be special cases of the new distribution. Some properties of the distribution are also studied. The second part of the paper deals with the application of the distribution in the Bayesian analysis of the normal multivariate linear model.

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“…In Bayesian analyses, (1) arises as: (a) the posterior distribution of the mean of a multivariate normal distribution [22,51]; (b) the marginal posterior distribution of the regression coefficient vector of the traditional multivariate regression model [54]; (c) the marginal prior distribution of the mean of a multinormal process [4]; (d) the marginal posterior distribution of the mean and the predictive distribution of a future observation of the multivariate normal structural model [20]; (e) an approximation to posterior distributions arising in location-scale regression models [52,53]; and (f) the prior distribution for set estimation of a multivariate normal mean [11]. Additional applications of (1) can be seen in the numerous books dealing with the Bayesian aspects of multivariate analysis.…”

Section: Definitionmentioning

confidence: 99%