
Accession Number : ADA132303
Title : Enriched Multinormal Priors Revisited.
Descriptive Note : Research rept.,
Corporate Author : CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER
Personal Author(s) : Jewell,William S
PDF Url : ADA132303
Report Date : Nov 1982
Pagination or Media Count : 50
Abstract : In a 1974 paper, the author indicated how natural conjugate priors for multidimensional exponential family likelihoods could be enriched in certain cases through linear transformations of independent marginal priors. In particular, it was shown how the usual NormalWishart prior for the multinormal distribution with unknown mean vector and precision matrix could have the number of hyperparameters increased; thinness of the traditional prior is wellknown. The new, linearlydependent prior leads to fulldimensional credibility prediction formulae for the observational mean vector and covariance matrix, as contrasted with the simpler, selfdimensional forecasts obtained in prior literature. However, there was an error made in the sufficientstatistics term of the covariance predictor which is corrected in this work. In addition, this paper explains in detail the properties of the enriched multinormal prior and why revised statistics are needed, and interprets the important relationship between the linear transformation matrix and the matrix of credibility time constants. An enumeration of the additional number of hyperparameters needed for the enriched prior shows its value in modelling multinormal problems; it is shown that the estimation of these hyperparameters can be carried out in a natural way, in the space of the observable variables. (Author)
Descriptors : *Multivariate analysis, *Exponential functions, Bayes theorem, Mathematical prediction, Covariance, Matrices(Mathematics), Transformations(Mathematics), Random variables, Distribution functions, Errors, Corrections
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE