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Non-conjugate prior distribution assessment for multivariate normal sampling

Garthwaite, Paul H. and Al-Awadhi, Shafeeqah A. (2001). Non-conjugate prior distribution assessment for multivariate normal sampling. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 63(1) pp. 95–110.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1111/1467-9868.00278
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Abstract

Elicitation methods are proposed for quantifying expert opinion about a multivariate normal sampling model. The natural conjugate prior family imposes a relationship between the mean vector and the covariance matrix that can portray an expert's opinion poorly. Instead we assume that opinions about the mean and the covariance are independent and suggest innovative forms of question which enable the expert to quantify separately his or her opinion about each of these parameters. Prior opinion about the mean vector is modelled by a multivariate normal distribution and about the covariance matrix by both an inverse Wishart distribution and a generalized inverse-Wishart (GIW) distribution. To construct the latter, results are developed that give insight into the GIW parameters and their interrelationships. Certain of the elicitation methods exploit unconditional assessments as fully as possible, since these can reflect an expert's beliefs more accurately than conditional assessments. Methods are illustrated through an example.

Item Type: Journal Article
ISSN: 1467-9868
Keywords: Assessment tasks; Elicitation; Generalized inverse Wishart distribution; Non-conjugate distribution; Prior distribution; Subjective probability
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 3444
Depositing User: Users 2598 not found.
Date Deposited: 27 Jun 2006
Last Modified: 10 Jul 2013 13:53
URI: http://oro.open.ac.uk/id/eprint/3444
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