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Non‐conjugate prior distribution assessment for multivariate normal sampling

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  • Paul H. Garthwaite
  • Shafeeqah A. Al‐Awadhi

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.

Suggested Citation

  • Paul H. Garthwaite & Shafeeqah A. Al‐Awadhi, 2001. "Non‐conjugate prior distribution assessment for multivariate normal sampling," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 95-110.
    • Handle: RePEc:bla:jorssb:v:63:y:2001:i:1:p:95-110
    DOI: 10.1111/1467-9868.00278
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    Cited by:

    1. Triantafyllopoulos, K., 2008. "Missing observation analysis for matrix-variate time series data," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2647-2653, November.
    2. Werner, Christoph & Bedford, Tim & Cooke, Roger M. & Hanea, Anca M. & Morales-Nápoles, Oswaldo, 2017. "Expert judgement for dependence in probabilistic modelling: A systematic literature review and future research directions," European Journal of Operational Research, Elsevier, vol. 258(3), pages 801-819.
    3. S. A. Al-Awadhi & P. H. Garthwaite, 2001. "Prior distribution assessment for a multivariate normal distribution: An experimental study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(1), pages 5-23.
    4. Shafiqah Al-Awadhi & Paul Garthwaite, 2006. "Quantifying expert opinion for modelling fauna habitat distributions," Computational Statistics, Springer, vol. 21(1), pages 121-140, March.
    5. Mary Kynn, 2008. "The ‘heuristics and biases’ bias in expert elicitation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(1), pages 239-264, January.

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