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Prior distribution assessment for a multivariate normal distribution: An experimental study

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  • S. A. Al-Awadhi
  • P. H. Garthwaite

Abstract

A variety of methods of eliciting a prior distribution for a multivariate normal (MVN) distribution have recently been proposed. This paper reports an experiment in which 16 meteorologists used the methods to quantify their opinions about climatology variables. Our results compare prior models and show, in particular, that it can be better to assume the mean and variance of an MVN distribution are independent a priori, rather than to model opinion by the conjugate prior distribution. Using a proper scoring rule, different forms of assessment task are examined and alternative ways of estimating parameters are compared. To quantify opinion about means, it proved preferable to ask directly about the means rather than individual observations while, to quantify opinion about the variance matrix, it was best to ask about deviations from the mean. Further results include recommendations for the way parameters of the prior distribution are estimated.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:japsta:v:28:y:2001:i:1:p:5-23
    DOI: 10.1080/02664760120011563
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    References listed on IDEAS

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    1. van Lenthe, Jelle, 1994. "Scoring-Rule Feedforward and the Elicitation of Subjective Probability Distributions," Organizational Behavior and Human Decision Processes, Elsevier, vol. 59(2), pages 188-209, August.
    2. Garthwaite, Paul H. & Dickey, James M., 1985. "Double- and single-bisection methods for subjective probability assessment in a location-scale family," Journal of Econometrics, Elsevier, vol. 29(1-2), pages 149-163.
    3. 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.
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    Cited by:

    1. 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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