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The Estimation of Prior Distributions in Problems of Decision

D. A. Sprott
Sankhyā: The Indian Journal of Statistics, Series A (1961-2002)
Vol. 29, No. 3 (Sep., 1967), pp. 227-238
Published by: Springer on behalf of the Indian Statistical Institute
Stable URL: http://www.jstor.org/stable/25049474
Page Count: 12
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The Estimation of Prior Distributions in Problems of Decision
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Abstract

The problems of inference associated with unique decisions and repetitive decisions are considered. For a repetitive inference under changing states of nature μ, the actual frequency distribution of these states g(μ;θ) must be known or estimated, so that Bayes' theorem can be applied. This is done assuming the frequency distribution g(μ; θ) belongs to a family of distributions specified by parameters θ. Previous samples s are used to obtain the fiducial distribution or likelihood of θ, which is then subsequently used to obtain an estimate of prior distribution f(μ;s). This differs from previous empirical methods by not only estimating the distribution, but in taking note of the uncertainty of the estimate. In this way fiducial and frequency distributions are combined to form an overall measure of uncertainty. This is compared with alternative procedures that have occurred in the literature. The case of inference for a unique decision is considered, where it seems only the fiducial distribution or likelihood are necessary or available. This is essentially the problem of inference from a unique sample considered by Fisher, and may lead to procedures that are inadmissible. It is pointed out that admissibility seems to be an irrelevant considerations for such situations.

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