Restricted Bayes Estimates for Binomial Parameters

James D. Broffitt
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James D. Broffitt: University of Iowa

A chapter in Probability and Bayesian Statistics, 1987, pp 61-72 from Springer

Abstract: Abstract Let θ = (θ1,...,θk) be the parameters for k independent binomial random variables. We wish to estimate θ under the restriction θ ∊ R where R is a k-dimensional subset of the full parameter space {θ; 0 ≤ θi ≤ 1, i = 1,...,k}. Bayes estimators (means of posteriors) are developed for θ which correspond to prior distributions that assign probability one to the set R. Since the support of the resulting posterior is R, the posterior mean will be in R if R is a convex set. A bioassay example is given where the parameters are assumed to be increasing, or increasing and S-shaped.

Date: 1987
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DOI: 10.1007/978-1-4613-1885-9_7

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