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Abstract
Journal of Official Statistics, Vol.11, No.4, 1995. pp. 379390

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Comparison Between Maximum Likelihood and Bayes Methods for Estimation of Binomial Probability with Sample Compositing

Abstract:
This article focuses on the Bayesian approach to estimating a population prevalence rate through the method of sample compositing which has important applications in environmental sampling as well as in estimating the prevalence of certain diseases, etc. This method requires random samples of fixed size k, which is determined before the experimentation based on cost consideration as well as the target error in the form of the mean squared error of the estimator. Thus, two choices of prior may be available to the experimenter, (i) the prior on P, the population proportion, (ii) the prior on P′=1−;(1−;P)k, the group prevalence proportion. These two choices are considered in this article and their performance has been evaluated in comparison with the maximum likelihood estimator. It is observed that the Bayes methodology offers different choices to the experimenter with possible reduction in cost as well as error.

Keywords:
Batch sampling; composite sample; Bayes estimate; MLE; bias correction.

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