Bayes Estimators in Group Testing

Title & Authors
Bayes Estimators in Group Testing
Kwon, Se-Hyug;

Abstract
Binomial group testing or composite sampling is often used to estimate the proportion, p, of positive(infects, defectives) in a population when that proportion is known to be small; the potential benefits of group testing over one-at-a-time testing are well documented. The literature has focused on maximum likelihood estimation. We provide two Bayes estimators and compare them with the MLE. The first of our Bayes estimators uses an uninformative Uniform (0, 1) prior on p; the properties of this estimator are poor. Our second Bayes estimator uses a much more informative prior that recognizes and takes into account key aspects of the group testing context. This estimator compares very favorably with the MSE, having substantially lower mean squared errors in all of the wide range of cases we considered. The priors uses a Beta distribution, Beta ($\small{\alpha}$, $\small{\beta}$), and some advice is provided for choosing the parameter a and $\small{\beta}$ for that distribution.
Keywords
Group testing;Bayes;MLE;Beta prior;Uniform prior;
Language
English
Cited by
1.
Bayesian Inference for Multinomial Group Testing,;;

Communications for Statistical Applications and Methods, 2007. vol.14. 1, pp.81-92
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