Document Type
Thesis
Degree
Master of Science (MS)
Department
Statistics
Advisor's Name
Jie Mi
Advisor's Title
Committee Chair
Advisor's Name
Kai Huang
Advisor's Name
Florence George
Keywords
Group Test, Bayes Estimator, Beta Distribution, MLE, MSE.
Date of Defense
11-9-2012
Abstract
Group testing has long been considered as a safe and sensible relative to one-at-a-time testing in applications where the prevalence rate p is small. In this thesis, we applied Bayes approach to estimate p using Beta-type prior distribution. First, we showed two Bayes estimators of p from prior on p derived from two different loss functions. Second, we presented two more Bayes estimators of p from prior on π according to two loss functions. We also displayed credible and HPD interval for p. In addition, we did intensive numerical studies. All results showed that the Bayes estimator was preferred over the usual maximum likelihood estimator (MLE) for small p. We also presented the optimal β for different p, m, and k.
Recommended Citation
Luo, Shihua, "Bayesian Estimation of Small Proportions Using Binomial Group Test" (2012). FIU Electronic Theses and Dissertations. Paper 744.
http://digitalcommons.fiu.edu/etd/744