Bayesian Estimation of Small Proportions Using Binomial Group Test

Authors

Shihua Luo, Florida International UniversityFollow

Document Type

Thesis

Degree

Master of Science (MS)

Major/Program

Statistics

First Advisor's Name

Jie Mi

First Advisor's Committee Title

Committee Chair

Second Advisor's Name

Kai Huang

Third 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.

Identifier

FI12112706

Recommended Citation

Luo, Shihua, "Bayesian Estimation of Small Proportions Using Binomial Group Test" (2012). FIU Electronic Theses and Dissertations. 744.
https://digitalcommons.fiu.edu/etd/744