Simultaneous estimation of gamma means in the presence of a nuisance parameter

Abstract

The problem of simultaneously estimating Gamma means is investigated when the parameters are believed a priori to be similar in size and the shape parameter is unknown. A hierarchical Bayes analysis is performed and a sampling based approach called Gibbs sampling is utilized to perform the necessary calculations. This procedure is then extended to the problem of simultaneously estimating Gamma means with unknown shape parameter when the means are believed a priori to satisfy an r-dimensional generalized linear model. Examples are given to illustrate the proposed methodology.

Keywords:

• Conditional posterior
• Generalized linear model
• Gibbs sampling
• Hierarchical Bayes
• Link function
• Nuisance parameter
• Simultaneous estimation
• Unconditional posterior