On a Proper Bayes, but Inadmissible Estimator

We present an example of a proper Bayes point estimator which is inadmissible. It occurs for a negative binomial model with shape parameter a, probability parameter p, prior densities of the form .(a,p) = . g(a) (1.p)..1, and for estimating the population mean .=a(1.p)/p under squared error loss. Other intriguing features are exhibited such as the constancy of the Bayes estimator with respect to the choice of g, including degenerate or known a cases.