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Parametric empirical Bayes PEB may perform poorly when the assumed prior distribution is seriously invalid Nonparametric empirical Bayes NEB is more robust since it imposes no restric tion on the prior But compared with the PEB the NEB may be ine cient for small to medium samples due to the large variation and under dispersion of the NPMLE of the prior Using Monte Carlo simulations we compare t...

The Borel-Tanner probability distribution was derived by Borel (1942) and Tanner (1953) to characterize the distribution behavior of the number of customers served in a queuing system with Poisson input and constant service time. Later this probability distribution was applied in some models for random trees and branching processes. In the latter case one of the parameters can be interpreted as...

Microarrays are a novel technology that facilitates the simultaneous measurement of thousands of gene expression levels. A typical microarray experiment can produce millions of data points, raising serious problems of data reduction, and simultaneous inference. We consider one such experiment in which oligonucleotide arrays were employed to assess the genetic effects of ionizing radiation on se...

In empirical Bayes inference one is typically interested in sampling from the posterior distribution of a parameter with a hyper-parameter set to its maximum likelihood estimate. This is often problematic particularly when the likelihood function of the hyper-parameter is not available in closed form and the posterior distribution is intractable. Previous works have dealt with this problem usin...

The empirical Bayes estimator of the probability of a successful event is deduced from mixed distributions. Specially, binomial and Poisson mixed distributions are analyzed. Some mixing distributions, well known in Reliability, Queuing Theory and other areas of Engineering, are considered. As it will be shown, a family of estimators with interesting characteristics is obtained for different mix...