| The Poisson distribution is often used to model counts of occurrences of certain events. Many applications exist where these counts are fallible. Both classical and Bayesian research exists on the Poisson model that allows for false negatives. In this dissertation a Poisson model that allows for both false positives and false negatives is presented. The parameters of this model are estimated from both the Bayesian and classical perspectives.;Computational procedures such as the Gibbs sampler, weighted bootstrap, and the EM algorithm are presented for inference when the sample size is large. These methods are used in the applications of the model to real data sets. Applications include interval estimation, a subset selection procedure, and a multiple comparisons procedure. Poisson regression is also considered from both the Bayesian and classical perspective. |
