Bayesian analysis of an intervened poisson distribution

Abstract

The intervened Poisson distribution (IPD) was introduced by Shanmugam (1985) as a replacement for the zero-truncated Poisson distribution in order to model rare event count data when some intervention process may alter the mean of the rare event generating process under observation. This paper will demonstrate how a full Bayesian analysis of an intervened Poisson model may proceed by making use of the Gibbs sampler and adaptive rejection sampling methods for logconcave densities. Both posterior and predictive inferences are discussed and developed. These Bayesian inferential procedures are then applied to the same cholera data previously examined by Shanmugam (1985). The posterior analysis based upon the simulation consistent Gibbs sampling methodology is also compared to the exact analysis developed on the basis of numerical integration.