Bayesian inference for comparing several treatment means under a poisson model
The inference problem of comparing Poisson parameters of k treatment groups with that of a control. is considered from a Bayesian viewpoint assuming independent conjucate prior distributions on . The joint posterior distribution of , is obtained. For studying a hypothesis concerning , a function of having an asymptotic chi-square distribution is derived. The results are useful in biological applications when a scientist is interested in the comparison of k sets of Poisson counts for the treated groups with those of a control group.