Bayesian Interval Estimates for Cases of Clinical Mastitis

A great deal of recent research has focused on the theory and application of computationally intensive statistical techniques such as bootstrapping kernel density estimation Gibbs samplers etc Many of these techniques are especially well suited for complex models yet are still very underutilized by scienti c researchers Our interest is in the application of such Bayesian inferential methodology to a data set taken from veterinary epidemiology Schukken et al describe counts of clinical mastitis cases taken from dairy herds over a one year period the parameter of interest is the mean number of cases Because of dependence within herds though caution must be taken in light of possible overdispersion Thus con dence intervals calculated from a Poisson model for counts assuming independence may not be of the correct precision Schukken et al attempt to correct for this by approximating a Poisson model which has an extra parameter for overdispersion but this makes the construction of interval estimates somewhat di cult We approach these data from a Bayesian point of view and introduce a hierarchical Poisson model which allows more exibility to accomodate the overdispersion Analysis of this somewhat complex model necessitates the use of a computational algorithm such as the Gibbs sampler Four estima tors of an equal tailed credible interval for the mean number of cases of clinical mastitis are considered They are an estimator found by aver aging quantities across Gibbs sampler iterations a similarly constructed weighted average estimator an order statistics estimator and an estima tor based on density estimation Additional comparisons are made with the frequentist intervals based on the Schukken et al analysis Our comparisons take into account bias precision and computing time The in tervals surprisingly di er only slightly in location and therefore o er similar conclusions about the prevalence of the disease in the study area Standard errors though are considerably di erent