Bayesian approaches to the detection of outliers in poisson samples

This paper is concerned with the detection of upper outliers in a Poisson sample.The approach is Bayesian throughout. It is supposed that a small number of observations are contaminated, that is they are generated from a Poisson sample with mean inflated by a factor §.Bayes factors for the cases when (i) § is known, (ii) it is given a proper conjugate prior or (iii) it is completely unknown are discussed. It is suggested, in contrast to classical approaches, that transforming the data to normality does not simplify the problem.