Bayesian approaches to the detection of outliers in poisson samples

Abstract

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.

Keywords:

• Bayes factor
• Imaginary observation
• Outliers