A Bayesian approach to some outlier problems

The problem of outlying observations is considered from a Bayesian viewpoint. We suppose that each of the observations in an experiment in an experiment may come from either a ‘good’ run or a ‘bad’ run. By specifying the models corresponding to good and bad runs and the prior probabilities of which runs being bad, we then employ standard Bayesian inference procedures to derive the appropriate analysis. In particular, we consider the linear model and assume that a good observation is normally distributed about its mean with variance σ2, and a bad one is normal with the same mean but a larger variance k2σ2. An example is given.