Effect of the sample on the posterior probability in bayesian analysis

This paper examines Bayesian posterior probabilities as a function of selected elements within the set of data, x, when the prior distribution is assumed fixed. The posterior probabilities considered here are those of the parameter vector lying in a subset of the total parameter space. The theorems of this paper provide insight into the effect of elements within x on this posterior probability. These results have applications, for example, in the study of the impact of outliers within the data and in the isolation of misspecified parameters in a model.