Some results about Bayesian experiments with discrete sample space and positive sampling probabilities

Abstract

Assuming that the sample space is discrete and sampling distributions assign positive probability to any point of the sample space, whatever is the prior distribution we have a regular Bayesian experiment. In this note we show that, if we consider two different priors, we have two different families of posterior distributions; moreover we give a characterization for the families of probability measures on the parameter space which can be seen as families of posterior distributions for a prior distribution.