ABSTRACT
In this chapter, results of a general theory for invariant experiments are used to analyze two classes of models which are particularly important for empirical work, namely, stationary and exchangeable processes. The authors consider experiments constructed from stationary or exchangeable sampling processes, viewed as processes invariant with respect to shifts or to finite permutations. These sampling invariance properties lead to the invariance of the joint probability characterizing the Bayesian experiment, which is, in turn, equivalent to invariance properties of the predictive process and of the posterior expectations. The authors present the concept of representation precise and a basic result that allows one to translate results obtained with respect to a representation to the original experiment.
