 The key insight is that in many applications the infinite dimensional distributions appear only as an intermediary computational device and are not required for either the initial specification of prior beliefs or for the statement of the final inference.Given a measurable set "S", a base probability distribution "H" and a positive real number formula_2, the Dirichlet process formula_33 is a stochastic process whose sample path (or realization, i.e.an infinite sequence of random variates drawn from the process) is a probability distribution over "S", such that the following holds.