Formal Definition
A Dirichlet process over a set S is a stochastic process whose sample path (i.e. an infinite-dimensional set of random variates drawn from the process) is a probability distribution on S. The finite dimensional distributions are from the Dirichlet distribution: If H is a finite measure on S, is a positive real number and X is a sample path drawn from a Dirichlet process, written as
then for any measureable partition of S, say, we have that
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