Dirichlet Processes

Introduction: A Dirichlet process (DP) is a distribution over probability distributions. We generally think of distributions as defined over numbers of some sort (real numbers, non-negative integers etc.), so at first it may seem a little exotic to talk about distributions over distributions. If you feel that way at this point, one obvious but very reassuring fact that we would like to point out is that probability theory still applies to these objects, however exotic they may seem initially. So, as we will see shortly, it is quite possible to gain considerable insight into the properties of these objects without having a clear intuition as to what they “look like”.