 A third alternative is the stick-breaking process, which defines the Dirichlet process constructively by writing a distribution sampled from the process as formula_41, where formula_42 are samples from the base distribution formula_1, formula_44 is an indicator function centered on formula_45 (zero everywhere except for formula_46) and the formula_47 are defined by a recursive scheme that repeatedly samples from the beta distribution formula_48.To understand what Dirichlet processes are and the problem they solve we consider the example of data clustering.It is a common situation that data points are assumed to be distributed in a hierarchical fashion where each data point belongs to a (randomly chosen) cluster and the members of a cluster are further distributed randomly within that cluster.