- E. Xing, Lavanya Viswanathan. 2014. 20 : Hierarchical Dirichlet Processes. Abstract: Figure 1: Bayesian Mixture Model For a Bayesian Mixture Model as shown in figure 1, as k →∞, we shall have G = ∑∞ c=1 πcδφc , where all the φc are i.i.d. samples from G0, while the random sequence {πc}c=1 sum up to one, shall be constructed by the “Stick Breaking” process [3]. Suppose there is a stick with length 1. Let βc ∼ Beta(1, α) for c = 1, 2, 3, . . . , and regard them as fractions we take away from the remainder of the stick every time. Then πc can be calculated by the length we take away each time. π1 = β1, π2 = (1− β1)β2, . . . , πc = βc c−1 ∏
