Polynomial Time Approximate Sampler for Discretized Dirichlet Distribution

Abstract. In this paper, we propose a Markov chain for sampling a random vector distributed according to a discretized Dirichlet distribution. We show that our Markov chain is rapidly mixing, that is, the mixing time of our chain is bounded by 1=2nn , 1ln
, n",1  where n is the dimension the number of parameters, 1=
is the grid size for discretization, and " is the error bound. Thus the obtained bound does not depend on the magnitudes of parameters. We estimate the mixing time by using the path coupling method. When the magnitudes of parameters are large, the log-concavity of the density function implies the rapidity straightforwardly. In the case that parameters are less than 1, the density function is convex and so we need a speci ed approach to use the path coupling method. We also show the rate of convergence of our chain experimentally.

• Type: Conference
• Year: 2003
• Where: ISAAC
• Authors: Tomomi Matsui, Mitsuo Motoki, Naoyuki Kamatani
• Keywords: ISAAC 2003, Markov Chain, Mixing Time, Path Coupling Method