Polynomial Time Perfect Sampler for Discretized Dirichlet Distribution (2003)
| Venue: | MATHEMATICAL ENGINEERING TECHNICAL REPORTS, UNIVERSITY OF TOKYO |
| Citations: | 2 - 2 self |
BibTeX
@TECHREPORT{Matsui03polynomialtime,
author = {Tomomi Matsui and Shuji Kijima},
title = {Polynomial Time Perfect Sampler for Discretized Dirichlet Distribution},
institution = {MATHEMATICAL ENGINEERING TECHNICAL REPORTS, UNIVERSITY OF TOKYO},
year = {2003}
}
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Abstract
In this paper, we propose a perfect (exact) sampling algorithm according to a discretized Dirichlet distribution. Our algorithm is a monotone coupling from the past algorithm, which is a Las Vegas type randomized algorithm. We propose a new Markov chain whose limit distribution is a discretized Dirichlet distribution. Our algorithm simulates transitions of the chain O(n ln #) times where n is the dimension (the number of parameters) and 1/# is the grid size for discretization. Thus the obtained bound does not depend on the magnitudes of parameters. In each transition, we need to sample a random variable according to a discretized beta distribution (2-dimensional Dirichlet distribution). To show the polynomiality, we employ the path coupling method carefully and show that our chain is rapidly mixing.
