TY - GEN

T1 - Polynomial time perfect sampler for discretized dirichlet distribution

AU - Matsui, Tomomi

AU - Kijima, Shuji

PY - 2008

Y1 - 2008

N2 - In this paper, we propose a perfect (exact) sampling algorithm according to a discretized Dirichlet distribution. The Dirichlet distribution appears as prior and posterior distribution for the multinomial distribution in many statistical methods in bioinformatics. 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(n3 lnΔ) times where n is the dimension (the number of parameters) and 1/Δ 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.

AB - In this paper, we propose a perfect (exact) sampling algorithm according to a discretized Dirichlet distribution. The Dirichlet distribution appears as prior and posterior distribution for the multinomial distribution in many statistical methods in bioinformatics. 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(n3 lnΔ) times where n is the dimension (the number of parameters) and 1/Δ 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.

UR - http://www.scopus.com/inward/record.url?scp=84897975262&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84897975262&partnerID=8YFLogxK

U2 - 10.1007/978-4-431-75232-5_13

DO - 10.1007/978-4-431-75232-5_13

M3 - Conference contribution

AN - SCOPUS:84897975262

SN - 9784431752318

T3 - The Grammar of Technology Development

SP - 179

EP - 199

BT - The Grammar of Technology Development

PB - Kluwer Academic Publishers

T2 - 2005 Workshop on the Grammar of Technology Development

Y2 - 15 January 2005 through 16 January 2005

ER -