Polynomial time perfect sampler for discretized dirichlet distribution

Tomomi Matsui, Shuji Kijima

研究成果: Chapter in Book/Report/Conference proceedingConference contribution

2 引用 (Scopus)

抜粋

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.

元の言語英語
ホスト出版物のタイトルThe Grammar of Technology Development
出版者Kluwer Academic Publishers
ページ179-199
ページ数21
ISBN(印刷物)9784431752318
DOI
出版物ステータス出版済み - 2008
外部発表Yes
イベント2005 Workshop on the Grammar of Technology Development - Tokyo, 日本
継続期間: 1 15 20051 16 2005

出版物シリーズ

名前The Grammar of Technology Development

その他

その他2005 Workshop on the Grammar of Technology Development
日本
Tokyo
期間1/15/051/16/05

All Science Journal Classification (ASJC) codes

  • Management of Technology and Innovation

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  • これを引用

    Matsui, T., & Kijima, S. (2008). Polynomial time perfect sampler for discretized dirichlet distribution. : The Grammar of Technology Development (pp. 179-199). (The Grammar of Technology Development). Kluwer Academic Publishers. https://doi.org/10.1007/978-4-431-75232-5_13