### Abstract

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.

Original language | English |
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Title of host publication | The Grammar of Technology Development |

Publisher | Kluwer Academic Publishers |

Pages | 179-199 |

Number of pages | 21 |

Publication status | Published - 2008 |

Externally published | Yes |

Event | 2005 Workshop on the Grammar of Technology Development - Tokyo, Japan Duration: Jan 15 2005 → Jan 16 2005 |

### Other

Other | 2005 Workshop on the Grammar of Technology Development |
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Country | Japan |

City | Tokyo |

Period | 1/15/05 → 1/16/05 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Management of Technology and Innovation

### Cite this

*The Grammar of Technology Development*(pp. 179-199). Kluwer Academic Publishers.

**Polynomial time perfect sampler for discretized dirichlet distribution.** / Matsui, Tomomi; Kijima, Shuji.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*The Grammar of Technology Development.*Kluwer Academic Publishers, pp. 179-199, 2005 Workshop on the Grammar of Technology Development, Tokyo, Japan, 1/15/05.

}

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.

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M3 - Conference contribution

AN - SCOPUS:84897975262

SP - 179

EP - 199

BT - The Grammar of Technology Development

PB - Kluwer Academic Publishers

ER -