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Polynomial time approximate or perfect samplers for discretized Dirichlet distribution

  • Tomomi Matsui
  • Mitsuo Motoki
  • Naoyuki Kamatani
  • Shuji KijimaEmail author
Original Paper Area 2
  • 46 Downloads

Abstract

In this paper, we propose two Markov chains for sampling random vectors that are distributed according to discretized Dirichlet distribution. Their mixing rates are bounded by O(n 2 log Δ) and O(n 3 log Δ), where n is the dimension and 1/Δ is the grid size for discretization. Our second chain gives a perfect sampler that is based on monotone coupling from the past. We also report the results of simulations.

Keywords

Markov chains Dirichlet distribution Path coupling Coupling from the past Perfect simulation 

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Copyright information

© The JJIAM Publishing Committee and Springer 2010

Authors and Affiliations

  • Tomomi Matsui
    • 1
  • Mitsuo Motoki
    • 2
  • Naoyuki Kamatani
    • 3
  • Shuji Kijima
    • 4
    Email author
  1. 1.Department of Information and System Engineering, Faculty of Science and EngineeringChuo UniversityTokyoJapan
  2. 2.Department of Computer Engineering and International CommunicationKanazawa Technical CollegeKanazawa, IshikawaJapan
  3. 3.Institute of RheumatologyTokyo Women’s Medical UniversityTokyoJapan
  4. 4.Department of InformaticsGraduate School of ISEE, Kyushu UniversityFukuokaJapan

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