Next generation Monte Carlo methods based on reversible proposal Metropolis-Hastings algorithms

• Project/Area Number: 16K00046
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Statistical science
• Research Institution: Osaka University
• Principal Investigator: Kamatani Kengo 大阪大学, 基礎工学研究科, 准教授 (00569767)
• Project Period (FY): 2016-04-01 – 2020-03-31
• Project Status: Completed (Fiscal Year 2019)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: ベイズ統計学 / マルコフ連鎖 / モンテカルロ法 / 確率過程 / Monte Carlo / Markov chain / Stochastic process / Bayesian analysis / 多変量解析 / フィッシャー情報量 / 時系列解析 / 統計数学 / 確率論

Outline of Final Research Achievements

I worked on Monte Carlo methods for the integral evaluations that appear in Bayesian statistics. We focused on the simplest class of Markov kernels for Monte Carlo methods. I showed that a minor generalization of a simple method worked quite well in both high-dimensional and heavy-tailed target distributions. No other method of having the same properties is known. Another result is the non-reversible Markov process. In collaboration with the UK and Netherlands' researchers, we obtained quantitative results for non-reversible Markov processes in a Monte Carlo context.

Academic Significance and Societal Importance of the Research Achievements

対称なマルコフ連鎖の研究の成果により，研究開始以前に提案していた手法が，高次元にも，裾の重い分布にも有効に働くことがわかった．おなじ性質を持つ手法は知られていない．また，研究開始前後に，非対称なマルコフ過程の重要性がベイズ統計学者に認識され始めていた．我々がはじめて定量的な評価をしたことによって実際にどの程度有効であるか，どんな場合に有効であるかがよりはっきりわかった．

Research Products

• [Int'l Joint Research] University College London/Warwick University(英国)
• [Int'l Joint Research] Delft University of Technology/Vrije Universiteit Amsterdam(オランダ)
• [Int'l Joint Research] Paris Dauphine University(フランス)
• [Int'l Joint Research] Warwick University/University College London/Manchester University(英国)
• [Int'l Joint Research] TU Delft(オランダ)
• [Int'l Joint Research] University of Gottingen(ドイツ)
• [Int'l Joint Research] National University of Singapore(シンガポール)
• [Int'l Joint Research] University College London/Warwick University(United Kingdom)
• [Int'l Joint Research] National University of Singapore(Singapore)
• [Int'l Joint Research] National University of Singapore(Singapore)
• [Int'l Joint Research] University College London(United Kingdom)
• [Int'l Joint Research] Oak Ridge National Laboratory(米国)
• [Journal Article] Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions (2020)
  • Author(s): Kamatani Kengo
  • Journal Title: Stochastic Processes and their Applications Volume: 130 Issue: 1 Pages: 297-327
  • DOI: 10.1016/j.spa.2019.03.002
  • Peer Reviewed
• [Journal Article] On one-dimensional Riccati diffusions (2019)
  • Author(s): Bishop A. N.、Del Moral P.、Kamatani K.、R?millard B.
  • Journal Title: The Annals of Applied Probability Volume: 29 Issue: 2 Pages: 1127-1187
  • DOI: 10.1214/18-aap1431
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Bayesian inference for stable Levy-driven stochastic differential equations with high-frequency data (2019)
  • Author(s): Jasra Ajay、Kamatani Kengo、Masuda Hiroki
  • Journal Title: Scandinavian Journal of Statistics Volume: 46 Issue: 2 Pages: 545-574
  • DOI: 10.1111/sjos.12362
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Multilevel Particle Filters (2017)
  • Author(s): Jasra Ajay、Kamatani Kengo、Law Kody J. H.、Zhou Yan
  • Journal Title: SIAM Journal on Numerical Analysis Volume: 55 Issue: 6 Pages: 3068-3096
  • DOI: 10.1137/17m1111553
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] A stable particle filter for a class of high-dimensional state-space models (2017)
  • Author(s): Beskos Alexandros、Crisan Dan、Jasra Ajay、Kamatani Kengo、Zhou Yan
  • Journal Title: Advances in Applied Probability Volume: 49 Issue: 1 Pages: 24-48
  • DOI: 10.1017/apr.2016.77
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Ergodicity of Markov chain Monte Carlo with reversible proposal (2017)
  • Author(s): Kamatani K.
  • Journal Title: Journal of Applied Probability Volume: 54 Issue: 2 Pages: 638-654
  • DOI: 10.1017/jpr.2017.22
  • Peer Reviewed
• [Journal Article] Ergodicity of Markov chain Monte Carlo with reversible proposal (2017)
  • Author(s): Kengo Kamatani
  • Journal Title: Journal of Applied Probability Volume: 54
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Multilevel Particle Filters: Normalizing Constant Estimation (2016)
  • Author(s): Ajay Jasra, Kengo Kamatani, Prince Peprah Osei, and Yan Zhou
  • Journal Title: Statistics and Computing Volume: online Issue: 1 Pages: 47-60
  • DOI: 10.1007/s11222-016-9715-5
  • Peer Reviewed / Int'l Joint Research
• [Presentation] Robust Markov chain Monte Carlo methodologies with respect to tail properties (2020)
  • Author(s): Kengo Kamatani
  • Organizer: BayesComp
  • Int'l Joint Research
• [Presentation] 対称な提案を用いる次世代モンテカルロ法の研究 (2019)
  • Author(s): 鎌谷研吾
  • Organizer: 日本応用統計学会
  • Invited
• [Presentation] High-dimensional scaling limit of Monte Carlo methods (2019)
  • Author(s): Kengo Kamatani
  • Organizer: Dynstoch
  • Int'l Joint Research
• [Presentation] High-dimensional scaling limit of Monte Carlo methods (2019)
  • Author(s): Kengo Kamatani
  • Organizer: EcoSta
  • Int'l Joint Research
• [Presentation] Analysis of Markov Chain Monte Carlo Method with Heavy-tailed Target Distributions (2019)
  • Author(s): Kengo Kamatani
  • Organizer: ISBA-EAC
  • Int'l Joint Research
• [Presentation] Scaling limits of piecewise deterministic Monte Carlo methods (2019)
  • Author(s): Kengo Kamatani
  • Organizer: European Meeting of Statisticians
  • Int'l Joint Research
• [Presentation] Metropolis-within-piecewise deterministic Markov processes (2019)
  • Author(s): Kengo Kamatani
  • Organizer: ERCIM
  • Int'l Joint Research
• [Presentation] Reversible proposal MCMC with heavy-tailed target distributions (2018)
  • Author(s): Kengo Kamatani
  • Organizer: AIMS Conference
  • Int'l Joint Research
• [Presentation] Reversible proposal MCMC with heavy-tailed target distributions (2018)
  • Author(s): Kengo Kamatani
  • Organizer: Bayesian Computation for High-Dimensional Statistical Models
  • Int'l Joint Research
• [Presentation] Bayesian inference for stable Levy driven stochastic differential equations with high-frequency data (2018)
  • Author(s): Kengo Kamatani
  • Organizer: ERCIM 2018
  • Int'l Joint Research
• [Presentation] Reversible proposal MCMC in high dimension (2016)
  • Author(s): Kengo Kamatani
  • Organizer: SIAM Conference on Uncertainty Quantification (UQ16)
  • Place of Presentation: Lausanne (Switzerland)
  • Int'l Joint Research
• [Presentation] Some properties of the mixed preconditioned Crank-Nicolson algorithm (2016)
  • Author(s): Kengo Kamatani
  • Organizer: IMS-APRM
  • Place of Presentation: Hong Kong (China)
  • Int'l Joint Research
• [Presentation] マルコフ連鎖モンテカルロ法の高次元解析 (2016)
  • Author(s): 鎌谷研吾
  • Organizer: 日本統計学会
  • Place of Presentation: 金沢大学 (石川県・金沢市)
• [Book] モンテカルロ統計計算 (2020)
  • Author(s): 鎌谷 研吾、駒木 文保
  • Total Pages: 192
  • Publisher: 講談社
  • ISBN: 9784065191835
• [Remarks] HOMEPAGE OF KENGO KAMATANI
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~kamatani/research/
• [Remarks] HOMEPAGE OF KENGO KAMATANI
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~kamatani/research/index.html
• [Remarks] KAMATANI, Kengo/ 鎌谷 研吾
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~kamatani/research/