Asymptotic analysis of statistical computation methods for hidden Markov models

• Project/Area Number: 24740062
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Osaka University
• Principal Investigator: Kamatani Kengo 大阪大学, 基礎工学研究科, 講師 (00569767)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
• Keywords: ベイズ統計 / モンテカルロ / 漸近理論 / 高次元解析 / 複雑モデル / 大規模データ / Markov chain / Bayesian Statistics / Monte Carlo / モンテカルロ法 / 数理統計学 / 確率過程 / 統計数理 / マルコフ連鎖 / ベイズ統計学 / 隠れマルコフモデル

Outline of Final Research Achievements

For the project, I performed analysis on (a) sequential monte carlo methods and (b) markov chain monte carlo (MCMC) methods for high-dimensional complicated models. For (a), we proposed (a-1) efficient strategy for high-dimensional state space models, and (a-2) ensemble strategy with multi-level monte carlo. For (b) we proposed a scale-free MCMC and analysed its performance via high-dimensional asymptotic and ergodicity analysis.

Research Products

• [Int'l Joint Research] National University of Singapore(Singapore)
• [Int'l Joint Research] University College of London(United Kingdom)
• [Int'l Joint Research] Oak Ridge National Laboratory(米国)
• [Journal Article] Hybrid multi-step estimators for stochastic differential equations based on sampled data (2015)
  • Author(s): Kengo Kamatani and Masayuki Uchida
  • Journal Title: Statistical Inference for Stochastic Processes Volume: 未定 Issue: 2 Pages: 0-0
  • DOI: 10.1007/s11203-014-9107-4
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The yuima project: A computational framework for simulation and inference of stochastic differential equations. (2014)
  • Author(s): Alexandre Brouste, Masaaki Fukasawa, Hideitsu Hino, Stefano M. Iacus, Kengo Kamatani, Yuta Koike, Hiroki Masuda, Ryosuke Nomura, Teppei Ogihara, Yasutaka Shimuzu, Masayuki Uchida, and Nakahiro Yoshida.
  • Journal Title: Journal of Statistical Software Volume: 57(4) Pages: 1-51
  • Peer Reviewed
• [Journal Article] Asymptotic properties of Monte Carlo strategies for cumulative link model. (2014)
  • Author(s): Kengo Kamatani
  • Journal Title: Journal of the Japan Statistical Society Volume: 44(1) Pages: 1-23
  • NAID: 130004951124
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Yuima project : a computational framework for simulation and inference of stochastic differential equations, journal of statistical software. (2014)
  • Author(s): A. Brouste, M. Fukasawa, H. Hino, S. Iacus, K. Kamatani, Y. Koike, H. Masuda, R. Nomura, Y. Shimuzu, M. Uchida, and N. Yoshida.
  • Journal Title: Journal of Statistical Software Volume: 印刷中
  • Peer Reviewed
• [Journal Article] Local consistency of Markov chain Monte Carlo methods. (2014)
  • Author(s): Kengo Kamatani
  • Journal Title: Annals of the Institute of Statistical Mathematics Volume: 66 Issue: 1 Pages: 63-74
  • DOI: 10.1007/s10463-013-0403-3
  • NAID: 40019941027
  • Peer Reviewed
• [Journal Article] Local degeneracy of markov chain monte carlo methods. (2014)
  • Author(s): Kengo Kamatani
  • Journal Title: ESAIM: Probability and Statistics Volume: 印刷中 Pages: 713-725
  • DOI: 10.1051/ps/2014004
  • Peer Reviewed
• [Journal Article] Local weak consistency of Markov chain Monte Carlo methods with application to mixture model. (2013)
  • Author(s): Kengo Kamatani
  • Journal Title: Bulletin of Informatics and Cybernetics Volume: 45 Pages: 103-123
  • NAID: 120005703633
  • Peer Reviewed
• [Journal Article] The order of degeneracy of markov chain monte carlo method (2013)
  • Author(s): Kengo Kamatani
  • Journal Title: Journal of the Japan Statistical Society Volume: 43 Pages: 203-220
  • NAID: 130004696125
  • Peer Reviewed
• [Presentation] High-dimensional asymptotic properties of Markov chain Monte Carlo methods for heavy-tailed target distributions (2016)
  • Author(s): Kengo Kamatani
  • Organizer: Statistics for Stochastic Processes and Analysis of High Frequency Data V
  • Place of Presentation: University Pierre and Marie Curie (Paris 6), Paris, France
  • Year and Date: 2016-03-23
  • Int'l Joint Research
• [Presentation] マルコフ連鎖のエルゴード性とregular variation (2016)
  • Author(s): 鎌谷研吾
  • Organizer: 日本統計学会春季集会
  • Place of Presentation: 東北大学川内南キャンパス, 仙台, 宮城
  • Year and Date: 2016-03-05
• [Presentation] Markov chain Monte Carlo in high-dimension with heavy-tailed target probability distributions (2016)
  • Author(s): Kengo Kamatani
  • Organizer: MCMski V
  • Place of Presentation: Lenzerheide, Switzerland
  • Year and Date: 2016-01-05
  • Int'l Joint Research / Invited
• [Presentation] Efficient strategy for the Markov chain Monte Carlo in high-dimension and its implementation (2015)
  • Author(s): Kengo Kamatani
  • Organizer: IASC-ARS
  • Place of Presentation: National University of Singapore, Singapore
  • Year and Date: 2015-12-17
  • Int'l Joint Research
• [Presentation] On some ergodic properties of the MpCN algorithm (2015)
  • Author(s): Kengo Kamatani
  • Organizer: ERCIM
  • Place of Presentation: University College London, London, United Kingdom
  • Year and Date: 2015-12-12
  • Int'l Joint Research
• [Presentation] Efficient strategy of MCMC in high-dimension and its application to diffusion processes (2015)
  • Author(s): Kengo Kamatani
  • Organizer: Statistique Asymptotique des Processus Stochastiques-X
  • Place of Presentation: ル・マン，フランス
  • Year and Date: 2015-03-17 – 2015-03-20
  • Invited
• [Presentation] Hybrid multi-step estimators for stochastic differential equations based on sampled data (2014)
  • Author(s): Kengo Kamatani
  • Organizer: 7th International Conference of the ERCIM WG on Computational and Methodological Statistics
  • Place of Presentation: ピサ，イタリア
  • Year and Date: 2014-12-06 – 2014-12-08
  • Invited
• [Presentation] Rate optimality of Random walk Metropolis algorithm in high-dimension with heavy-tailed target distribution (2014)
  • Author(s): Kengo Kamatani
  • Organizer: DynStoch 2014
  • Place of Presentation: ウォーリック，イギリス
  • Year and Date: 2014-09-10 – 2014-09-12
  • Invited
• [Presentation] The order of degeneracy of Markov chain Monte Carlo Method (2014)
  • Author(s): Kengo Kamatani
  • Organizer: IMS-APRM 2014
  • Place of Presentation: 台北，台湾
  • Year and Date: 2014-06-29 – 2014-07-03
• [Presentation] Various order of degeneracies of Markov chain Monte Carlo for categorical data (2013)
  • Author(s): Kengo Kamatani
  • Organizer: the 29th European Meeting of Statisticians
  • Place of Presentation: Eotvos Lorand University, Budapest, Hungary
• [Presentation] 混合モデルのマルコフ連鎖モンテカルロ法の漸近理論 (2013)
  • Author(s): 鎌谷研吾
  • Organizer: 2013年度 統計関連学会連合大会
  • Place of Presentation: 大阪大学豊中キャンパス（大阪府豊中市）
• [Presentation] Asymptotic properties of Monte Carlo strategies for cumulative link model (2012)
  • Author(s): Kengo KAMATNI
  • Organizer: ISBA 2012
  • Place of Presentation: 京都テルサ（京都府）
• [Presentation] Markov chain Monte Carlo methods for simple mixture model (2012)
  • Author(s): Kengo KAMATANI
  • Organizer: ISM-APRM 2012
  • Place of Presentation: つくば国際会議場（茨城県）
• [Presentation] Local consistency of MCMC and its application to cumulative link model (2012)
  • Author(s): Kengo KAMATANI
  • Organizer: Big MC
  • Place of Presentation: The Institute Henri Poincare (Paris, France)
• [Presentation] Efficient Monte Carlo Strategy for Simple Mixture Model (2012)
  • Author(s): Kengo KAMATANI
  • Organizer: Structure and uncertainty
  • Place of Presentation: University of Bristol (Bristol, UK)
• [Remarks] KAMATANI, Kengo
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~kamatani/research/
• [Remarks] K. KAMATANI WEB
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~kamatani/research/
• [Remarks] K. KAMATANI WEB - Osaka University
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~kamatani/research/
• [Remarks] K. KAMATANI WEB
  • URL: http://www.sigmath.es.osaka-u.ac.jp/~kamatani/research/