Publication
See https://orcid.org/0000-0002-1537-3446 for a complete list of my publication.
Joris Bierkens, Kengo Kamatani and Gareth O. Roberts. Scaling of Piecewise Deterministic Monte Carlo for Anisotropic Targets, https://arxiv.org/abs/2305.00694
Kengo Kamatani, and Xiaolin Song. Non-reversible guided Metropolis kernel.. arXiv:2005.05584, J. Appl Probab, 60 (3) , 2023 , pp. 955 - 981. DOI: https://doi.org/10.1017/jpr.2022.109
See also on YouTube video by Xiaolin Song.
See the comment in Xi'an's Og with a beautiful photo of Koyasan, Wakayama prefecture in Japan.
This paper explores a class of non-reversible Markov chain Monte Carlo (MCMC) methods. Non-reversible methods can be advantageous over their reversible counterparts, but designing non-reversible methods is technically challenging as the detailed balance condition cannot be relied upon. The Gustafson method is a well-known approach that addresses non-reversibility by introducing a directional aspect. However, the direction in this method is limited to one dimension. In this paper, we propose a generalization of the Gustafson method that extends to multidimensional cases, using the Haar measure on a locally compact topological group to introduce a more natural direction. We are pleased with the outcome of our research, as we successfully developed a class of simple and natural non-reversible MCMCs.
Our work began with the hope of a face-to-face meeting with the legendary Prof. Persi Diaconis at a non-reversible MCMC workshop. Alas, the COVID-19 turned the workshop into an online meeting, leaving us without the chance to meet him in person.
Joris Bierkens, Kengo Kamatani, and Gareth O. Roberts. High-dimensional scaling limits of piecewise deterministic sampling algorithms. arXiv:1807.11358, Ann. Appl. Probab. 32(5): 3361-3407 (October 2022). DOI: 10.1214/21-AAP1762
Kengo Kamatani, and Xiaolin Song. Haar-Weave-Metropolis kernel, 2021. arxiv:2111.06148, Bulletin of informatics and cybernetics, Volume 54, Issue 1, 2022, Pages 1-31, https://doi.org/10.5109/4755997
Joris Bierkens, Sebastiano Grazzi, Kengo Kamatani, and Gareth O. Roberts. Boomerang Sampler, Proceedings of the 37th International Conference on Machine Learning, Vienna, Austria, PMLR 119, 2020, Pages 7742--7752, arXiv:2006.13777
See also the video.
Kengo Kamatani. Random walk Metropolis algorithm in high dimension with non-Gaussian target distributions. Stochastic processes and their applications, Volume 130, Issue 1, January 2020, Pages 297-327
A. N. Bishop, P. Del Moral, K. Kamatani, and B. Remillard. On one-dimensional Riccati diffusions. Ann. Appl. Probab. , Volume 29, Number 2 (2019), 1127-1187. DOI: 10.1214/18-AAP1431
A. Jasra, K. Kamatani, and H. Masuda. Bayesian inference for Stable Levy driven stochastic differential equations with high-frequency data, Scandinavian journal of statistics, Volume46, Issue2, June 2019 Pages 545-574: Erratum! The algorithm in the remark of Algorithm 1 is useless, since the joint distribution of V and V star is not exchangable. Simply ignore the remark. The main algorithm, Algorithm 1 is valid.
Kengo Kamatani. Efficient strategy for the markov chain monte carlo in high-dimension with heavy-tailed target probability distribution. Bernoulli, 24(4B):3711–3750, 2018. (doi:10.3150/17-BEJ976)
A. Jasra, K. Kamatani, K. J. H. Law, and Y. Zhou. Bayesian static parameter estimation for partially observed diffusions via multilevel monte carlo. SIAM Journal on Scientific Computing, 40(2):A887–A902, 2018. (doi:10.1137/17M1112595)
Ajay Jasra, Kengo Kamatani, Kody J. H. Law, and Yan Zhou. A multi-index markov chain monte carlo method. International Journal for Uncertainty Quantification, 8(1):61–73, 2018.
Ajay Jasra, Kengo Kamatani, Prince Peprah Osei, and Yan Zhou. Multilevel particle filters: normalizing constant estimation. Statistics and Computing, 28(1):47–60, Jan 2018. (doi:10.1007/s11222-016-9715-5)
Kengo Kamatani. Ergodicity of Markov chain Monte Carlo with reversible proposal. Journal of Applied Probability, 54:638–654, 2017. (doi: 10.1017/jpr.2017.22)
Alexandros Beskos, Dan Crisan, Ajay Jasra, Kengo Kamatani, and Yan Zhou. A stable particle filter for a class of high-dimensional state-space models. Advances in Applied Probability, 49(1):24 UTF 201348, 2017. doi: 10.1017/apr.2016.77
A. Jasra, K. Kamatani, K. J. H. Law, and Y. Zhou. Multilevel particle filters. SIAM Journal on Numerical Analysis, 55(6):3068–3096, 2017. (doi:10.1137/17M1111553)
Kengo Kamatani, Akihiro Nogita, and Masayuki Uchida. Hybrid multi-step estimation of the volatility for stochastic regression models.Bulletin of Informatics and Cybernetics, 48:19–35, 2016.
Kengo Kamatani and Masayuki Uchida. Hybrid multi-step estimators for stochastic differential equations based on sampled data.Statistical Inference for Stochastic Processes, 18(2):177–204, 2015. (doi:10.1007/s11203-014-9107-4)
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. The yuima project: A computational framework for simulation and inference of stochastic differential equations. Journal of Statistical Software, 57(4):1–51, 2014.
Kengo Kamatani. Asymptotic properties of Monte Carlo strategies for cumulative link model. Journal of the Japan Statistical Society, 44(1):1–23, 2014.
Kengo Kamatani. Local consistency of Markov chain Monte Carlo methods. Ann. Inst. Statist. Math., 66(1):63–74, 2014. (doi:10.1007/s10463-013-0403-3)
Kengo Kamatani. Local degeneracy of markov chain monte carlo methods. ESAIM: Probability and Statistics, 18:713–725, 1 2014. (doi:10.1051/ps/2014004)
Kengo Kamatani. Local weak consistency of Markov chain Monte Carlo methods with application to mixture model. Bulletin of Informatics and Cybernetics, 45:103–123, 2013.
Kengo Kamatani. Note on asymptotic properties of probit gibbs sampler. RIMS Kokyuroku, 1860:140–146, 2013.
Kengo Kamatani. The order of degeneracy of markov chain monte carlo method. Journal of the Japan Statistical Society, 43(2):203–220, 2013.
Kengo Kamatani. マルコフ連鎖モンテカルロ法のエルゴード性の解析. RIMS Kokyuroku, 1768:73–84, 2011.
Kengo Kamatani. Metropolis-Hastings Algorithm for Mixture Model and its Weak Convergence. In Gilbert Lechevallier, Yves; Saporta, editor, Proceedings of COMPSTAT'2010, volume eBook, pages 1175–1182, 2010.
Kengo Kamatani. Metropolis-Hastings algorithms with acceptance ratios of nearly 1. Ann. Inst. Statist. Math., 61(4):949–967, 2009. (doi:10.1007/s10463-008-0180-6)
Other
Kengo Kamatani, Joris Bierkens and Sebastiano Grazzi. Discussion on the Paper by Murray Pollock, Paul Fearnhead, Adam Johansen, and Gareth O. Roberts. J. R. Statist. Soc. B, 82(5), p. 1216, 2020
Japanese
マルコフ連鎖モンテカルロ法における平均回帰 （日本統計学会研究業績賞受賞者特別寄稿論文）鎌谷 研吾 ，日本統計学会誌, 第50巻 (第2号), pp. 381-402, 2021
モンテカルロ統計計算 著：鎌谷 研吾 編：駒木 文保，講談社サイエンティフィック, 2020
演習問題回答とエラーについてを御覧ください．
乙部達志, 鎌谷研吾. (2020). 走行速度の違いによる強風時の安全性を評価する, 特集 鉄道の空気力学. RRR, 77(10), pp. 24-27.
Kengo Kamatani, Yosuke Nagumo and Tatsushi Otobe. 確率的風速モデルによる強風時の列車の走行安全性評価. 土木学会論文集A1(構造・地震工学), Vol. 75, No. 2, 88-94, 2019