Next generation Monte Carlo methods based on reversible proposal Metropolis-Hastings algorithms
| Project/Area Number |
16K00046
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | Osaka University |
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Principal Investigator |
Kamatani Kengo 大阪大学, 基礎工学研究科, 准教授 (00569767)
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| Project Period (FY) |
2016-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥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)
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| 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 |
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| 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.
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| 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．
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Report
(5 results)
Research Products
(37 results)
