| Project/Area Number |
18K18016
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Ritsumeikan University |
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Principal Investigator |
Harase Shin 立命館大学, 理工学部, 講師 (80610576)
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| Project Period (FY) |
2018-04-01 – 2023-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | 擬似乱数 / モンテカルロ法 / 準モンテカルロ法 / マルコフ連鎖モンテカルロ法 / 統計計算 / ベイズ統計学 / 計算統計 |
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| Outline of Final Research Achievements |
We developed quasi-random point sets for Markov chain Monte Carlo. We proposed a method to use the output values generated by short-period Tausworthe generators as quasi-random points and conducted an exhaustive search in terms of the t-value, which is a measure of uniformity. We implemented our new generators and applied them to Bayesian computation in practice. We demonstrated the effectiveness in numerical examples, such as hierarchical models and regression models.
Motivated by recent progress on 64-bit pseudorandom number generators, we analyzed the conversion from 32-bit Mersenne Twister to 53-bit double-precision floating-point numbers. From this point of view, we presented that MT19937 with a specific lag set fails several statistical tests. As another research, we conducted a comparative study of Sobol' quasi-random sequences in financial applications; in particular, we investigated the relationship between the t-value and the rate of convergence in numerical integration.
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| Academic Significance and Societal Importance of the Research Achievements |
MCMC法は、統計科学において必要不可欠な道具となっているが、収束が非常に遅い。しかるに、MCMC法では、従来の準乱数はそのまま適用できない。ここで、CUD列と呼ばれる特殊な点列を用いると、準モンテカルロ法による期待値計算に適用できることが理論的に示されているが、具体的な点列の構成は不十分であった。本研究課題では、擬似乱数と準モンテカルロ法の手法を駆使して、MCMC法のための新しい準乱数を開発した。実際に、ベイズ統計学に現れるMCMC法に適用して、収束性の向上を確認した。この結果は、統計計算において、非常に広範な応用を持つことが期待される。
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