2022 Fiscal Year Final Research Report
Efficiencies by Bayesian information inequalities
| Project/Area Number |
20K11702
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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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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Nihon University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
橋本 真太郎 広島大学, 先進理工系科学研究科(理), 准教授 (60772796)
赤平 昌文 筑波大学, 数理物質系(名誉教授), 名誉教授 (70017424)
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| Project Period (FY) |
2020-04-01 – 2023-03-31
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| Keywords | ベイズ推測 / ベイズリスク / ベイジアン情報不等式 / 有効性 |
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| Outline of Final Research Achievements |
In Bayesian inference, asymptotic large and small comparisons were obtained for the van Trees-type and the Borovkov-Sakhanenko type lower bounds for Bayesian risk under quadratic loss function(Koike (2020)). The content of this reserach reinforces the results of Abu-Shanab and Veretennikov (2015). We also obtained a lower bound of difference type applicable to the non-singular case (Koike and Hashimoto (2021)). Furthermore, the necessary and sufficient conditions for achieving the lower bounds were also obtained (Koike (2021), Banno and Koike (2022)).
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| Free Research Field |
数理統計学
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| Academic Significance and Societal Importance of the Research Achievements |
ベイズ推測では、ベイズリスクを用いて推定量の良さの評価を考える．ベイズリスクの評価を与える下界にはvan Trees (1968)やBorovkov and Sakhanenko(1980)によるものがよく知られている．これらの不等式の評価の良し悪しを検討した．また、これらの不等式において等号が成り立つための条件を示した．これらのことから、ベイズ推測において推測方式の有効性評価の際にどの不等式を用いるべきかを見極めることができる．
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