2020 Fiscal Year Final Research Report
A new development of Bayesian prediction from the viewpoints of thermodynamics
| Project/Area Number |
17K00053
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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 | Kyushu University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Keywords | Bayes予測 / ダイバージェンス / Jeffreysの事前分布 / Tweedie分布 |
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| Outline of Final Research Achievements |
The following two results were obtained by theoretical researches. One is about Bayesian prediction problem. While the functional form of a true distribution is assumed to be known and its unknown parameter is estimated in the estimation problem, the probability distribution itself is estimated in the prediction problem. Bayesian prediction problem considers the prediction problem in the framework of Bayesian statistics. I made a research on improving a typical predictive distribution when the goodness of prediction is measured by what is called the alpha-divergence.
The other result is a characterization of Jeffreys prior. In Bayesian statistics the prior distribution is assumed by using the information about an unknown parameter. Jeffreys prior is such a prior distribution that is assumed when no information is available.
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| Free Research Field |
統計科学
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| Academic Significance and Societal Importance of the Research Achievements |
Bayes予測問題では，無情報量事前分布と呼ばれる事前分布に基づくBayes予測分布がデフォルトとして用いられることがある．一定の条件の下でこれが改善されることを示した．
Jeffreysの事前分布は無情報量事前分布の代表的なものである．パラメータを変換したときでも事前分布が不変という意味で無情報量とされているが，本研究では，指数型分布族における自然パラメータを対象にするという舞台設定の下で，この代表的な無情報量事前分布の特徴づけを行った．
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