2011 Fiscal Year Final Research Report
Differential geometrical approach to Bayesian prediction theory to classical and quantum correlated systems
| Project/Area Number |
20700250
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Statistical science
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| Research Institution | The University of Tokyo |
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Principal Investigator |
TANAKA Fuyuhiko 東京大学, 大学院・情報理工学系研究科, 助教 (90456161)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 統計的予測 / 情報幾何 / 時系列解析 / 量子情報 / 事前分布 |
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| Research Abstract |
We obtain a useful parametrization of superharmonic priors in AR models, which are often used in time series analysis. It is shown to be useful not only in theoretical development but also in numerical analysis. We show that there is no alpha parallel prior except for the Jeffreys prior in the ARMA model by using differential geometry. We give a general definition of noninformative prior in a statistical model of wave functions and prove a minimax theorem with respect to this prior. We also derive the optimal estimation of wave functions and give an explicit example where our estimator has a uniformly better performance than that based on MLE.
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Research Products
(7 results)
