2015 Fiscal Year Final Research Report
Bayesian prediction theory to high-dimensional statistical models in spacial temporal statistics and quantum statistics
| Project/Area Number |
24700273
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Statistical science
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| Research Institution | Osaka University (2013-2015)
The University of Tokyo (2012) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Keywords | 統計数学 / 数理工学 / 量子コンピュータ / 情報工学 / 応用数学 / ベイズ統計 / 無情報事前分布 / 統計的決定理論 |
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| Outline of Final Research Achievements |
We derived an explicit form of Bayes estimate in the problem of estimating a wave function (a pure state) that describes the qunatum system. We also give an example where Bayes estimate with respect to a noninformative prior gets uniformly smaller estimation error than that based on the maximum likelihood estimate.
In addition, we proposed a new formulation where we consider the choice of a noninformative prior, which is a fundamental issue not only in Bayesian statistics but also in traditional statistics. It includes both classical and quantum statistics. We introduce a restricted class of (physical) measurements and estimates and among them we show minimax theorem connecting Bayes methods with minimax methods. Under regularity conditions, we show the existence of least favorable priors.
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| Free Research Field |
統計理論
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