Information theoretic study of empirical probability
Project/Area Number |
22654015
|
Research Category |
Grant-in-Aid for Challenging Exploratory Research
|
Allocation Type | Single-year Grants |
Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
Research Institution | Osaka University |
Principal Investigator |
FUJIWARA Akio 大阪大学, 理学研究科, 教授 (30251359)
|
Project Period (FY) |
2010 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥3,210,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥510,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,000,000 (Direct Cost: ¥1,000,000)
|
Keywords | 統計数学 / 経験確率 / 情報理論 / ユニバーサル符号化 / ランダムネス / ダイバージェンス |
Research Abstract |
We explored an information theoretic study of empirical probability. The main results are summarized as follows: 1) A novel Martin-Loef randomness criterion for two distinct computable probability measures was obtained based on finite-type quasi-symmetric divergence functions. 2) An alternative proof of a game-theoretic law of large numbers was given based on the Lynch-Davisson universal coding algorithm, and a possibility of generalizing the law of large numbers and the theorem of convergence of opinions to a general prediction game was pointed out.
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Report
(4 results)
Research Products
(7 results)