Elucidation of information structures in anomalous statistics and its applications

2019 Fiscal Year Final Research Report

• Project/Area Number: 17K19957
• Research Category: Grant-in-Aid for Challenging Research (Exploratory)
• Allocation Type: Multi-year Fund
• Research Field: Information science, computer engineering, and related fields
• Research Institution: Chiba University
• Principal Investigator: Suyari Hiroki 千葉大学, 大学院工学研究院, 教授 (70246685)
• Project Period (FY): 2017-06-30 – 2020-03-31
• Keywords: 異常統計 / Tsallis統計 / 複雑系 / べき分布

Outline of Final Research Achievements

Addition and subtraction of observed values can be computed under the obvious and implicit assumption that the scale unit of measurement should be the same for all arguments, which is valid even for any nonlinear systems.This study starts with the distinction between exponential and non-exponential family in the sense of the scale unit of measurement. In the simplest nonlinear model,
it is shown how typical effects such as rescaling and shift emerge in the nonlinear systems and affect observed data. Based on the present results, the two representations, namely the q-exponential and the q-logarithm ones, are proposed. The former is for rescaling, the latter for unied understanding
with a fixed scale unit. For the theoretical study of nonlinear systems, q-logarithm representation is shown to have significant advantages over q-exponential representation.

Free Research Field

情報数理

Academic Significance and Societal Importance of the Research Achievements

べき分布が現れる系（異常統計）においては，個々の観測により得られる観測値のスケールが観測によって変わってしまうことを明らかにした．これは，従来の指数関数族の世界でなかった事実であり，これにより，異常統計の背景となる確率論の理論構築が難しくなる．しかし，これに対して，見通しの良い解決法を見つけることができた．これにより，なぜ，べき分布が観測されるのかが理解でき，べき分布が現れる系（異常統計）のモデリングが可能になる．