Bulletin of the Japan Society for Industrial and Applied Mathematics
Online ISSN : 2432-1982
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Volume 32, Issue 2
Displaying 1-10 of 10 articles from this issue
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  • Transport Plan, Transport Map and Transport Path—Difference of the Optimal Transport Problem between ℝ2 and Finite Set—
    Asuka Takatsu
    2022 Volume 32 Issue 2 Pages 69-79
    Published: June 24, 2022
    Released on J-STAGE: September 30, 2022
    DOIhttps://doi.org/10.11540/bjsiam.32.2_69
    JOURNAL FREE ACCESS
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    This paper is concerned with a variational problem on the space of probability measures over either ℝ2 or a finite set, the so-called optimal transport problem. We discussed three ways to formulate the optimal transport problem on ℝ2 as follows: the use of a probability measure (transport plan) on ℝ2 × ℝ2, a map (transport map) from ℝ2 to ℝ2, and a family of paths (transport path) on ℝ2. The definition of transport path requires the property that each pair of points in ℝ2 should be connected by a length minimizing curve. To define transport paths on a finite set, we explained how to modify the optimal transport problem on a finite set.

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  • Statistics and Philosophy—Reading behind the Data Analysis—
    Nobuhiro Minaka
    2022 Volume 32 Issue 2 Pages 80-86
    Published: June 24, 2022
    Released on J-STAGE: September 30, 2022
    DOIhttps://doi.org/10.11540/bjsiam.32.2_80
    JOURNAL FREE ACCESS
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    In the field of statistical data analysis in research, there is considerable discussion about the details of statistical methods and statistical modeling applied to the actual data. However, the fact that philosophical and conceptual issues in statistical science lie behind a variety of practical problems is not often discussed in the open. Meanwhile, this paper discusses the relative comparison of competing hypotheses, model selection by AIC (Akaike’s Information Criterion), and the nature of statistics as “abduction” as nondeductive reasoning, which is based on the statistical criterion of “simplicity.”

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