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      Use of the fundamental problem of statistics to define the validity limit of Occam's razor principle

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      ScienceOpen Preprints
      ScienceOpen
      Occam's razor principle, Statistical hypothesis test, Complexity theory
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            Abstract

            ABSTRACT: In statistics, to evaluate the significance of a result, one of the most used methods is the statistical hypothesis test. Using this theory, the fundamental problem of statistics can be expressed as follows: " A statistical data does not represent useful information, but becomes useful information only when it is shown that it was not obtained randomly ". Consequently, according to this point of view, among the hypotheses that perform the same prediction, we must choose the result that has a lower probability of being produced randomly. Therefore, the fundamental aspect of this approach is to calculate correctly this probability value. This problem is addressed by redefining what is meant by hypothesis. The traditional approach considers the hypothesis as the set of rules that actively participate in the forecast. Instead, we consider as hypotheses the sum of all the hypotheses made, also considering the hypotheses preceding the one used. Therefore, each time a prediction is made, our hypothesis increases in complexity and consequently increases its ability to adapt to a random data set. In this way, the complexity of a hypothesis can be precisely determined only if all previous attempts are known. Consequently, Occam's razor principle no longer has a general value, but its application depends on the information we have on the tested hypotheses.

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            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            30 July 2021
            Affiliations
            [1 ] University of Bologna
            Author notes
            Article
            10.14293/S2199-1006.1.SOR-.PPLQN78.v1
            b62b483d-9575-460f-a218-99b0e177b8ff

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


            All data generated or analysed during this study are included in this published article (and its supplementary information files).
            Applied mathematics,Game theory,Statistics,General mathematics,History & Philosophy,Mathematics
            Statistical hypothesis test,Occam's razor principle,Complexity theory

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