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Why Some Families of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation

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Causal Inference in Econometrics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 622))

Abstract

Out of many possible families of probability distributions, some families turned out to be most efficient in practical situations. Why these particular families and not others? To explain this empirical success, we formulate the general problem of selecting a distribution with the largest possible utility under appropriate constraints. We then show that if we select the utility functional and the constraints which are invariant under natural symmetries—shift and scaling corresponding to changing the starting point and the measuring unit for describing the corresponding quantity x— then the resulting optimal families of probability distributions indeed include most of the empirically successful families. Thus, we get a symmetry-based explanation for their empirical success.

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Acknowledgments

We acknowledge the partial support of the Center of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Thailand.

This work was also supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE- 0926721.

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Texas at El Paso, 500 W. University, El Paso, TX, 79968, USA

    Vladik Kreinovich

  2. University of Texas at El Paso, 500 W. University, El Paso, TX, 79968, USA

    Olga Kosheleva

  3. Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM, 88003, USA

    Hung T. Nguyen

  4. Faculty of Economics, Chiang Mai University, Chiang Mai, Thailand

    Hung T. Nguyen & Songsak Sriboonchitta

Authors
  1. Vladik Kreinovich
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  2. Olga Kosheleva
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  3. Hung T. Nguyen
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  4. Songsak Sriboonchitta
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Corresponding author

Correspondence to Vladik Kreinovich .

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Editors and Affiliations

  1. School of Knowledge Science, Japan Advanced Ins. of Sci. & Tech, Ishikawa, Japan

    Van-Nam Huynh

  2. Department of Computer Science, University of Texas at El Paso, El Paso, Texas, USA

    Vladik Kreinovich

  3. Faculty of Economics, Chiang Mai University, Chiangmai, Thailand

    Songsak Sriboonchitta

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Kreinovich, V., Kosheleva, O., Nguyen, H.T., Sriboonchitta, S. (2016). Why Some Families of Probability Distributions Are Practically Efficient: A Symmetry-Based Explanation . In: Huynh, VN., Kreinovich, V., Sriboonchitta, S. (eds) Causal Inference in Econometrics. Studies in Computational Intelligence, vol 622. Springer, Cham. https://doi.org/10.1007/978-3-319-27284-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-27284-9_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27283-2

  • Online ISBN: 978-3-319-27284-9

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