Why some families of probability distributions are practically efficient: A symmetry-based explanation

© Springer International Publishing Switzerland 2016. 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 o...

Full description

Saved in:
Bibliographic Details
Main Authors: Vladik Kreinovich, Olga Kosheleva, Hung T. Nguyen, Songsak Sriboonchitta
Format: Book Series
Published: 2018
Subjects:
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84952685290&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/55598
Tags: Add Tag
No Tags, Be the first to tag this record!
Institution: Chiang Mai University
Description
Summary:© Springer International Publishing Switzerland 2016. 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.