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Foundations of Physics

, Volume 3, Issue 4, pp 477–492 | Cite as

The well-posed problem

  • E. T. Jaynes
Article

Abstract

Many statistical problems, including some of the most important for physical applications, have long been regarded as underdetermined from the standpoint of a strict frequency definition of probability; yet they may appear wellposed or even overdetermined by the principles of maximum entropy and transformation groups. Furthermore, the distributions found by these methods turn out to have a definite frequency correspondence; the distribution obtained by invariance under a transformation group is by far the most likely to be observed experimentally, in the sense that it requires by far the least “skill.” These properties are illustrated by analyzing the famous Bertrand paradox. On the viewpoint advocated here, Bertrand's problem turns out to be well posed after all, and the unique solution has been verified experimentally. We conclude that probability theory has a wider range of useful applications than would be supposed from the standpoint of the usual frequency definitions.

Keywords

Entropy Unique Solution Probability Theory Physical Application Statistical Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • E. T. Jaynes
    • 1
  1. 1.Department of PhysicsWashington UniversitySt. Louis

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