Quantum theory and the bayesian inference problems

Abstract

Many physicists take it for granted that their theories can be either refuted or verified by comparison with experimental data. In order to evaluate such data, however, one must employ statistical estimation and inference methods which, unfortunately, always involve an ad hoc proposition. The nature of the latter depends upon the statistical method adopted; in the Bayesian approach, for example, one must usesome Lebesgue measure in the “set of all possible distributions.” The ad hoc proposition has usually nothing in common with the physical theory in question, thus subjecting its verification (or refutation) to further doubt. This paper points out one notable exception to this rule. It turns out that in the case of the quantum mechanical systems associated with finite-dimensional Hilbert spaces the proposition is completely determined by the premises of the quantum theory itself.

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Supported by the National Science Foundation (USA).

This work was completed at the Department of Chemistry, University of Illinois, Urbana, Illinois.

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Sýkora, S. Quantum theory and the bayesian inference problems. J Stat Phys 11, 17–27 (1974). https://doi.org/10.1007/BF01019475

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Key words

  • Quantum theory
  • statistical inference
  • Bayesian inference