Uncertainty in prediction and in inference

Foundations of Physics 21 (3):323-341 (1991)
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Abstract

The concepts of uncertainty in prediction and inference are introduced and illustrated using the diffraction of light as an example. The close relationship between the concepts of uncertainty in inference and resolving power is noted. A general quantitative measure of uncertainty in inference can be obtained by means of the so-called statistical distance between probability distributions. When applied to quantum mechanics, this distance leads to a measure of the distinguishability of quantum states, which essentially is the absolute value of the matrix element between the states. The importance of this result to the quantum mechanical uncertainty principle is noted. The second part of the paper provides a derivation of the statistical distance on the basis of the so-called method of support

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Jos Uffink
University of Minnesota

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References found in this work

Logic of Statistical Inference.Ian Hacking - 1965 - Cambridge, England: Cambridge University Press.
Likelihood.Anthony William Fairbank Edwards - 1972 - Cambridge University Press.
Theory of Probability.Ernest Nagel - 1940 - Journal of Philosophy 37 (19):524-528.

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