Uncertainty in prediction and in inference

Abstract

The concepts of uncertainty in prediction and inference are introduced and illustrated using the diffraction of light as an example. The close re-lationship between the concepts of uncertainty in inference and resolving power is noted. A general quantitative measure of uncertainty in infer-ence can be obtained by means of the so-called statistical distance between probability distributions. When applied to quantum mechanics, this dis-tance 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 prin-ciple is noted. The second part of the paper provides a derivation of the statistical distance on basis of the so-called method of support.