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 basis of
the so-called method of support.
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