  The inverse relation between mutual information (MI) and Bayesian error is
sharpened by deriving finite sequences of upper and lower bounds on MI in terms
of the minimum probability of error (MPE) and related Bayesian quantities. The
well known Fano upper bound and Feder-Merhav lower bound on equivocation are
tightened by including a succession of posterior probabilities starting at the
largest, which directly controls the MPE, and proceeding to successively lower
ones. A number of other interesting results are also derived, including a
sequence of upper bounds on the MPE in terms of a previously introduced
sequence of generalized posterior distributions. The tightness of the various
bounds is illustrated for a simple application of joint spatial localization
and spectral typing of a point source.
