  We introduce an information theoretic measure of statistical structure,
called 'binding information', for sets of random variables, and compare it with
several previously proposed measures including excess entropy, Bialek et al.'s
predictive information, and the multi-information. We derive some of the
properties of the binding information, particularly in relation to the
multi-information, and show that, for finite sets of binary random variables,
the processes which maximises binding information are the 'parity' processes.
Finally we discuss some of the implications this has for the use of the binding
information as a measure of complexity.
