Some Properties of the Expectation Coordinate System of a Binary Exponential (Distribution) Family

摘要

It has been shown that there exist monotonic relations between the elements of the normalized Fisher information matrix (correlation coefficients) and the natural parameters, if a certain inclusion relation is satisfied in a binary expo- nential family which is defined on n probability variables taking a binary value of either 1 to 0, and if their higher- order mutual interactions are taken into account. Due tot his property, changes of correlation coefficients can be ap- proximately predicted from the changes in the values of the parameters alone.