Bin number selection for equidistant mutual information estimaton

In the present work the problem of optimal bin number selection for equidistant Mutual Information (MI) estimator is addressed. New technique of bin number selection is proposed, giving a range of bin numbers which do not influence the mutual information value. The proposed technique is based on estimation of MI on the range of bins, finding the difference quotient and its second order approximate and restricting the bin number by the lower bound. The comparison of developed technique with existing Sturge´s, Scott´s, Friedman-Diaconis´ rules and Shimazaki method for finding optimal bin number is made for the case of MI calculation of two correlated random Gaussian signals.