Predictive optimality criterion for idealization of ion channel data and exact Akaike's criterion

Abstract

Different statistical or low-pass filters may be used for the idealization of ion channel data. We address the problem of predicting optimal filter parameters, represented by a threshold test-value for statistical filters and by a cut-off frequency for low-pass filters. Optimal idealization is understood in the sense of maximal similarity between recovered and real signals. Special procedures are suggested to quantitatively characterize the difference between the recovered and the real signals, the latter being known for simulated data. These procedures, called objective criteria, play the role of referees in estimating the performance of different predictive optimality criteria. We have tested standard Akaike's AIC and its modification by Rissanen, MDL. Both gave unsatisfactory results. We have shown analytically, that the Akaike-type criterion, based on the use of a certain penalty for the log likelihood function per transition, indicates the correct optimum point only if the penalty is set equal to half the optimal threshold. As the latter varies significantly for different data sets, this criterion is not particularly helpful. A new universal predictive optimality criterion, valid for real data and any idealization method, is suggested. It is formally similar to AIC, but instead of log likelihood it uses the doubled number of false transitions. The predictive power of the new criterion is demonstrated with different types of data for Hinkley and 50% amplitude methods.