Algorithms for removing recovery-related distortion from auditory-nerve discharge patterns

The probability that a cochlear nerve fiber discharges during some specified time interval depends on both the acoustic stimulus and on refractory effects due to earlier spike discharges. With the objective of separating the stimulus-related effects from refractory-related effects seen in poststimulus-time histograms, various maximum-likelihood estimation schemes have been developed. By modeling auditory-nerve fiber discharges as a self-exciting point process in which the intensity depends on both the time during stimulation and the history of discharge, we have been able to independently verify the likelihood estimates of Gaumond et al. [J. Acoust. Soc. Am. 74, 1392–1398 (1983)] under conditions when the recovery function is known. Secondly by maximizing the likelihood function of the neural event process subject to periodic stimulus constraints we have derived estimates which as the number of stimulus presentations and or stimulus periods increase are free from the effects of both absolute and relative recovery-related distortion. Under conditions when the recovery function is unknown, a recursive algorithm is proposed that yields the joint maximum-likelihood estimates of both the stimulus-and recovery-related components in the response histograms. We state the conditions under which unique maximum-likelihood estimates exist and prove that the recursive algorithm converges to those unique estimates.