IDENTIFICATION OF INDIVIDUAL CHANNEL KINETICS FROM RECORDINGS CONTAINING MANY IDENTICAL CHANNELS

Given a discrete-time signal consisting of N identical, independent, b inary Markov chains observed in white noise, we consider the problem o f estimating the non-zero state level, the number of chains and the el ementary transition probability matrix. We derive formulae for the cen tral moments, first- and second-order auto-correlation functions and t he power spectrum of a first-order, discrete-time Markov chain. We sho w that the mean, variance, third central moment and power spectrum pro vide sufficient information for the estimation of the parameters of th e signal in question. We demonstrate the estimation procedure with num erical examples for both simulated and real biological data, and descr ibe a method for estimating the non-unity eigenvalue of the transition matrix as well as the noise variance from the power spectrum of the n oisy signal.