Modelling and identification of coupled Markov chain model with application

Abstract

A parametrized Markov chain model is developed to model the action of a biological ion channel. The proposed model takes the form of a set of identical binary chains which are dependent according to a coupling parameter. The outputs of these chains combine additively to give a record of ion current buried in large amounts of noise versus time. When varied, the coupling parameter realizes a range of behaviours from tight coupling to complete independence. Other model parameters describe the intrinsic characteristics of the binary chains as well as their behaviour when fully coupled. An identification procedure for the model parameters is developed based on hidden Markov modelling ideas but incorporating a gradient descent estimation algorithm. In this way we cope with the non-linear form of the dependence of the model on the parameters. The model and identification methods are tested and verified on simulated data and real biological data. Show more