Data Reduction in Markov model using EM algorithm

TL;DR

This paper introduces a method for reducing data in Markov chains by filtering transitions and estimating parameters using the EM algorithm, applicable to models with structural zeros and multiple chains.

Contribution

It develops a filtering-based data reduction technique and extends EM estimation to complex Markov models with structural zeros and multiple chains.

Findings

Method performs well on simulated data

Effective in models with structural zeros

Validated on real-life data

Abstract

This paper describes a data reduction technique in case of a markov chain of specified order. Instead of observing all the transitions in a markov chain we record only a few of them and treat the remaining part as missing. The decision about which transitions to be filtered is taken before the observation process starts. Based on the filtered chain we try to estimate the parameters of the markov model using EM algorithm. In the first half of the paper we characterize a class of filtering mechanism for which all the parameters remain identifiable. In the later half we explain methods of estimation and testing about the transition probabilities of the markov chain based on the filtered data. The methods are first developed assuming a simple markov model with each probability of transition positive, but then generalized for models with structural zeroes in the transition probability matrix. Further extension is also done for multiple markov chains. The performance of the developed method of estimation is studied using simulated data along with a real life data.