The recursive estimation of a Markov chain

Abstract

For every hth member of a two-state Markov chain the value of a random variable Y is observed where the distribution of Y is conditional on the state of the corresponding member of the chain. A recursive set of equations is derived giving the posterior probabilities for both the observed and unobserved members. The use of this recursive solution to investigate the optimality of certain simple classification rules is discussed, and a “classification by runs” is also presented.