Fitting interconnected Markov chain models – DNA sequences and test cricket matches

Discrete state series can often be modelled by stationary Markov chains. However, if the Markov chain depends on the value of an additional variable, then it may be necessary to fit a set of interconnected Markov chains. This paper shows how this can be done using log-linear modelling. The methods are exemplified by modelling the human alpha-fetoprotein DNA sequence and the results of Australia versus England test cricket matches. In the former case, the additional variable is reading frame position and in the latter it is the country in which the match is played. Practical problems such as the power of the tests and the effect of cells with small expected values are discussed.