for “ BioHMM : a heterogeneous hidden Markov model for segmenting array CGH data

1.1 The structure of the model when there are more than two states We now describe how BioHMM is used when there are more than two underlying states. Most of the components of the model can be extended in an obvious way using the framework described in the Approach section of the paper. Because of the constraints imposed upon the parameters in the transition matrix, its structure is slightly counter-intuitive. Hence we give a brief description of the structure of the transition matrix in the situation where there are three underlying states. The extension to four or more states is, indeed, straightforward. Suppose that we wish to fit our heterogeneous HMM when there are three underlying states. We assume that there are n clones located on a chromosome and that a measure of the distance between adjacent clones is captured in a vector, x, of length n − 1. We then define the transition matrix A i for 1 ≤ i ≤ n − 1 as follows: