Multiple changepoint fitting via quasilikelihood, with application to DNA sequence segmentation

We consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship, while the variance of the observations depends on their mean. This model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints. The basic statistical problem consists of identification of the number of changepoints, their locations and the levels the function assumes in between. We embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model; for the choice of the number of changepoints, we discuss a modified Schwarz criterion. A dynamic programming algorithm makes the segmentation feasible for sequences of moderate length. The performance of the segmentation method is demonstrated in an application to the segmentation of the Bacteriophage λ sequence.