Fitting multiple change-point models to data

Change-point problems arise when different subsequences of a data series follow different statistical distributions - commonly of the same functional form but having different parameters. This paper develops an exact approach for finding maximum likelihood estimates of the change points and within-segment parameters when the functional form is within the general exponential family. The algorithm, a dynamic program, has execution time only linear in the number of segments and quadratic in the number of potential change points. The details are worked out for the normal, gamma, Poisson and binomial distributions.