Recursive Bayesian location of a discontinuity in time series

This paper presents a Bayesian approach to the location of a discontinuity in linearly modelled data. A matrix formulation is introduced which allows the modelling of changepoints in general linear models. Linear models investigated include abrupt changes in the mean of a Gaussian random variable, and piecewise polynomials such as splines, as well as autoregressive models. The approach facilitates the removal of nuisance parameters by integration. A general recursive technique for updating Bayesian posterior densities, which can result in large savings in computation, is also described