Simple and Multiple Change Point Detection in Multiple Linear Regression and Application to Hydroclimatic Variables

Two Bayesian methods of changepoint detection in multivariate linear regression are proposed. The first approach allows simultaneous single changepoint detection in a multivariate sample. It improves on recently published changepoint detection methodologies by allowing a more flexible prior specification for the existence of a change, the date of change and for the regression parameters. The estimation of parameters is achieved by MCMC simulations. The second approach is a multiple changepoint detection model in multivariate linear regression. A new class of priors for the parameters of the multivariate linear model is introduced and useful formulas are derived that permit straightforward computation of the posterior distribution of the changepoints. The second method is numerically efficient and does not involve MCMC simulation. It allows fast simulation of the probability of each possible number of changepoints and the posterior probability distribution of each changepoint conditional on the number of changes.