Recursion-based multiple changepoint detection in multiple linear regression and application to river streamflows

[1] A large number of models in hydrology and climate sciences rely on multiple linear regression to explain the link between key variables. The relationship in the physical world may experiment sudden changes because of climatic, environmental, or anthropogenic perturbations. To deal with this issue, a Bayesian method of multiple changepoint detection in multiple linear regression is proposed in this paper. It is an adaptation of the recursion-based multiple changepoint method of Fearnhead (2005, 2006) to the classical multiple linear model. A new class of priors for the parameters of the multiple linear model is introduced, and useful formulas are derived that permit straightforward computation of the posterior distribution of the changepoints. The proposed method is numerically efficient and does not involve time consuming Monte-Carlo Markov Chain simulation as opposed to other Bayesian changepoint methods. It allows fast and straightforward simulation of the probability of each possible number of changepoints as well as the posterior probability distribution of each changepoint conditional on the number of changes. The approach is validated on simulated data sets and then compared to the methodology of Seidou et al. (2006) on two practical problems, as follows: (1) the changepoint detection in the multiple linear relationship between mean basin scale precipitation at different periods of the year and the summer-autumn flood peaks of the Broadback River located in Northern Quebec, Canada; and (b) the detection of trend variations in the streamflows of the Ogoki River located in the province of Ontario, Canada.