Bayesian multivariate linear regression with application to change point models in hydrometeorological variables

Abstract

Multivariate linear regression is one of the most popular modeling tools in hydrology and climate sciences for explaining the link between key variables. Piecewise linear regression is not always appropriate since the relationship may experiment sudden changes due to climatic, environmental, or anthropogenic perturbations. To address this issue, a practical and general approach to the Bayesian analysis of the multivariate regression model is presented. The approach allows simultaneous single change point detection in a multivariate sample and can account for missing data in the response variables and/or in the explicative variables. It also improves on recently published change point detection methodologies by allowing a more flexible and thus more realistic prior specification for the existence of a change and the date of change as well as for the regression parameters. The estimation of all unknown parameters is achieved by Monte Carlo Markov chain simulations. It is shown that the developed approach is able to reproduce the results of Rasmussen (2001) as well as those of Perreault et al. (2000a, 2000b). Furthermore, two of the examples provided in the paper show that the proposed methodology can readily be applied to some problems that cannot be addressed by any of the above‐mentioned approaches because of limiting model structure and/or restrictive prior assumptions. The first of these examples deals with single change point detection in the multivariate 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. The second one addresses the problem of missing data estimation with uncertainty assessment in multisite streamflow records with a possible simultaneous shift in mean streamflow values that occurred at an unknown date.