Bayesian change-point analysis in hydrometeorological time series. Part 1. The normal model revisited

A Bayesian method is presented for the analysis of two types of sudden change at an unknown time-point in a sequence of energy inflows modeled by independent normal random variables. First, the case of a single shift in the mean level is revisited to show how such a problem can be straightforwardly addressed through the Bayesian framework. Second, a change in variability is investigated. In hydrology, to our knowledge, this problem has not been studied from a Bayesian perspective. Even if this model is quite simple, no analytic solutions for parameter inference are available, and recourse to approximations is needed. It is shown that the Gibbs sampler is particularly suitable for change-point analysis, and this Markovian updating scheme is used. Finally, a case study involving annual energy inflows of two large hydropower systems managed by Hydro-Québec is presented in which informative prior distributions are specified from regional information.