Différents procédés statistiques pour détecter la non-stationnarité dans les séries de précipitation
The main goal of this master's thesis is to find whether the summer convective precipitations simulated  by the Canadian Regional Climate Model (CRCM) are stationary over time or not.  In order to answer that question, we propose both a frequentist and Bayesian statistical methodology. For the frequentist approach, we used  standard quality control and the CUSUM to determine if the mean has increased over the years. For the Bayesian approach, we compared the posterior distributions of the precipitations over time. In order to do the comparison, we  used a statistic based on the Hellinger's distance, the J-divergence and the L2 norm.  In this master's thesis, we  used the ARL (average run length) to calibrate each of our methods. Therefore, a big part of this thesis is about studying the actual property of the ARL. Once our tools are well calibrated, we  used the simulation to compare them together. Finally, we studied the data from the CRCM to decide, whether or not, the data are stationary.
Cusum Arl J-divergence Stationarity Bayesian quality control Posteriori distribution comparaison Hellinger's distance