Bayesian methods for electricity load forecasting

In this manuscript, we develop Bayesian statistics tools to forecast the French electricity load. We first prove the asymptotic normality of the posterior distribution (Bernstein-von Mises theorem) for the piecewise linear regression model used to describe the heating effect and the consistency of the Bayes estimator. We then build a a hierarchical informative prior to help improve the quality of the predictions for a high dimension model with a short dataset. We typically show, with two examples involving the non metered EDF customers, that the method we propose allows a more robust estimation of the model with regard to the lack of data. Finally, we study a new nonlinear dynamic model to predict the electricity load online. We develop a particle filter algorithm to estimate the model et compare the predictions obtained with operationnal predictions from EDF.