La régression linéaire vue sous l'angle Bayesien

These notes aim at clarifying different strategies to perform linear regression from given dataset. Methods like the weighted and ordinary least squares, ridge regression or LASSO are proposed in the literature. The present article is my understanding of these methods which are, according to me, better unified in the Bayesian framework. The formulas to address linear regression with these methods are derived. The KIC for model selection is also derived in the end of the document

Interzone short wave radiative couplings through windows and large openings : proposal of a simplified model

International audienceA simplified model of indoor short wave radiation couplings adapted to multi-zone simulations is proposed, thanks to a simplifying hypothesis and to the introduction of an indoor short wave exchange matrix. The specific properties of this matrix appear useful to quantify the thermal radiation exchanges between the zones separated by windows or large openings. Integrated in CODYRUN software, this module is detailed and compared to experimental measurements carried out on a real scale tropical buildin

Sensitivity analysis for models with dynamic inputs: a case study to control the heat consumption of a real passive house

International audienceIn this communication, we perform the sensitivity analysis of a building energy model. The aim is to assess the impact of the weather data on the performance of a model of a passive house, in order to better control it. The weather data are uncertain dynamic inputs to the model. To evaluate their impact, the problem of generating coherent weather data arises. To solve it, we carry out the Karhunen-Loève decomposition of the uncertain dynamic inputs. We then propose an approach for the sensitivity analysis of this kind of models. The originality for sensitivity analysis purpose is to separate the random variable of the dynamic inputs, propagated to the model response, from the deterministic spatio/temporal function. This analysis highlights the role of the solar gain on a high-insulated passive building, during winter time

Sensitivity analysis of complex models: coping with dynamic and static inputs

International audienceIn this paper, we address the issue of performing sensitivity analysis of complex models presenting uncertain static and dynamic inputs. The dynamic inputs are viewed as random processes which can be represented by a linear combination of the deterministic functions depending on time whose coefficients are uncorrelated random variables. To achieve this, the Karhunen-Loève decomposition of the dynamic inputs is performed. For sensitivity analysis purposes, the influence of the dynamic inputs onto the model response is then given by the one of the uncorrelated random coefficients of the Karhunen-Loève decomposition, which is the originality here. The approach is applied to a building energy model, in order to assess the impact of the uncertainties of the material properties and the weather data on the energy performance of a real low energy consumption house