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Abstract: In this paper, we are interested in the statistical forecasting of the daily mean PM10 concentration. Hourly concentrations of PM10 have been measured in the city of Rouen, in Haute-Normandie, France. Located at northwest of Paris, near the south side of Manche sea and heavily industrialised. We consider three monitoring stations reflecting the diversity of situations: an urban background station, a traffic station and an industrial station near the cereal harbour of Rouen. We have focused our attention on data for the months that register higher values, from December to March, on years 2004–2009. The models are obtained from the winter days of the four seasons 2004/2005 to 2007/2008 (training data) and then the forecasting performance is evaluated on the winter days of the season 2008/2009 (test data). We show that it is possible to accurately forecast the daily mean concentration by fitting a function of meteorological predictors and the average concentration measured on the previous day. The values of observed meteorological variables are used for fitting the models and are also considered for the test data. We have compared the forecasts produced by three different methods: persistence, generalized additive nonlinear models and clusterwise linear regression models. This last method gives very impressive results and the end of the paper tries to analyze the reasons of such a good behavior. [Copyright &y& Elsevier]

Abstract: This paper proposes, focusing on random forests, the increasingly used statistical method for classification and regression problems introduced by Leo Breiman in 2001, to investigate two classical issues of variable selection. The first one is to find important variables for interpretation and the second one is more restrictive and try to design a good parsimonious prediction model. The main contribution is twofold: to provide some experimental insights about the behavior of the variable importance index based on random forests and to propose a strategy involving a ranking of explanatory variables using the random forests score of importance and a stepwise ascending variable introduction strategy. [Copyright &y& Elsevier]

The understanding of many physical and engineering problems involves running complex computational models. Such models take as input a high number of numerical and physical explanatory variables. The information on these underlying input parameters is often limited or uncertain. It is therefore important, based on the relationships between the input variables and the output, to identify and prioritize the most influential inputs. One may use global sensitivity analysis (GSA) methods which aim at ranking input random variables according to their importance in the output uncertainty, or even quantify the global influence of a particular input on the output. Using sensitivity metrics to ignore less important parameters is a form of dimension reduction in the model's input parameter space. This suggests the use of meta-modeling as a quantitative approach for nonparametric GSA, where the original input/output relation is first approximated using various statistical regression techniques. Subsequently, the main goal of our work is to provide a comprehensive review paper in the domain of sensitivity analysis focusing on some interesting connections between random forests and GSA. The idea is to use a random forests methodology as an efficient non-parametric approach for building meta-models that allow an efficient sensitivity analysis. Apart its easy applicability to regression problems, the random forests approach presents further strong advantages by its ability to implicitly deal with correlation and high dimensional data, to handle interactions between variables and to identify informative inputs using a permutation based RF variable importance index which is easy and fast to compute. We further review an adequate set of tools for quantifying variable importance which are then exploited to reduce the model's dimension enabling otherwise infeasible sensibility analysis studies. Numerical results from several simulations and a data exploration on a real dataset are presented to illustrate the effectiveness of such an approach. • Global Sensitivity Analysis ranks inputs according to their importance on output. • Random Forests is an efficient non-parametric approach for building meta-models. • Random forests variable importance measure is used to define sensitivity measures. • Provide a comprehensive review paper in sensitivity analysis using random forests. • Focus on connections between random forests and Global Sensitivity Analysis. [ABSTRACT FROM AUTHOR]