Advanced Residual Analysis Techniques for Model Selection A.Murari 1, D.Mazon 2, J.Vega 3, P.Gaudio 4, M.Gelfusa 4, A.Grognu 5, I.Lupelli 4, M.Odstrcil University of Rome Tor Vergata 5 The Scientific Method and Models Model building is a innate faculty of human beings because it allows handling information in a much more economic way. Model validation: process of assessing the quality of your model Model selection: process of selecting the best model, among many, to interpret the available data. A subject value approach is advocated: both model selection and model validation are utility based Model Model selection =No established and universal methodology available Model Falsification Criterion (MFC) : Estimates the most appropriate model among a set of competing and independent ones Based both on the accuracy and the robustness of the candidate models Implements a form of falsification principle more than the Occam razor A model is not penalised for its complexity but on the basis of its lack of robustness Model selection: introduction ROBUSTNESS: a model is not penalised for its complexity but more for its lack of robustness, i.e. the fact that its estimates degrade if errors in the parameters are made small errors introduced on each model parameter study of the repercussions on the global estimates The repercussions of the parameter errors are quantified with some sort of information theoretic quantity (Shannon entropy) calculated for the residuals MFC : THE BASIC PHYLOSOPHY Details in the paper A.Murari et al Preliminary discussion on a new Model Selection Criterion, based on the statistics of the residuals and the falsification principle Conference FDT2 (Frontiers in Diagnostic Technologies) The correlation tests method Hypothesis: the noise is random and additive Consequence: the residuals of a perfect model should be randomly distributed The model with the distribution of the residuals closer to a random one is to be preferred A random distribution of numbers (residuals) maximizes the Shannon entropy Mathematical expression of the Model Falsification Criterion : r i the absolute value of the i-th residual p i r the quantised probability of the i-th residual r par,i calculated after varying each parameter one at time ( 10 %) p par,i the quantised probability of this new residual n par the number of model parameters 1