Fast robust estimation of prediction error based on resampling

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Simultaneous Selection of Multiple Important Single Nucleotide Polymorphisms in Familial Genome Wide Association Studies Data

We propose a resampling-based fast variable selection technique for selecting important Single Nucleotide Polymorphisms (SNP) in multi-marker mixed effect models used in twin studies. Due to computational complexity, current practice includes testing the effect of one SNP at a time, commonly termed as `single SNP association analysis'. Joint modeling of genetic variants within a gene or pathway may have better power to detect the relevant genetic variants, hence we adapt our recently proposed framework of $e$-values to address this. In this paper, we propose a computationally efficient approach for single SNP detection in families while utilizing information on multiple SNPs simultaneously. We achieve this through improvements in two aspects. First, unlike other model selection techniques, our method only requires training a model with all possible predictors. Second, we utilize a fast and scalable bootstrap procedure that only requires Monte-Carlo sampling to obtain bootstrapped copies of the estimated vector of coefficients. Using this bootstrap sample, we obtain the $e$-value for each SNP, and select SNPs having $e$-values below a threshold. We illustrate through numerical studies that our method is more effective in detecting SNPs associated with a trait than either single-marker analysis using family data or model selection methods that ignore the familial dependency structure. We also use the $e$-values to perform gene-level analysis in nuclear families and detect several SNPs that have been implicated to be associated with alcohol consumption

Determination of Bootstrap confidence intervals on sensitivity indices obtained by polynomial chaos expansion

L’analyse de sensibilité a pour but d’évaluer l’influence de la variabilité d’un ou plusieurs paramètres d’entrée d’un modèle sur la variabilité d’une ou plusieurs réponses. Parmi toutes les méthodes d’approximations, le développement sur une base de chaos polynômial est une des plus efficace pour le calcul des indices de sensibilité, car ils sont obtenus analytiquement grâce aux coefficients de la décomposition (Sudret (2008)). Les indices sont donc approximés et il est difficile d’évaluer l’erreur due à cette approximation. Afin d’évaluer la confiance que l’on peut leur accorder nous proposons de construire des intervalles de confiance par ré-échantillonnage Bootstrap (Efron, Tibshirani (1993)) sur le plan d’expérience utilisé pour construire l’approximation par chaos polynômial. L’utilisation de ces intervalles de confiance permet de trouver un plan d’expérience optimal garantissant le calcul des indices de sensibilité avec une précision donnée

A new adaptive response surface method for reliability analysis

Response surface method is a convenient tool to assess reliability for a wide range of structural mechanical problems. More specifically, adaptive schemes which consist in iteratively refine the experimental design close to the limit state have received much attention. However, it is generally difficult to take into account a lot of variables and to well handle approximation error. The method, proposed in this paper, addresses these points using sparse response surface and a relevant criterion for results accuracy. For this purpose, a response surface is built from an initial Latin Hypercube Sampling (LHS) where the most significant terms are chosen from statistical criteria and cross-validation method. At each step, LHS is refined in a region of interest defined with respect to an importance level on probability density in the design point. Two convergence criteria are used in the procedure: The first one concerns localization of the region and the second one the response surface quality. Finally, a bootstrap method is used to determine the influence of the response error on the estimated probability of failure. This method is applied to several examples and results are discussed

A One-Sample Test for Normality with Kernel Methods

We propose a new one-sample test for normality in a Reproducing Kernel Hilbert Space (RKHS). Namely, we test the null-hypothesis of belonging to a given family of Gaussian distributions. Hence our procedure may be applied either to test data for normality or to test parameters (mean and covariance) if data are assumed Gaussian. Our test is based on the same principle as the MMD (Maximum Mean Discrepancy) which is usually used for two-sample tests such as homogeneity or independence testing. Our method makes use of a special kind of parametric bootstrap (typical of goodness-of-fit tests) which is computationally more efficient than standard parametric bootstrap. Moreover, an upper bound for the Type-II error highlights the dependence on influential quantities. Experiments illustrate the practical improvement allowed by our test in high-dimensional settings where common normality tests are known to fail. We also consider an application to covariance rank selection through a sequential procedure