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We introduce a Bayesian framework for simultaneous feature selection and outlier detection in sparse high-dimensional regression models, with a focus on quantitative trait locus (QTL) mapping in experimental crosses. More specifically, we incorporate the robust mean shift outlier handling mechanism into the multiple QTL mapping regression model and apply LASSO regularization concurrently to the genetic effects and the mean-shift terms through the flexible extended Bayesian LASSO (EBL) prior structure, thereby combining QTL mapping and outlier detection into a single sparse model representation problem. The EBL priors on the mean-shift terms prevent outlying phenotypic values from distorting the genotype-phenotype association and allow their detection as cases with outstanding mean shift values following the LASSO shrinkage. Simulation results demonstrate the effectiveness of our new methodology …