Adaptive Bayesian SLOPE: Model Selection With Incomplete Data

We consider the problem of variable selection in high-dimensional settings with missing observations among covariates. To address this relatively understudied problem, we propose a new synergistic procedure—adaptive Bayesian SLOPE values—which effectively combines (sorted l1 regularization) spike-and-slab LASSO (SSL) and is accompanied by an efficient stochastic approximation expected maximization (SAEM) algorithm to handle data. Similarly as SSL, regression coefficients are regarded arising from hierarchical model consisting two groups: spike for inactive slab active. However, instead assigning independent Laplace priors each covariate, here deploy joint “spike-and-slab” prior which takes into account ordering coefficient magnitudes order control false discoveries. position our approach within framework allows simultaneous parameter estimation while handling Through extensive simulations, demonstrate satisfactory performance terms power, discovery rate (FDR) bias under wide range scenarios including complete data existence missingness. Finally, analyze real dataset patients Paris hospitals who underwent severe trauma, where show competitive predicting platelet levels. Our methodology has been implemented C++ wrapped open source R programs public use. Supplemental files article available online.