Bayesian Variable Selection via Perfect Gibbs Coupler Using Approximate Bounds

Variable selection is one of the most fundamental problems in regression analysis. By sampling from the posterior distributions of candidate models, Bayesian variable selection via MCMC （Markov chain Monte-Carlo） is effective to overcome the computational burden of all-subset variable selection approaches. However, the convergence of the MCMC is often hard to determine and one is often not sure about if obtained samples are unbiased. This complication has limited the application of Bayesian variable selection in practice. Based on the idea of CFTP （coupling from the past）, perfect sampling schemes have been developed to obtain independent samples from the posterior distribution for a variety of problems. Here the authors propose an efficient and effective perfect sampling algorithm for Bayesian variable selection of linear regression models, which independently and identically sample from the posterior distribution of the model space and can efficiently handle thousands of variables. The effectiveness of the authors＇ algorithm is illustrated by three simulation studies, which have up to thousands of variables, the authors＇ method is further illustrated in SNPs （single nucleotide polymorphisms） association study among RA （rheumatoid arthritis） patients.

Nearly optimal Bayesian shrinkage for high-dimensional regression

During the past decade,shrinkage priors have received much attention in Bayesian analysis of high-dimensional data.This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,which has a heavy and flat tail and allocates a sufficiently large probability mass in a very small neighborhood of zero.While enjoying its efficiency in posterior simulations,the shrinkage prior can lead to a nearly optimal posterior contraction rate and the variable selection consistency as the spike-and-slab prior.Our numerical results show that under the posterior consistency,Bayesian methods can yield much better results in variable selection than the regularization methods such as LASSO and SCAD.This paper also establishes a BvM-type result,which leads to a convenient way of uncertainty quantification for regression coefficient estimates.

A model for discrimination and prediction of mental workload of aircraft cockpit display interface

With respect to the ergonomic evaluation and optimization in the mental task design of the aircraft cockpit display interface, the experimental measurement and theoretical modeling of mental workload were carried out under flight simulation task conditions using the performance evaluation, subjective evaluation and physiological measurement methods. The experimental results show that with an increased mental workload, the detection accuracy of flight operation significantly reduced and the reaction time was significantly prolonged; the standard deviation of R-R intervals（SDNN） significantly decreased, while the mean heart rate exhibited little change; the score of NASA_TLX scale significantly increased. On this basis, the indexes sensitive to mental workload were screened, and an integrated model for the discrimination and prediction of mental workload of aircraft cockpit display interface was established based on the Bayesian Fisher discrimination and classification method. The original validation and cross-validation methods were employed to test the accuracy of the results of discrimination and prediction of the integrated model, and the average prediction accuracies determined by these two methods are both higher than 85%. Meanwhile, the integrated model shows a higher accuracy in discrimination and prediction of mental workload compared with single indexes. The model proposed in this paper exhibits a satisfactory coincidence with the measured data and could accurately reflect the variation characteristics of the mental workload of aircraft cockpit display interface, thus providing a basis for the ergonomic evaluation and optimization design of the aircraft cockpit display interface in the future.