Bayesian Variable Selection for Semiparametric Logistic Regression

Lasso variable selection is an attractive approach to improve the prediction accuracy. Bayesian lasso approach is suggested to estimate and select the important variables for single index logistic regression model. Laplace distribution is set as prior to the coefficients vector and prior to the unknown link function (Gaussian process). A hierarchical Bayesian lasso semiparametric logistic regression model is constructed and MCMC algorithm is adopted for posterior inference. To evaluate the performance of the proposed method BSLLR is through comparing it to three existing methods BLR, BPR and BBQR. Simulation examples and numerical data are to be considered. The results indicate that the proposed method get the smallest bias, SD, MSE and MAE in simulation and real data. The proposed method BSLLR performs better than other methods.

An Extreme Value Bayesian Lasso for the Conditional Left and Right Tails

We introduce a novel regression model for the conditional left and right tail of a possibly heavy-tailed response. The proposed model can be used to learn the effect of covariates on an extreme value setting via a Lasso-type specification based on a Lagrangian restriction. Our model can be used to track if some covariates are significant for the lower values, but not for the (right) tail—and vice versa; in addition to this, the proposed model bypasses the need for conditional threshold selection in an extreme value theory framework. We assess the finite-sample performance of the proposed methods through a simulation study that reveals that our method recovers the true conditional distribution over a variety of simulation scenarios, along with being accurate on variable selection. Rainfall data are used to showcase how the proposed method can learn to distinguish between key drivers of moderate rainfall, against those of extreme rainfall. Supplementary materials accompanying this paper appear online.

Single-Trait and Multiple-Trait Genomic Prediction From Multi-Class Bayesian Alphabet Models Using Biological Information

Genomic prediction has been widely used in multiple areas and various genomic prediction methods have been developed. The majority of these methods, however, focus on statistical properties and ignore the abundant useful biological information like genome annotation or previously discovered causal variants. Therefore, to improve prediction performance, several methods have been developed to incorporate biological information into genomic prediction, mostly in single-trait analysis. A commonly used method to incorporate biological information is allocating molecular markers into different classes based on the biological information and assigning separate priors to molecular markers in different classes. It has been shown that such methods can achieve higher prediction accuracy than conventional methods in some circumstances. However, these methods mainly focus on single-trait analysis, and available priors of these methods are limited. Thus, in both single-trait and multiple-trait analysis, we propose the multi-class Bayesian Alphabet methods, in which multiple Bayesian Alphabet priors, including RR-BLUP, BayesA, BayesB, BayesCΠ, and Bayesian LASSO, can be used for markers allocated to different classes. The superior performance of the multi-class Bayesian Alphabet in genomic prediction is demonstrated using both real and simulated data. The software tool JWAS offers open-source routines to perform these analyses.

Bayesian Gene Selection Based on Pathway Information and Network-Constrained Regularization

High-throughput data make it possible to study expression levels of thousands of genes simultaneously under a particular condition. However, only few of the genes are discriminatively expressed. How to identify these biomarkers precisely is significant for disease diagnosis, prognosis, and therapy. Many studies utilized pathway information to identify the biomarkers. However, most of these studies only incorporate the group information while the pathway structural information is ignored. In this paper, we proposed a Bayesian gene selection with a network-constrained regularization method, which can incorporate the pathway structural information as priors to perform gene selection. All the priors are conjugated; thus, the parameters can be estimated effectively through Gibbs sampling. We present the application of our method on 6 microarray datasets, comparing with Bayesian Lasso, Bayesian Elastic Net, and Bayesian Fused Lasso. The results show that our method performs better than other Bayesian methods and pathway structural information can improve the result.

Evaluation of Bayesian Alphabet and GBLUP Based on Different Marker Density for Genomic Prediction in Alpine Merino Sheep

ABSTRACT The marker density, the heritability level of trait and the statistical models adopted are critical to the accuracy of genomic prediction (GP) or selection (GS). If the potential of GP is to be fully utilized to optimize the effect of breeding and selection, in addition to incorporating the above factors into simulated data for analysis, it is essential to incorporate these factors into real data for understanding their impact on GP accuracy, more clearly and intuitively. Herein, we studied the genomic prediction of six wool traits of sheep by two different models, including Bayesian Alphabet (BayesA, BayesB, BayesC π and Bayesian LASSO) and genomic best linear unbiased prediction (GBLUP). We adopted 5-fold cross-validation to perform the accuracy evaluation based on the genotyping data of Alpine Merino sheep (n = 821). The main aim was to study the influence and interaction of different models and marker densities on GP accuracy. The GP accuracy of the six traits was found to be between 0.28 and 0.60, as demonstrated by the cross-validation results. We showed that the accuracy of GP could be improved by increasing the marker density, which is closely related to the model adopted and the heritability level of the trait. Moreover, based on two different marker densities, it was derived that the prediction effect of GBLUP model for traits with low heritability was better; while with the increase of heritability level, the advantage of Bayesian Alphabet would be more obvious, therefore, different models of GP are appropriate in different traits. These findings indicated the significance of applying appropriate models for GP which would assist in further exploring the optimization of GP.