How to apply Bayesian stochastic search variable selection with multiply imputed data.

Combining cow and bull reference populations to increase accuracy of genomic prediction and genome-wide association studies

Selecting a small number of relevant genes for classification has received a great deal of attention in microarray data analysis. While the development of methods for microarray data with only two classes is relevant, developing more efficient algorithms for classification with any number of classes is important. In this paper, we propose a Bayesian stochastic search variable selection approach for multi-class classification, which can identify relevant genes by assessing sets of genes jointly. We consider a multinomial probit model with a generalized $$g$$g-prior for the regression coefficients. An efficient algorithm using simulation-based MCMC methods are developed for simulating parameters from the posterior distribution. This algorithm is robust to the choice of initial value, and produces posterior probabilities of relevant genes for biological interpretation. We demonstrate the performance of the approach with two well-known gene expression profiling data: leukemia data, lymphoma data, SRBCTs data and NCI60 data. Compared with other classification approaches, our approach selects smaller numbers of relevant genes and obtains competitive classification accuracy based on obtained results.

Across multiply imputed data sets, variable selection methods such as stepwise regression and other criterion-based strategies that include or exclude particular variables typically result in models with different selected predictors, thus presenting a problem for combining the results from separate complete-data analyses. Here, drawing on a Bayesian framework, we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates. One approach, which we call "impute, then select" (ITS) involves initially performing multiple imputation and then applying Bayesian variable selection to the multiply imputed data sets. A second strategy is to conduct Bayesian variable selection and missing data imputation simultaneously within one Gibbs sampling process, which we call "simultaneously impute and select" (SIAS). The methods are implemented and evaluated using the Bayesian procedure known as stochastic search variable selection for multivariate normal data sets, but both strategies offer general frameworks within which different Bayesian variable selection algorithms could be used for other types of data sets. A study of mental health services utilization among children in foster care programs is used to illustrate the techniques. Simulation studies show that both ITS and SIAS outperform complete-case analysis with stepwise variable selection and that SIAS slightly outperforms ITS.

BackgroundWe applied stochastic search variable selection (SSVS), a Bayesian model selection method, to the simulated data of Genetic Analysis Workshop 13. We used SSVS with the revisited Haseman-Elston method to find the markers linked to the loci determining change in cholesterol over time. To study gene-gene interaction (epistasis) and gene-environment interaction, we adopted prior structures, which incorporate the relationship among the predictors. This allows SSVS to search in the model space more efficiently and avoid the less likely models.ResultsIn applying SSVS, instead of looking at the posterior distribution of each of the candidate models, which is sensitive to the setting of the prior, we ranked the candidate variables (markers) according to their marginal posterior probability, which was shown to be more robust to the prior. Compared with traditional methods that consider one marker at a time, our method considers all markers simultaneously and obtains more favorable results.ConclusionsWe showed that SSVS is a powerful method for identifying linked markers using the Haseman-Elston method, even for weak effects. SSVS is very effective because it does a smart search over the entire model space.

Multiple imputation (MI) is a commonly used technique for handling missing data in large-scale medical and public health studies. However, variable selection on multiply-imputed data remains an important and longstanding statistical problem. If a variable selection method is applied to each imputed dataset separately, it may select different variables for different imputed datasets, which makes it difficult to interpret the final model or draw scientific conclusions. In this paper, we propose a novel multiple imputation-least absolute shrinkage and selection operator (MI-LASSO) variable selection method as an extension of the least absolute shrinkage and selection operator (LASSO) method to multiply-imputed data. The MI-LASSO method treats the estimated regression coefficients of the same variable across all imputed datasets as a group and applies the group LASSO penalty to yield a consistent variable selection across multiple-imputed datasets. We use a simulation study to demonstrate the advantage of the MI-LASSO method compared with the alternatives. We also apply the MI-LASSO method to the University of Michigan Dioxin Exposure Study to identify important circumstances and exposure factors that are associated with human serum dioxin concentration in Midland, Michigan.

Observed variable and factor selection are critical components of factor analysis, particularly when the optimal subset of observed variables and the number of factors are unknown and results cannot be replicated across studies. The Replicable Factor Analytic Solutions (RFAS) algorithm was developed to assess the replicability of factor structures-both in terms of the number of factors and the variables retained-while identifying the "best" or most replicable solutions according to predefined criteria. This study evaluated RFAS performance across 54 experimental conditions that varied in model complexity (six-factor models), interfactor correlations (ρ = 0, .30, and .60), and sample sizes (n = 300, 500, and 1000). Under default settings, RFAS generally performed well and demonstrated its utility in producing replicable factor structures. However, performance declined with highly correlated factors, smaller sample sizes, and more complex models. RFAS was also compared to four alternative variable selection methods: Ant Colony Optimization (ACO), Weighted Group Least Absolute Shrinkage and Selection Operator (LASSO), and stepwise procedures based on target Tucker-Lewis Index (TLI) and ΔTLI criteria. Stepwise and LASSO methods were largely ineffective at eliminating problematic variables under the studied conditions. In contrast, both RFAS and ACO successfully removed variables as intended, although the resulting factor structures often differed substantially between the two approaches. As with other variable selection methods, refining algorithmic criteria may be necessary to further enhance model performance.

Evaluation of the effect of chance correlations on variable selection using Partial Least Squares-Discriminant Analysis

The goal of genome-wide association studies (GWAS) is to identify the best subset of single-nucleotide polymorphisms (SNPs) that strongly influence a certain trait. State of the art GWAS comprise several thousand or even millions of SNPs, scored on a substantially lower number of individuals. Hence, the number of variables greatly exceeds the number of observations, which also is known as the p≫n problem. This problem has been tackled by using Bayesian variable selection methods, for example stochastic search variable selection (SSVS) and Bayesian penalized regression methods (Bayesian lasso; BLA and Bayesian ridge regression; BRR). Even though the above mentioned approaches are capable of dealing with situations where p≫n, it is also known that these methods experience problems when the predictor variables are correlated. The potential problem that linkage disequilibrium (LD) between SNPs can introduce is often ignored. The main contribution of this study is to assess the performance of SSVS, BLA, BRR and a recently introduced method denoted hybrid correlation based search (hCBS) with respect to their ability to identify quantitative trait loci, where SNPs are partially highly correlated. Furthermore, each method’s capability to predict phenotypes based on the selected SNPs and their computational demands are studied. Comparison is based upon three simulated datasets where the simulated phenotypes are assumed to be normally distributed. Results indicate that all methods perform reasonably well with respect to true positive detections but often detect too many false positives on all datasets. As the heritability decreases, the Bayesian penalized regression methods are no longer able to detect any predictors because of shrinkage. Overall, BLA slightly outperformed the other methods and provided superior results in terms of highest true positive/ false positive ratio, but SSVS achieved the best properties on the real LD data.

Agencies that regulate electricity providers often apply nonparametric data envelopment analysis (DEA) to assess the relative efficiency of each firm. The reliability and validity of DEA are contingent upon selecting relevant input variables. In the era of big (wide) data, the assumptions of traditional variable selection techniques are often violated due to challenges related to high-dimensional data and their standard empirical properties. Currently, regulators have access to a large number of potential input variables. Therefore, our aim is to introduce new machine learning methods for regulators of the energy market. We also propose a new two-step analytical approach where, in the first step, the machine learning-based adaptive least absolute shrinkage and selection operator (ALASSO) is used to select variables and, in the second step, selected variables are used in a DEA model. In contrast to previous research, we find, by using a more realistic data-generating process common for production functions (i.e., Cobb–Douglas and Translog), that the performance of different machine learning techniques differs substantially in different empirically relevant situations. Simulations also reveal that the ALASSO is superior to other machine learning and regression-based methods when the collinearity is low or moderate. However, in situations of multicollinearity, the LASSO approach exhibits the best performance. We also use real data from the Swedish electricity distribution market to illustrate the empirical relevance of selecting the most appropriate variable selection method.

Variable (wavelength) selection is critical in the multivariate calibration of spectra that improves prediction performance and provides clearer interpretation. Most variable selection methods use Y information (chemical reference of interest) to evaluating the importance of variables. In this work, a novel variable selection is proposed that requires no reference information. Replicate spectra of a sample under various acquisition conditions were used with an index to evaluate the importance of variables. The results show that the proposed method achieves better results than the original partial least squares model with a few available calibration samples. When a large number of calibration samples are available, this method provided comparable results to the state-of-the-art variable selection methods while reduced the risk of model over-fitting.

This study proposes methods for estimating Bayesian vector autoregressions (VARs) with a (semi-) automatic variable selection and an informative prior on the unconditional mean or steady-state of the system. We show that extant Gibbs sampling methods for Bayesian variable selection can be efficiently extended to incorporate prior beliefs on the steady-state of the economy. Empirical analysis, based on three major US macroeconomic time series, indicates that the out-of-sample forecasting accuracy of a VAR model is considerably improved when it combines both variable selection and steady-state prior information.

Reconciling phylogeography and ecological niche models for New Zealand beetles: Looking beyond glacial refugia

BackgroundIn contrast to currently used single nucleotide polymorphism (SNP) panels, the use of whole-genome sequence data is expected to enable the direct estimation of the effects of causal mutations on a given trait. This could lead to higher reliabilities of genomic predictions compared to those based on SNP genotypes. Also, at each generation of selection, recombination events between a SNP and a mutation can cause decay in reliability of genomic predictions based on markers rather than on the causal variants. Our objective was to investigate the use of imputed whole-genome sequence genotypes versus high-density SNP genotypes on (the persistency of) the reliability of genomic predictions using real cattle data.MethodsHighly accurate phenotypes based on daughter performance and Illumina BovineHD Beadchip genotypes were available for 5503 Holstein Friesian bulls. The BovineHD genotypes (631,428 SNPs) of each bull were used to impute whole-genome sequence genotypes (12,590,056 SNPs) using the Beagle software. Imputation was done using a multi-breed reference panel of 429 sequenced individuals. Genomic estimated breeding values for three traits were predicted using a Bayesian stochastic search variable selection (BSSVS) model and a genome-enabled best linear unbiased prediction model (GBLUP). Reliabilities of predictions were based on 2087 validation bulls, while the other 3416 bulls were used for training.ResultsPrediction reliabilities ranged from 0.37 to 0.52. BSSVS performed better than GBLUP in all cases. Reliabilities of genomic predictions were slightly lower with imputed sequence data than with BovineHD chip data. Also, the reliabilities tended to be lower for both sequence data and BovineHD chip data when relationships between training animals were low. No increase in persistency of prediction reliability using imputed sequence data was observed.ConclusionsCompared to BovineHD genotype data, using imputed sequence data for genomic prediction produced no advantage. To investigate the putative advantage of genomic prediction using (imputed) sequence data, a training set with a larger number of individuals that are distantly related to each other and genomic prediction models that incorporate biological information on the SNPs or that apply stricter SNP pre-selection should be considered.Electronic supplementary materialThe online version of this article (doi:10.1186/s12711-015-0149-x) contains supplementary material, which is available to authorized users.

The tea green leafhopper, Empoasca onukii Matsuda, is the most destructive insect pest of tea plantations in East Asia. Despite its economic importance and previous studies on this species, it remains unclear as to how this small-sized pest can have such wide range. By sequencing three mitochondrial genes and 17 microsatellite loci, we revealed the regional structure and demographic expansion of 59 E. onukii populations in China. Bayesian analysis of population genetic structure (BAPS) on microsatellites identified four genetic groups with spatial discontinuities, while analysis on mitochondrial genes inferred five nested and differentiated clusters. Both the Mantel test and the generalized linear model indicated a significant pattern of isolation by geographic distance in E. onukii populations. Based on the approximate Bayesian computation approach, E. onukii was found to have originated from southwestern China and expanded northward and eastward. While MIGRATE-N and Bayesian stochastic search variable selection (BSSVS) procedure in BEAST confirmed the possible eastward and northward dispersal from Yunnan, they also detected more gene flow from the derived populations in central and southeastern China. Our results suggest that the current distribution and structure of E. onukii is complicatedly influenced by human activities of cultivation, wide dissemination of tea in ancient China as well as recent transportation of tea seedlings for establishing new tea plantations. Insights into genetic differentiation and demographic expansion patterns from this study provide an important basis for the development of area-wide management of the E. onukii populations. © 2022 Society of Chemical Industry.

Makeup of the genetic correlation between milk production traits using genome-wide single nucleotide polymorphism information