Bayesian Least Absolute Shrinkage And Selection Operator Research Articles

A data-driven B-spline-enhanced Kriging method for uncertainty quantification based on Bayesian compressive sensing

Kriging is a powerful surrogate method for fitting smooth functions, and has been widely used in uncertainty quantification. However, for non-smooth functions, the performance of Kriging may be unsatisfactory. To overcome this drawback, we combine the advantages of spline functions and the Kriging model, and propose a data-driven B-spline-enhanced Kriging method (DDBSEK). Firstly, we establish the data-consistent orthogonal B-spline basis functions with the aid of the sample data of the input variables and replace the trend terms of the traditional Kriging model with these orthogonal B-spline bases. Then, by leveraging the fast marginal likelihood maximization algorithm and the Bayesian compressive sensing technique, an improved analytical Bayesian LASSO (least absolute shrinkage and selection operator) algorithm is developed to retain the active orthogonal B-spline bases. The proposed DDBSEK is validated using two types of numerical examples and one implicit engineering example. Results show that the proposed method is superior to the B-spline function model or the Kriging model alone.

Genome-enabled prediction of indicator traits of resistance to gastrointestinal nematodes in sheep using parametric models and artificial neural networks

This study aimed to assess the predictive ability of parametric models and artificial neural network method for genomic prediction of the following indicator traits of resistance to gastrointestinal nematodes in Santa Inês sheep: packed cell volume (PCV), fecal egg count (FEC), and Famacha© method (FAM). After quality control, the number of genotyped animals was 551 (PCV), 548 (FEC), and 565 (FAM), and 41,676 SNP. The average prediction accuracy (ACC) calculated by Pearson correlation between observed and predicted values and mean squared errors (MSE) were obtained using genomic best unbiased linear predictor (GBLUP), BayesA, BayesB, Bayesian least absolute shrinkage and selection operator (BLASSO), and Bayesian regularized artificial neural network (three and four hidden neurons, BRANN_3 and BRANN_4, respectively) in a 5-fold cross-validation technique. The average ACC varied from moderate to high according to the trait and models, ranging between 0.418 and 0.546 (PCV), between 0.646 and 0.793 (FEC), and between 0.414 and 0.519 (FAM). Parametric models presented nearly the same ACC and MSE for the studied traits and provided better accuracies than BRANN. The GBLUP, BayesA, BayesB and BLASSO models provided better accuracies than the BRANN_3 method, increasing by around 23% for PCV, and 18.5% for FEC. In conclusion, parametric models are suitable for genome-enabled prediction of indicator traits of resistance to gastrointestinal nematodes in sheep. Due to the small differences in accuracy found between them, the use of the GBLUP model is recommended due to its lower computational costs.

Comparative efficacy of three Bayesian variable selection methods in the context of weight loss in obese women.

The use of high-dimensional data has expanded in many fields, including in clinical research, thus making variable selection methods increasingly important compared to traditional statistical approaches. The work aims to compare the performance of three supervised Bayesian variable selection methods to detect the most important predictors among a high-dimensional set of variables and to provide useful and practical guidelines of their use. We assessed the variable selection ability of: (1) Bayesian Kernel Machine Regression (BKMR), (2) Bayesian Semiparametric Regression (BSR), and (3) Bayesian Least Absolute Shrinkage and Selection Operator (BLASSO) regression on simulated data of different dimensions and under three scenarios with disparate predictor-response relationships and correlations among predictors. This is the first study describing when one model should be preferred over the others and when methods achieve comparable results. BKMR outperformed all other models with small synthetic datasets. BSR was strongly dependent on the choice of its own intrinsic parameter, but its performance was comparable to BKMR with large datasets. BLASSO should be preferred only when it is reasonable to hypothesise the absence of synergies between predictors and the presence of monotonous predictor-outcome relationships. Finally, we applied the models to a real case study and assessed the relationships among anthropometric, biochemical, metabolic, cardiovascular, and inflammatory variables with weight loss in 755 hospitalised obese women from the Follow Up OBese patients at AUXOlogico institute (FUOBAUXO) cohort.

A novel polynomial dimension decomposition method based on sparse Bayesian learning and Bayesian model averaging

The polynomial dimensional decomposition (PDD), an orthogonal polynomial-based metamodel, has received increasing attention in uncertainty quantification (UQ). Nevertheless, for complex high-dimensional problems, its computational burden may become unaffordable, which is usually called curse of dimensionality. To solve this problem, sparse regression methods can be considered to establish a sparse PDD model. However, when the design samples are limited, their computational accuracy may be low due to the enormous size of the polynomial bases. Aimed at this issue, we proposed a novel sparse PDD metamodel based on the Bayesian LASSO (least absolute shrinkage and selection operator) method and an adaptive candidate basis selection and model updating method (CBSMU). Firstly, to improve the CPU efficiency, an analytical Bayesian LASSO based on the sparse Bayesian learning is used for the regression analysis, which replaces the time-consuming Markov chain Monte Carlo sampling of the traditional method with the efficient iteration algorithm for calculating the posterior estimations. Then, to reduce the size of the polynomial bases, this study proposes the adaptive CBSMU for screening the significant candidate polynomial bases and updating the metamodel sequentially. The CBSMU can find out the candidate bases that contributes to improve the prediction accuracy in the view of Bayesian model averaging. Thus, during the process of the sparse PDD modeling, the size of candidate bases is relatively small, which facilitates to improve the final computational accuracy when the design samples are limited. We verify the proposed method using three high-dimensional numerical examples, and apply it to solve one complex high-dimensional engineering problem. The results show that the proposed method is more accurate for UQ than the two common methods with the same computational costs, and is well-suited for solving complex high-dimensional structural dynamic problem.

Operational factor analysis of the aggressive taxi speeders using random parameters Bayesian LASSO modeling approach

Partial taxi speeders are observed with both high speeding frequency and severity (range). They thereby can be viewed as aggressive speeders whose behaviors may result in more hazards than others. Among the factors contributing to taxi speeding, the operational factors are proven to be deterministic. However, previous studies mainly investigate the operational factors of taxi speeding frequency, which fail to comprehensively unveil the impact of factors on speeders, especially for aggressive speeders. This study intends to disclose the operational factors affecting the aggressive taxi speeders with the random parameters Bayesian least absolute shrinkage and selection operator (LASSO) modeling approach. Taxi speeding behaviors and several operational factors are extracted from taxi GPS trajectory data in Chengdu, China. Based on the hourly speeding frequency and average speeding severity of each speeder, the fuzzy C-means clustering algorithm is employed to categorize taxi speeders into three cohorts: restrained speeder (RS), moderate speeder (MS), and belligerent speeder (BS). Compared to RS, MS and BS are treated as the aggressive taxi speeders. Several binary logistic models are developed with RS as the reference category. The random parameters Bayesian binary logistic LASSO model that captures the unobserved heterogeneity and tackles the multicollinearity is found to be the best fit model to identify the significant operational factors. The results indicate that aggressive taxi speeders are linked to longer daily driving distance and cruise distance, shorter delivery time, higher hourly income, driving at night, and driving on low-speed limit roads. However, intensive lane-changes and sufficient daily naps do not contribute to aggressive taxi speeders. Moreover, BS is more sensitive to the operational factors than MS. This study stresses the necessity of implementing speeder classification in taxi driver management and conceiving countermeasures considering the operational factors which are significantly associated with the aggressive taxi speeders.

Comparing methods for estimating patient-specific treatment effects in individual patient data meta-analysis.

Meta‐analysis of individual patient data (IPD) is increasingly used to synthesize data from multiple trials. IPD meta‐analysis offers several advantages over meta‐analyzing aggregate data, including the capacity to individualize treatment recommendations. Trials usually collect information on many patient characteristics. Some of these covariates may strongly interact with treatment (and thus be associated with treatment effect modification) while others may have little effect. It is currently unclear whether a systematic approach to the selection of treatment‐covariate interactions in an IPD meta‐analysis can lead to better estimates of patient‐specific treatment effects. We aimed to answer this question by comparing in simulations the standard approach to IPD meta‐analysis (no variable selection, all treatment‐covariate interactions included in the model) with six alternative methods: stepwise regression, and five regression methods that perform shrinkage on treatment‐covariate interactions, that is, least absolute shrinkage and selection operator (LASSO), ridge, adaptive LASSO, Bayesian LASSO, and stochastic search variable selection. Exploring a range of scenarios, we found that shrinkage methods performed well for both continuous and dichotomous outcomes, for a variety of settings. In most scenarios, these methods gave lower mean squared error of the patient‐specific treatment effect as compared with the standard approach and stepwise regression. We illustrate the application of these methods in two datasets from cardiology and psychiatry. We recommend that future IPD meta‐analysis that aim to estimate patient‐specific treatment effects using multiple effect modifiers should use shrinkage methods, whereas stepwise regression should be avoided.

Genomic prediction ability for feed efficiency traits using different models and pseudo-phenotypes under several validation strategies in Nelore cattle

There is a growing interest to improve feed efficiency (FE) traits in cattle. The genomic selection was proposed to improve these traits since they are difficult and expensive to measure. Up to date, there are scarce studies about the implementation of genomic selection for FE traits in indicine cattle under different scenarios of pseudo-phenotypes, models, and validation strategies on a commercial large scale. Thus, the aim was to evaluate the feasibility of genomic selection implementation for FE traits in Nelore cattle applying different models and pseudo-phenotypes under validation strategies. Phenotypic and genotypic information from 4 329 and 3 467 animals were used, respectively, which were tested for residual feed intake, DM intake, feed efficiency, feed conversion ratio, residual BW gain, and residual intake and BW gain. Six prediction methods were used: single-step genomic best linear unbiased prediction, Bayes A, Bayes B, Bayes Cπ, Bayesian least absolute shrinkage and selection operator (BLASSO), and Bayes R. Phenotypes adjusted for fixed effects (Y*), estimated breeding value (EBV), and EBV deregressed (DEBV) were used as pseudo-phenotypes. The validation approaches used were: (1) random: the data was randomly divided into ten subsets and the validation was done in each subset at a time; (2) age: the partition into training and testing sets was based on year of birth and testing animals were born after 2016; and (3) EBV accuracy: the data was split into two groups, being animals with accuracy above 0.45 the training set; and below 0.45 the validation set. In the analyses that used the Y* as pseudo-phenotype, prediction ability (PA) was obtained by dividing the correlation between pseudo-phenotype and genomic EBV (GEBV) by the square root of the heritability of the trait. When EBV and DEBV were used as the pseudo-phenotype, the simple correlation of this quantity with the GEBV was considered as PA. The prediction methods show similar results for PA and bias. The random cross-validation presented higher PA (0.17) than EBV accuracy (0.14) and age (0.13). The PA was higher for Y* than for EBV and DEBV (30.0 and 34.3%, respectively). Random validation presented the highest PA, being indicated for use in populations composed mainly of young animals and traits with few generations of data recording. For high heritability traits, the validation can be done by age, enabling the prediction of the next-generation genetic merit. These results would support breeders to identify genomic approaches that are more viable for genomic prediction for FE-related traits.

Triple categorical regression for genomic selection: application to cassava breeding

Genome-wide selection (GWS) is currently a technique of great importance in plant breeding, since it improves efficiency of genetic evaluations by increasing genetic gains. The process is based on genomic estimated breeding values (GEBVs) obtained through phenotypic and dense marker genomic information. In this context, GEBVs of N individuals are calculated through appropriate models, which estimate the effect of each marker on phenotypes, allowing the early identification of genetically superior individuals. However, GWS leads to statistical challenges, due to high dimensionality and multicollinearity problems. These challenges require the use of statistical methods to approach the regularization of the estimation process. Therefore, we aimed to propose a method denominated as triple categorical regression (TCR) and compare it with the genomic best linear unbiased predictor (G-BLUP) and Bayesian least absolute shrinkage and selection operator (BLASSO) methods that have been widely applied to GWS. The methods were evaluated in simulated populations considering four different scenarios. Additionally, a modification of the G-BLUP method was proposed based on the TCR-estimated (TCR/G-BLUP) results. All methods were applied to real data of cassava (Manihot esculenta) with to increase efficiency of a current breeding program. The methods were compared through independent validation and efficiency measures, such as prediction accuracy, bias, and recovered genomic heritability. The TCR method was suitable to estimate variance components and heritability, and the TCR/G-BLUP method provided efficient GEBV predictions. Thus, the proposed methods provide new insights for GWS.

Identifying the Driving Factors of Black Bloom in Lake Bay through Bayesian LASSO.

Black blooms are a serious and complex problem for lake bays, with far-reaching implications for water quality and drinking safety. While Fe(II) and S(−II) have been reported as the most important triggers of this phenomenon, little effort has been devoted in investigating the relationships between Fe(II) and S(−II) and the host of potentially important aquatic factors. However, a model involving many putative predictors and their interactions will be oversaturated and ill-defined, making ordinary least squares (OLS) estimation unfeasible. In such a case, sparsity assumption is typically required to exclude the redundant predictors from the model, either through variable selection or regularization. In this study, Bayesian least absolute shrinkage and selection operator (LASSO) regression was employed to identify the major influence variables from 11 aquatic factors for Fe(II), S(−II), and suspended sediment concentration (SSC) in the Chaohu Lake (Eastern of China) bay during black bloom maintenance. Both the main effects and the interactions between these factors were studied. The method successfully screened the most important variables from many items. The determination coefficients (R2) and adjusted determination coefficients (Adjust R2) showed that all regression equations for Fe(II), S(-II), and SSC were in good agreement with the situation observed in the Chaohu Lake. The outcome of correlation and LASSO regression indicated that total phosphorus (TP) was the single most important factor for Fe(II), S(-II), and SSC in black bloom with explanation ratios (ERs) of 76.1%, 37.0%, and 12.9%, respectively. The regression results showed that the interaction items previously deemed negligible have significant effects on Fe(II), S(−II), and SSC. For the Fe(II) equation, total nitrogen (TN) × dissolved oxygen (DO) and chlorophyll a (CHLA) × oxidation reduction potential (ORP), which contributed 10.6% and 13.3% ERs, respectively, were important interaction variables. TP emerged in each key interaction item of the regression equation for S(−II). Water depth (DEP) × Fe(II) (30.7% ER) was not only the main interaction item, but DEP (5.6% ER) was also an important single factor for the SSC regression equation. It also indicated that the sediment in shallow bay is an important source for SSC in water. The uncertainty of these relationships was also estimated by the posterior distribution and coefficient of variation (CV) of these items. Overall, our results suggest that TP concentration is the most important driver of black blooms in a lake bay, whereas the other factors, such as DO, DEP, and CHLA act in concert with other aquatic factors. There results provide a basis for the further control and management policy development of black blooms.

Combined index of genomic prediction methods applied to productivity

ABSTRACT: Rice cultivation has great national and global importance, being one of the most produced and consumed cereals in the world and the primary food for more than half of the world’s population. Because of its importance as food, developing efficient methods to select and predict genetically superior individuals in reference to plant traits is of extreme importance for breeding programs. The objective of this research was to evaluate and compare the efficiency of the Delta-p, G-BLUP (Genomic Best Linear Unbiased Predictor), BayesCpi, BLASSO (Bayesian Least Absolute Shrinkage and Selection Operator), Delta-p/G-BLUP index, Delta-p/BayesCpi index, and Delta-p/BLASSO index in the estimation of genomic values and the effects of single nucleotide polymorphisms on phenotypic data associated with rice traits. Use of molecular markers allowed high selective efficiency and increased genetic gain per unit time. The Delta-p method uses the concept of change in allelic frequency caused by selection and the theoretical concept of genetic gain. The Index is based on the principle of combined selection, using the information regarding the additive genomic values predicted via G-BLUP, BayesCpi, BLASSO, or Delta-p. These methods were applied and compared for genomic prediction using nine rice traits: flag leaf length, flag leaf width, panicles number per plant, primary panicle branch number, seed length, seed width, amylose content, protein content, and blast resistance. Delta-p/G-BLUP index had higher predictive abilities for the traits studied, except for amylose content trait in which the method with the highest predictive ability was BayesCpi, being approximately 3% greater than that of the Delta-p/G-BLUP index.

Genomic Prediction of Growth and Stem Quality Traits in Eucalyptus globulus Labill. at Its Southernmost Distribution Limit in Chile

The present study was undertaken to examine the ability of different genomic selection (GS) models to predict growth traits (diameter at breast height, tree height and wood volume), stem straightness and branching quality of Eucalyptus globulus Labill. trees using a genome-wide Single Nucleotide Polymorphism (SNP) chip (60 K), in one of the southernmost progeny trials of the species, close to its southern distribution limit in Chile. The GS methods examined were Ridge Regression-BLUP (RRBLUP), Bayes-A, Bayes-B, Bayesian least absolute shrinkage and selection operator (BLASSO), principal component regression (PCR), supervised PCR and a variant of the RRBLUP method that involves the previous selection of predictor variables (RRBLUP-B). RRBLUP-B and supervised PCR models presented the greatest predictive ability (PA), followed by the PCR method, for most of the traits studied. The highest PA was obtained for the branching quality (~0.7). For the growth traits, the maximum values of PA varied from 0.43 to 0.54, while for stem straightness, the maximum value of PA reached 0.62 (supervised PCR). The study population presented a more extended linkage disequilibrium (LD) than other populations of E. globulus previously studied. The genome-wide LD decayed rapidly within 0.76 Mbp (threshold value of r2 = 0.1). The average LD on all chromosomes was r2 = 0.09. In addition, the 0.15% of total pairs of linked SNPs were in a complete LD (r2 = 1), and the 3% had an r2 value >0.5. Genomic prediction, which is based on the reduction in dimensionality and variable selection may be a promising method, considering the early growth of the trees and the low-to-moderate values of heritability found in the traits evaluated. These findings provide new understanding of how develop novel breeding strategies for tree improvement of E. globulus at its southernmost range limit in Chile, which could represent new opportunities for forest planting that can benefit the local economy.

Ratemaking application of Bayesian LASSO with conjugate hyperprior

The generalized linear model (GLM) is a well developed statistical model widely used in actuarial practice for insurance ratemaking, risk classification, and reserving. Recently, there has been an explosion of data mining techniques to refine statistical models for better variable selection procedure and for improved prediction accuracy. Such techniques include the increased interest in regularization techniques, or penalized likelihood, to achieve these goals. In this paper, we explore the idea of Least Absolute Shrinkage and Selection Operator (LASSO) in a Bayesian framework within a dependent frequency-severity model as a refinement to the dependent GLM developed by Garrido et al. (2016). The LASSO technique is a penalized least squares procedure developed by Tibshirani (1996) and is extended to a Bayesian interpretation framework by Park and Casella (2008). We show that a new penalty function, which we call log-adjusted absolute deviation (LAAD), emerges if we further theoretically extend the Bayesian LASSO using conjugate hyperprior distributional assumptions. While this result has the ease of implementation for variable selection and prediction, we recognize that the use of least squares has been poorly viewed in insurance ratemaking. Instead however, we modify the setting to a penalized dependent GLM within this extended Bayesian LASSO framework. Within such framework, the regression estimates are derived by optimizing a penalized likelihood assuming a hyperprior distribution for the L1 penalty parameter lambda. This has the advantage of obtaining a consistent estimator for the regression coefficients as well as allowing variable selection. We calibrated our proposed model using an auto insurance dataset from a Singapore insurance company where we have observed claim counts and amounts from a portfolio of policyholders.

Logistic Bayesian LASSO for detecting association combining family and case-control data

Because of the limited information from the GAW20 samples when only case-control or trio data are considered, we propose eLBL, an extension of the Logistic Bayesian LASSO (least absolute shrinkage and selection operator) methodology so that both types of data can be analyzed jointly in the hope of obtaining an increased statistical power, especially for detecting association between rare haplotypes and complex diseases. The methodology is further extended to account for familial correlation among the case-control individuals and the trios. A 2-step analysis strategy was taken to first perform a genome-wise single single-nucleotide polymorphism (SNP) search using the Monte Carlo pedigree disequilibrium test (MCPDT) to determine interesting regions for the Adult Treatment Panel (ATP) binary trait. Then eLBL was applied to haplotype blocks covering the flagged SNPs in Step 1. Several significantly associated haplotypes were identified; most are in blocks contained in protein coding genes that appear to be relevant for metabolic syndrome. The results are further substantiated with a Type I error study and by an additional analysis using the triglyceride measurements directly as a quantitative trait.

Expanding the BLUP alphabet for genomic prediction adaptable to the genetic architectures of complex traits

Improvement of statistical methods is crucial for realizing the potential of increasingly dense genetic markers. Bayesian methods treat all markers as random effects, exhibit an advantage on dense markers, and offer the flexibility of using different priors. In contrast, genomic best linear unbiased prediction (gBLUP) is superior in computing speed, but only superior in prediction accuracy for extremely complex traits. Currently, the existing variety in the BLUP method is insufficient for adapting to new sequencing technologies and traits with different genetic architectures. In this study, we found two ways to change the kinship derivation in the BLUP method that improve prediction accuracy while maintaining the computational advantage. First, using the settlement under progressively exclusive relationship (SUPER) algorithm, we substituted all available markers with estimated quantitative trait nucleotides (QTNs) to derive kinship. Second, we compressed individuals into groups based on kinship, and then used the groups as random effects instead of individuals. The two methods were named as SUPER BLUP (sBLUP) and compressed BLUP (cBLUP). Analyses on both simulated and real data demonstrated that these two methods offer flexibility for evaluating a variety of traits, covering a broadened realm of genetic architectures. For traits controlled by small numbers of genes, sBLUP outperforms Bayesian LASSO (least absolute shrinkage and selection operator). For traits with low heritability, cBLUP outperforms both gBLUP and Bayesian LASSO methods. We implemented these new BLUP alphabet series methods in an R package, Genome Association and Prediction Integrated Tool (GAPIT), available at http://zzlab.net/GAPIT.

Iterative sure independence screening EM-Bayesian LASSO algorithm for multi-locus genome-wide association studies.

Genome-wide association study (GWAS) entails examining a large number of single nucleotide polymorphisms (SNPs) in a limited sample with hundreds of individuals, implying a variable selection problem in the high dimensional dataset. Although many single-locus GWAS approaches under polygenic background and population structure controls have been widely used, some significant loci fail to be detected. In this study, we used an iterative modified-sure independence screening (ISIS) approach in reducing the number of SNPs to a moderate size. Expectation-Maximization (EM)-Bayesian least absolute shrinkage and selection operator (BLASSO) was used to estimate all the selected SNP effects for true quantitative trait nucleotide (QTN) detection. This method is referred to as ISIS EM-BLASSO algorithm. Monte Carlo simulation studies validated the new method, which has the highest empirical power in QTN detection and the highest accuracy in QTN effect estimation, and it is the fastest, as compared with efficient mixed-model association (EMMA), smoothly clipped absolute deviation (SCAD), fixed and random model circulating probability unification (FarmCPU), and multi-locus random-SNP-effect mixed linear model (mrMLM). To further demonstrate the new method, six flowering time traits in Arabidopsis thaliana were re-analyzed by four methods (New method, EMMA, FarmCPU, and mrMLM). As a result, the new method identified most previously reported genes. Therefore, the new method is a good alternative for multi-locus GWAS.

Accuracy of genomic breeding values for meat tenderness in Polled Nellore cattle.

Zebu () cattle, mostly of the Nellore breed, comprise more than 80% of the beef cattle in Brazil, given their tolerance of the tropical climate and high resistance to ectoparasites. Despite their advantages for production in tropical environments, zebu cattle tend to produce tougher meat than Bos taurus breeds. Traditional genetic selection to improve meat tenderness is constrained by the difficulty and cost of phenotypic evaluation for meat quality. Therefore, genomic selection may be the best strategy to improve meat quality traits. This study was performed to compare the accuracies of different Bayesian regression models in predicting molecular breeding values for meat tenderness in Polled Nellore cattle. The data set was composed of Warner-Bratzler shear force (WBSF) of longissimus muscle from 205, 141, and 81 animals slaughtered in 2005, 2010, and 2012, respectively, which were selected and mated so as to create extreme segregation for WBSF. The animals were genotyped with either the Illumina BovineHD (HD; 777,000 from 90 samples) chip or the GeneSeek Genomic Profiler (GGP Indicus HD; 77,000 from 337 samples). The quality controls of SNP were Hard-Weinberg Proportion -value ≥ 0.1%, minor allele frequency > 1%, and call rate > 90%. The FImpute program was used for imputation from the GGP Indicus HD chip to the HD chip. The effect of each SNP was estimated using ridge regression, least absolute shrinkage and selection operator (LASSO), Bayes A, Bayes B, and Bayes Cπ methods. Different numbers of SNP were used, with 1, 2, 3, 4, 5, 7, 10, 20, 40, 60, 80, or 100% of the markers preselected based on their significance test (-value from genomewide association studies [GWAS]) or randomly sampled. The prediction accuracy was assessed by the correlation between genomic breeding value and the observed WBSF phenotype, using a leave-one-out cross-validation methodology. The prediction accuracies using all markers were all very similar for all models, ranging from 0.22 (Bayes Cπ) to 0.25 (Bayes B). When preselecting SNP based on GWAS results, the highest correlation (0.27) between WBSF and the genomic breeding value was achieved using the Bayesian LASSO model with 15,030 (3%) markers. Although this study used relatively few animals, the design of the segregating population ensured wide genetic variability for meat tenderness, which was important to achieve acceptable accuracy of genomic prediction. Although all models showed similar levels of prediction accuracy, some small advantages were observed with the Bayes B approach when higher numbers of markers were preselected based on their -values resulting from a GWAS analysis.

Hierarchical Bayesian LASSO for a negative binomial regression

ABSTRACTNumerous researches have been carried out to explain the relationship between the count data y and numbers of covariates x through a generalized linear model (GLM). This paper proposes a hierarchical Bayesian least absolute shrinkage and selection operator (LASSO) solution using six different prior models to the negative binomial regression. Latent variables Z have been introduced to simplify the GLM to a standard linear regression model. The proposed models regard two conjugate zero-mean Normal priors for the regression parameters and three independent priors for the variance: the Exponential, Inverse-Gamma and Scaled Inverse- distributions. Different types of priors result in different amounts of shrinkage. A Metropolis–Hastings-within-Gibbs algorithm is used to compute the posterior distribution of the parameters of interest through a data augmentation process. Based on the posterior samples, an original double likelihood ratio test statistic have been proposed to choose the most relevant covariates and shrink the insignificant coefficients to zero. Numerical experiments on a real-life data set prove that Bayesian LASSO methods achieved significantly better predictive accuracy and robustness than the classical maximum likelihood estimation and the standard Bayesian inference.

Balanced Bayesian LASSO for heavy tails

Regression procedures are not only hindered by large p and small n, but can also suffer in cases when outliers are present or the data generating mechanisms are heavy tailed. Since the penalized estimates like the least absolute shrinkage and selection operator (LASSO) are equipped to deal with the large p small n by encouraging sparsity, we combine a LASSO type penalty with the absolute deviation loss function, instead of the standard least squares loss, to handle the presence of outliers and heavy tails. The model is cast in a Bayesian setting and a Gibbs sampler is derived to efficiently sample from the posterior distribution. We compare our method to existing methods in a simulation study as well as on a prostate cancer data set and a base deficit data set from trauma patients.

Optimal population prediction of sandhill crane recruitment based on climate-mediated habitat limitations.

1. Prediction is fundamental to scientific enquiry and application; however, ecologists tend to favour explanatory modelling. We discuss a predictive modelling framework to evaluate ecological hypotheses and to explore novel/unobserved environmental scenarios to assist conservation and management decision-makers. We apply this framework to develop an optimal predictive model for juvenile (<1 year old) sandhill crane Grus canadensis recruitment of the Rocky Mountain Population (RMP). We consider spatial climate predictors motivated by hypotheses of how drought across multiple time-scales and spring/summer weather affects recruitment. 2. Our predictive modelling framework focuses on developing a single model that includes all relevant predictor variables, regardless of collinearity. This model is then optimized for prediction by controlling model complexity using a data-driven approach that marginalizes or removes irrelevant predictors from the model. Specifically, we highlight two approaches of statistical regularization, Bayesian least absolute shrinkage and selection operator (LASSO) and ridge regression. 3. Our optimal predictive Bayesian LASSO and ridge regression models were similar and on average 37% superior in predictive accuracy to an explanatory modelling approach. Our predictive models confirmed a priori hypotheses that drought and cold summers negatively affect juvenile recruitment in the RMP. The effects of long-term drought can be alleviated by short-term wet spring-summer months; however, the alleviation of long-term drought has a much greater positive effect on juvenile recruitment. The number of freezing days and snowpack during the summer months can also negatively affect recruitment, while spring snowpack has a positive effect. 4. Breeding habitat, mediated through climate, is a limiting factor on population growth of sandhill cranes in the RMP, which could become more limiting with a changing climate (i.e. increased drought). These effects are likely not unique to cranes. The alteration of hydrological patterns and water levels by drought may impact many migratory, wetland nesting birds in the Rocky Mountains and beyond. 5. Generalizable predictive models (trained by out-of-sample fit and based on ecological hypotheses) are needed by conservation and management decision-makers. Statistical regularization improves predictions and provides a general framework for fitting models with a large number of predictors, even those with collinearity, to simultaneously identify an optimal predictive model while conducting rigorous Bayesian model selection. Our framework is important for understanding population dynamics under a changing climate and has direct applications for making harvest and habitat management decisions.

Parametric and nonparametric statistical methods for genomic selection of traits with additive and epistatic genetic architectures.

Parametric and nonparametric methods have been developed for purposes of predicting phenotypes. These methods are based on retrospective analyses of empirical data consisting of genotypic and phenotypic scores. Recent reports have indicated that parametric methods are unable to predict phenotypes of traits with known epistatic genetic architectures. Herein, we review parametric methods including least squares regression, ridge regression, Bayesian ridge regression, least absolute shrinkage and selection operator (LASSO), Bayesian LASSO, best linear unbiased prediction (BLUP), Bayes A, Bayes B, Bayes C, and Bayes Cπ. We also review nonparametric methods including Nadaraya-Watson estimator, reproducing kernel Hilbert space, support vector machine regression, and neural networks. We assess the relative merits of these 14 methods in terms of accuracy and mean squared error (MSE) using simulated genetic architectures consisting of completely additive or two-way epistatic interactions in an F2 population derived from crosses of inbred lines. Each simulated genetic architecture explained either 30% or 70% of the phenotypic variability. The greatest impact on estimates of accuracy and MSE was due to genetic architecture. Parametric methods were unable to predict phenotypic values when the underlying genetic architecture was based entirely on epistasis. Parametric methods were slightly better than nonparametric methods for additive genetic architectures. Distinctions among parametric methods for additive genetic architectures were incremental. Heritability, i.e., proportion of phenotypic variability, had the second greatest impact on estimates of accuracy and MSE.