×

Statistical and computational challenges in whole genome prediction and genome-wide association analyses for plant and animal breeding. (English) Zbl 1329.62451

Summary: Whole genome prediction (WGP) modeling and genome-wide association (GWA) analyses are big data issues in agricultural quantitative genetics. Both areas require meaningful input from the statistical scholarly community in order to further improve the accuracy of prediction of genetic merit and inference on putative causal variants as well as improving the computational efficiency of existing methods and algorithms. These concerns have become increasingly critical as new sequencing technologies will only exacerbate current model dimensionality problems. We focus primarily on mixed model and hierarchical Bayesian analyses which have been most commonly pursued by animal and plant breeders for WGP thus far. We draw attention to our observation that many such previous analyses have not carefully inferred upon hyperparameters defined at the top levels of the Bayesian model hierarchy, but simply arbitrarily specify their values. We also reassess previous discussions on WGP model dimensionality, believing that useful data augmentation schemes utilized in various Markov Chain Monte Carlo (MCMC) schemes have led to a general misunderstanding that heavy-tailed or variable selection-based WGP models may be highly parameterized relative to more standard mixed model representations. Computational efficiency is addressed with respect to MCMC and competitive, albeit approximate, alternatives. Furthermore, GWA analyses are reassessed, encouraging a greater reliance on shrinkage-based inferences based on critically chosen priors, instead of potentially nonreproducible fixed effects \(P\) value-based inference.

MSC:

62P12 Applications of statistics to environmental and related topics
62F15 Bayesian inference
65C60 Computational problems in statistics (MSC2010)
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Aguilar, I., Misztal, I., Tsuruta, S., Legarra, A., and Wang, H. (2014). PREGSF90-POSTGSF90: computational tools for the implementation of single-step genomic selection and genome-wide association with ungenotyped individuals in BLUPF90 programs. Proceedings of the 10th World Congress on Genetics Applied to Livestock Production, ASAS, August 17-22, 2014, Vancouver, BC, Canada.
[2] Allenby, G. M., Bradlow, E. T., George, E. I., Liechty, J., and McCulloch, R. E. (2014). Perspectives on Bayesian Methods and Big Data. Customer Needs and Solutions 1, 169-175.
[3] Allison, D. B., Cui, X., Page, G. P., and Sabripour, M. (2006). Microarray data analysis: from disarray to consolidation and consensus. Nature Review Genetics 7, 55-65.
[4] Andrews, D. F., and Mallows, C. L. (1974). Scale Mixtures of Normal Distributions. Journal of the Royal Statistical Society. Series B (Methodological) 36, 99-102. · Zbl 0282.62017
[5] Beissinger, T. M., Rosa, G. J., Kaeppler, S. M., Gianola, D., and de Leon, N. (2015). Defining window-boundaries for genomic analyses using smoothing spline techniques. Genetics Selection Evolution 47, 30.
[6] Bello, N. M., Steibel, J. P., and Tempelman, R. J. (2010). Hierarchical Bayesian modeling of random and residual variance-covariance matrices in bivariate mixed effects models. Biometrical Journal 52, 297-313. · Zbl 1207.62058
[7] Blasco, A., and Toro, M. A. (2014). A short critical history of the application of genomics to animal breeding. Livestock Science 166, 4-9.
[8] Brown, E. N., and Kass, R. E. (2009). What Is Statistics? American Statistician 63, 105-123. · Zbl 1205.00035
[9] Calus, M. (2014). Right-hand-side updating for fast computing of genomic breeding values. Genetics Selection Evolution 46, 1-11.
[10] Calus, M. P. L., Schrooten, C., and Veerkamp, R. F. (2014). Genomic prediction of breeding values using previously estimated SNP variances. Genetics Selection Evolution 46, 13.
[11] Calus, M. P. L., and Veerkamp, R. F. (2007). Accuracy of breeding values when using and ignoring the polygenic effect in genomic breeding value estimation with a marker density of one SNP per cM. Journal of Animal Breeding and Genetics 124, 362-368.
[12] Chen, C., and Tempelman, R. J. (2015). An integrated approach to empirical Bayesian whole genome prediction modeling Journal of Agricultural Biological and Environmental Statistics (submitted for this special issue). · Zbl 1329.62442
[13] Christensen, O. F., and Lund, M. S. (2010). Genomic prediction when some animals are not genotyped. Genetics Selection Evolution 42, 2.
[14] Cuyabano, B. C., Su, G., and Lund, M. S. (2014). Genomic prediction of genetic merit using LD-based haplotypes in the Nordic Holstein population. BMC Genomics 15, 1171.
[15] Daetwyler, H. D., Capitan, A., Pausch, H., et al. (2014). Whole-genome sequencing of 234 bulls facilitates mapping of monogenic and complex traits in cattle. Nature Genetics 46, 858-865.
[16] de Koning, D.-J., and McIntyre, L. (2012). Setting the Standard: A Special Focus on Genomic Selection in GENETICS and G3. Genetics 190, 1151-1152.
[17] de los Campos, G., Gianola, D., and Allison, D. B. (2010a). Predicting genetic predisposition in humans: the promise of whole-genome markers. Nature Reviews Genetics 11, 880-886.
[18] de Los Campos, G., Gianola, D., and Rosa, G. J. (2009a). Reproducing kernel Hilbert spaces regression: a general framework for genetic evaluation. Journal of Animal Science 87, 1883-1887.
[19] De los Campos, G., Gianola, D., Rosa, G. J., Weigel, K. A., and Crossa, J. (2010b). Semi-parametric genomic-enabled prediction of genetic values using reproducing kernel Hilbert spaces methods. Genetics Research 92, 295-308.
[20] de los Campos, G., Hickey, J. M., Pong-Wong, R., Daetwyler, H. D., and Calus, M. P. L. (2013). Whole Genome Regression and Prediction Methods Applied to Plant and Animal Breeding. Genetics 193, 327-345.
[21] de los Campos, G., Naya, H., Gianola, D., et al. (2009b). Predicting Quantitative Traits With Regression Models for Dense Molecular Markers and Pedigree. Genetics 182, 375-385.
[22] de los Campos, G., Veturi, Y., Vazquez, A. I., Lehermeier, C., and Perez-Rodriguez, P. (2015). Incorpating genetic heterogeneity in whole-genome regressions using interactions. Journal of Agricultural Biological and Environmental Statistics (submitted for this special issue). · Zbl 1329.62452
[23] Desta, Z. A., and Ortiz, R. (2014). Genomic selection: genome-wide prediction in plant improvement. Trends in Plant Science 19, 592-601.
[24] Druet, T., Macleod, I. M., and Hayes, B. J. (2014). Toward genomic prediction from whole-genome sequence data: impact of sequencing design on genotype imputation and accuracy of predictions. Heredity 112, 39-47.
[25] Duchemin, S. I., Colombani, C., Legarra, A., et al. (2012). Genomic selection in the French Lacaune dairy sheep breed. Journal of Dairy Science 95, 2723-2733.
[26] Eisen, E. J. (2008). Can we rescue an endangered species? Journal of Animal Breeding and Genetics 125, 1-2.
[27] Endelman, J. B. (2011). Ridge Regression and Other Kernels for Genomic Selection with R Package rrBLUP. The Plant Genome Journal 4, 250.
[28] Erbe, M., Hayes, B. J., Matukumalli, L. K., et al. (2012). Improving accuracy of genomic predictions within and between dairy cattle breeds with imputed high-density single nucleotide polymorphism panels. Journal of Dairy Science 95, 4114-4129.
[29] Fernando, R., and Garrick, D. (2013). Bayesian Methods Applied to GWAS. In Genome-Wide Association Studies and Genomic Prediction, C. Gondro, J. van der Werf, and B. Hayes (eds), 237-274: Humana Press.
[30] Fernando, R. L. (2009). GenSel: User Manual for a Portfolio of Genomic Selection Related Analyses. Iowa State University, Ames, IA, U.S.A.
[31] Fernando, R. L., Dekkers, J. C. M., and Garrick, D. J. (2014). A class of Bayesian methods to combine large numbers of genotyped and non-genotyped animals for whole-genome analyses. Genetics Selection Evolution 46, 13.
[32] Fragomeni, B. O., Lourenco, D. A. L., Tsuruta, S., et al. (2015). Hot topic: Use of genomic recursions in single-step genomic best linear unbiased predictor (BLUP) with a large number of genotypes. Journal of Dairy Science 98, 4090-4094.
[33] Fragomeni, B. O., Misztal, I., Lourenco, D. L., Aguilar, I., Okimoto, R., and Muir, W. M. (2014). Changes in variance explained by top SNP windows over generations for three traits in broiler chicken. Frontiers in Genetics 5, 332.
[34] Garrick, D., Dekkers, J., and Fernando, R. (2014). The evolution of methodologies for genomic prediction. Livestock Science 166, 10-18.
[35] Gauldron-Duarte, J. L., Cantet, R. J. C., Bates, R. O., Ernst, C. W., Raney, N. E., and Steibel, J. P. (2014). Rapid screening for phenotype-genotype associations by linear transformations of genomic evaluations. BMC Bioinformatics 15, 11.
[36] Gelfand, A. E., Hills, S. E., Racine-Poon, A., and Smith, A. F. (1990). Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association 85, 972-985.
[37] Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B. (2014). Bayesian data analysis: Taylor & Francis. · Zbl 1279.62004
[38] Gelman, A., Hill, J., and Yajima, M. (2012). Why We (Usually) Don’t Have to Worry About Multiple Comparisons. Journal of Research on Educational Effectiveness 5, 189-211.
[39] George, E. I., and McCulloch, R. E. (1993). Variable selection via Gibbs sampling. Journal of the American Statistical Association 88, 881 - 889.
[40] Gianola, D. (2000). Statistics in animal breeding. Journal of the American Statistical Association 95, 296-299.
[41] ——- (2013). Priors in whole-genome regression: the Bayesian alphabet returns. Genetics 194, 573-596.
[42] Gianola, D., de los Campos, G., Hill, W. G., Manfredi, E., and Fernando, R. (2009). Additive Genetic Variability and the Bayesian Alphabet. Genetics 183, 347-363.
[43] Gianola, D., and Fernando, R. L. (1986). Bayesian methods in animal breeding theory. Journal of Animal Science 63, 217-244.
[44] Gianola, D., Foulley, J. L., and Fernando, R. (1986). Prediction of breeding values when variances are not known. Genetics, Selection, Evolution 18, 485-498.
[45] Gianola, D., and Rosa, G. J. (2015). One Hundred Years of Statistical Developments in Animal Breeding. Annual Review of Animal Biosciences 3, 19-56.
[46] Gilmour, A. R., Thompson, R., and Cullis, B. R. (1995). Average Information REML: An Efficient Algorithm for Variance Parameter Estimation in Linear Mixed Models. Biometrics 51, 1440-1450. · Zbl 0875.62314
[47] Goddard, M. E., Hayes, B. J., and Meuwissen, T. H. (2010). Genomic selection in livestock populations. Genetics Research 92, 413-421.
[48] Gondro, C., Van der Werf, J., and Hayes, B. (2013). Genome-wide association studies and genomic prediction: Springer: Humana Press, New York.
[49] González-Recio, O., Rosa, G. J. M., and Gianola, D. (2014). Machine learning methods and predictive ability metrics for genome-wide prediction of complex traits. Livestock Science 166, 217-231.
[50] Grattapaglia, D., and Resende, M. D. V. (2010). Genomic selection in forest tree breeding. Tree Genetics & Genomes 7, 241-255.
[51] Habier, D., Fernando, R. L., and Dekkers, J. C. (2007). The impact of genetic relationship information on genome-assisted breeding values. Genetics 177, 2389 - 2397.
[52] Habier, D., Fernando, R. L., Kizilkaya, K., and Garrick, D. J. (2011). Extension of the bayesian alphabet for genomic selection. BMC Bioinformatics 12, 186.
[53] Halsey, L. G., Curran-Everett, D., Vowler, S. L., and Drummond, G. B. (2015). The fickle P value generates irreproducible results. Nature Methods 12, 179-185.
[54] Hayes, B. (2013). Overview of Statistical Methods for Genome-Wide Association Studies (GWAS). In Genome-Wide Association Studies and Genomic Prediction, C. Gondro, J. van der Werf, and B. Hayes (eds), 149-169: Humana Press.
[55] Hazel, L. N. (1943). The genetic basis for constructing selection indexes. Genetics 28, 476-490.
[56] Henderson, C. R. (1976). A Simple Method for Computing the Inverse of a Numerator Relationship Matrix Used in Prediction of Breeding Values. Biometrics 32, 69-83. · Zbl 0359.65023
[57] Henderson, C. R., Kempthorne, O., Searle, S. R., and Krosigk, C. M. v. (1959). The Estimation of Environmental and Genetic Trends from Records Subject to Culling. Biometrics 15, 192-218. · Zbl 0128.40301
[58] Heslot, N., Yang, H.-P., Sorrells, M. E., and Jannink, J.-L. (2012). Genomic Selection in Plant Breeding: A Comparison of Models. Crop Science 52, 146.
[59] Hill, W. G. (2014). Applications of population genetics to animal breeding, from wright, fisher and lush to genomic prediction. Genetics 196, 1-16.
[60] Howard, R., Carriquiry, A. L., and Beavis, W. D. (2014). Parametric and Nonparametric Statistical Methods for Genomic Selection of Traits with Additive and Epistatic Genetic Architectures. G3: Genes/Genomes/Genetics 4, 1027-1046. · Zbl 0875.62314
[61] Irizarry, R. (2015). Correlation is not a measure of reproducibility. In http://simplystatistics.org/2015/08/12/correlation-is-not-a-measure-of-reproducibility/.
[62] Jannink, J. L., Lorenz, A. J., and Iwata, H. (2010). Genomic selection in plant breeding: from theory to practice. Briefings in Functional Genomics 9, 166-177.
[63] Janss, L. (2015). Experiences with bioinformatics. Journal of Animal Science 93, 198.
[64] Jarquin, D., Crossa, J., Lacaze, X., et al. (2014). A reaction norm model for genomic selection using high-dimensional genomic and environmental data. Theoretical and Applied Genetics 127, 595-607.
[65] Johnson, D. L., and Thompson, R. (1995). Restricted Maximum Likelihood Estimation of Variance Components for Univariate Animal Models Using Sparse Matrix Techniques and Average Information. Journal of Dairy Science 78, 449-456.
[66] Jonas, E., and de Koning, D. J. (2013). Does genomic selection have a future in plant breeding? Trends in Biotechnology 31, 497-504.
[67] Jorasch, P. (2005). Intellectual Property Rights in the Field of Molecular Marker Analysis. In Molecular Marker Systems in Plant Breeding and Crop Improvement, H. Lörz, and G. Wenzel (eds), 433-471: Springer Berlin Heidelberg.
[68] Kadarmideen, H. N. (2014). Genomics to systems biology in animal and veterinary sciences: Progress, lessons and opportunities. Livestock Science 166, 232-248.
[69] Käll, L., Storey, J. D., MacCoss, M. J., and Noble, W. S. (2008). Posterior Error Probabilities and False Discovery Rates: Two Sides of the Same Coin. Journal of Proteome Research 7, 40-44.
[70] Kang, H. M., Zaitlen, N. A., Wade, C. M., et al. (2008). Efficient Control of Population Structure in Model Organism Association Mapping. Genetics 178, 1709-1723.
[71] Kärkkäinen, H. P., and Sillanpää, M. J. (2012). Back to Basics for Bayesian Model Building in Genomic Selection. Genetics 191, 969-987.
[72] Kizilkaya, K., and Tempelman, R. J. (2005). A general approach to mixed effects modeling of residual variances in generalized linear mixed models. Genetics Selection Evolution 37, 31-56.
[73] Legarra, A., Aguilar, I., and Misztal, I. (2009). A relationship matrix including full pedigree and genomic information. Journal of Dairy Science 92, 4656-4663.
[74] Legarra, A., Christensen, O. F., Aguilar, I., and Misztal, I. (2014). Single Step, a general approach for genomic selection. Livestock Science 166, 54-65.
[75] Legarra, A., and Misztal, I. (2008). Technical Note: Computing Strategies in Genome-Wide Selection. Journal of Dairy Science 91, 360-366.
[76] Lehermeier, C., Wimmer, V., Albrecht, T., et al. (2013). Sensitivity to prior specification in Bayesian genome-based prediction models. Statistical Applications in Genetics and Molecular Biology 12, 375-391.
[77] Li, A., and Meyre, D. (2012). Challenges in reproducibility of genetic association studies: lessons learned from the obesity field. International Journal of Obesity 2012, 1-9. · Zbl 1289.74159
[78] Liu, J. S. (1994). The Collapsed Gibbs Sampler in Bayesian Computations with Applications to a Gene-Regulation Problem. Journal of the American Statistical Association 89, 958-966. · Zbl 0804.62033
[79] Liu, Z., Goddard, M. E., Reinhardt, F., and Reents, R. (2014). A single-step genomic model with direct estimation of marker effects. Journal of Dairy Science 97, 5833-5850.
[80] Logsdon, B. A., Hoffman, G. E., and Mezey, J. G. (2010). A variational Bayes algorithm for fast and accurate multiple locus genome-wide association analysis. BMC Bioinformatics 11, 58.
[81] Louis, T. A. (1982). Finding the Observed Information Matrix when Using the EM Algorithm. Journal of the Royal Statistical Society. Series B (Methodological) 44, 226-233. · Zbl 0488.62018
[82] Meng, X.-L., and Rubin, D. B. (1991). Using EM to Obtain Asymptotic Variance-Covariance Matrices: The SEM Algorithm. Journal of the American Statistical Association 86, 899-909.
[83] Meuwissen, T. H. E., Hayes, B. J., and Goddard, M. E. (2001). Prediction of total genetic value using genome-wide dense marker maps. Genetics 157, 1819-1829.
[84] Meyer, K. (1989). Restricted maximum likelihood to estimate variance components for animal models with several random effects using a derivative-free algorithm. Genetics Selection Evolution 21, 317-340.
[85] Misztal, I. (1990). Restricted Maximum Likelihood Estimation of Variance Components in Animal Model Using Sparse Matrix Inversion and a Supercomputer. Journal of Dairy Science 73, 163-172.
[86] ——- (2007). Shortage of quantitative geneticists in animal breeding. Journal of Animal Breeding and Genetics 124, 255-256.
[87] Misztal, I., and Perez-Enciso, M. (1993). Sparse Matrix Inversion for Restricted Maximum Likelihood Estimation of Variance Components by Expectation-Maximization. Journal of Dairy Science 76, 1479-1483.
[88] Morota, G., Abdollahi-Arpanahi, R., Kranis, A., and Gianola, D. (2014). Genome-enabled prediction of quantitative traits in chickens using genomic annotation. BMC Genomics 15, 109.
[89] Morota, G., and Gianola, D. (2014). Kernel-based whole-genome prediction of complex traits: a review. Frontiers in Genetics 5.
[90] Nadaf, J., Riggio, V., Yu, T.-P., and Pong-Wong, R. (2012). Effect of the prior distribution of SNP effects on the estimation of total breeding value. BMC Proceedings 6, S6.
[91] Nejati-Javaremi, A., Smith, C., and Gibson, J. (1997). Effect of total allelic relationship on accuracy of evaluation and response to selection. Journal of Animal Science 75, 1738-1745.
[92] O’Hara, R. B., and Sillanpää, M. J. (2009). A Review of Bayesian Variable Selection Methods: What, How and Which. Bayesian Analysis 4, 85-118. · Zbl 1330.62291
[93] Perez-Elizalde, S., Cuevas, J., Perez-Rodriguez, P., and Crossa, J. (2015). Selection of the bandwidth parameter in a Bayesian kernel regression model for genomic-enabled prediction. Journal of Agricultural Biological and Environmental Statistics (submitted for this special issue). · Zbl 1329.62449
[94] Pérez-Enciso, M. (1995). Use of the uncertain relationship matrix to compute effective population size. Journal of Animal Breeding and Genetics 112, 327-332.
[95] Pérez, P., and de los Campos, G. (2014). Genome-Wide Regression & Prediction with the BGLR Statistical Package. Genetics.
[96] Pinheiro, J. C., Liu, C., and Wu, Y. N. (2001). Efficient Algorithms for Robust Estimation in Linear Mixed-Effects Models Using the MultivariatetDistribution. Journal of Computational and Graphical Statistics 10, 249-276.
[97] Plummer, M., Best, N., Cowles, K., and Vines, K. (2006). CODA: convergence diagnostics and output analysis for MCMC. R News 6, 7-11.
[98] Pregitzer, C. C., Bailey, J. K., and Schweitzer, J. A. (2013). Genetic by environment interactions affect plant-soil linkages. Ecology and Evolution 3, 2322-2333. · Zbl 1293.93647
[99] Robinson, G. K. (1991). That BLUP is a Good Thing: The Estimation of Random Effects. 15-32. · Zbl 0955.62500
[100] Rockova, V., and George, E. I. (2014a). EMVS: The EM Approach to Bayesian Variable Selection. Journal of the American Statistical Association 109, 828-846. · Zbl 1367.62049
[101] ——- (2014b). Negotiating Multicollinearity with Spike-and-Slab Priors. Metron 72, 217-229. · Zbl 1310.62035
[102] Rosa, G. J. M., Padovani, C. R., and Gianola, D. (2003). Robust linear mixed models with normal/independent distributions and Bayesian MCMC implementation. Biometrical Journal 45, 573-590. · Zbl 1441.62474
[103] Rue, H., Martino, S., and Chopin, N. (2009). Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations. Journal of the Royal Statistical Society: Series B-Statistical Methodology 71, 319-392. · Zbl 1248.62156
[104] Ruppert, D., Wand, M. P., and Carroll, R. J. (2009). Semiparametric regression during 2003-2007. Electronic Journal of Statistics 3, 1193-1256. · Zbl 1326.62094
[105] Schaeffer, L. R., and Kennedy, B. W. (1986). Computing Strategies for Solving Mixed Model Equations. Journal of Dairy Science 69, 575-579.
[106] Schoen, C.-C., Wimmer, V., and Lehermeier, C. (2014). Efficiency of Variable Selection in Genome-Wide Prediction for Traits of Different Genetic Architecture. In Proceedings of the 10th World Congress on Genetics Applied to Livestock Production, ASAS, August 17-22, 2014, Vancouver, BC, Canada: Asas.
[107] Searle, S. R., Casella, G., and McCulloch, C. E. (1992). Variance Components. New York: John Wiley and Sons. · Zbl 0850.62007
[108] Shariati, M., and Sorensen, D. (2008). Efficiency of alternative MCMC strategies illustrated using the reaction norm model. Journal of Animal Breeding and Genetics 125, 176-186.
[109] Shariati, M. M., Korsgaard, I. R., and Sorensen, D. (2009). Identifiability of parameters and behaviour of MCMC chains: a case study using the reaction norm model. Journal of Animal Breeding and Genetics 126, 92-102.
[110] Sorensen, D., Andersen, S., Gianola, D., and Korsgaard, I. (1995). Bayesian inference in threshold models using Gibbs sampling. Genetics Selection Evolution 27, 229-249.
[111] Sorensen, D. A., Gianola, D., and Korsgaard, I. R. (1998). Bayesian mixed-effects model analysis of a censored normal distribution with animal breeding applications. Acta Agriculturae Scandinavica A—Animal Sciences 48, 222-229.
[112] Spiegelhalter, D. J., Best, N. G., Carlin, B. R., and van der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society Series B-Statistical Methodology 64, 583-616. · Zbl 1067.62010
[113] Storey, J. D., and Tibshirani, R. (2003). Statistical significance for genomewide studies. Proceedings of the National Academy of Sciences 100, 9440-9445. · Zbl 1130.62385
[114] Strandén, I., and Garrick, D. J. (2009). Technical note: Derivation of equivalent computing algorithms for genomic predictions and reliabilities of animal merit. Journal of Dairy Science 92, 2971-2975.
[115] Strandén, I., and Lidauer, M. (1999). Solving Large Mixed Linear Models Using Preconditioned Conjugate Gradient Iteration. Journal of Dairy Science 82, 2779-2787.
[116] Tanner, M. A., and Wong, W. H. (1987). The Calculation of Posterior Distributions by Data Augmentation. Journal of the American Statistical Association 82, 528-540. · Zbl 0619.62029
[117] Taylor, J. F. (2014). Implementation and accuracy of genomic selection. Aquaculture 420-421, S8-S14.
[118] Technow, F., Messina, C. D., Totir, L. R., and Cooper, M. (2015). Integrating Crop Growth Models with Whole Genome Prediction through Approximate Bayesian Computation. PLoS ONE 10, e0130855.
[119] Tierney, L., and Kadane, J. B. (1986). Accurate approximations for posterior moments and marginal densities. Journal of the American Statistical Association 81, 82-86. · Zbl 0587.62067
[120] Usai, M. G., Goddard, M. E., and Hayes, B. J. (2010). LASSO with cross-validation for genomic selection. Genetics Research 91, 427.
[121] Van Dyk, D. A., and Meng, X.-L. (2001). The art of data augmentation. Journal of Computational and Graphical Statistics 10, 1-50.
[122] Vattikuti, S., Lee, J. J., Chang, C. C., Hsu, S. D., and Chow, C. C. (2014). Applying compressed sensing to genome-wide association studies. Gigascience 3, 10.
[123] Verbyla, K. L., Hayes, B. J., Bowman, P. J., and Goddard, M. E. (2009). Accuracy of genomic selection using stochastic search variable selection in Australian Holstein Friesian dairy cattle. Genetics Research 91, 307 - 311.
[124] Wang, H., Misztal, I., Aguilar, I., Legarra, A., and Muir, W. M. (2012). Genome-wide association mapping including phenotypes from relatives without genotypes. Genetics Research 94, 73-83.
[125] Wang, Y. (1998). Smoothing Spline Models with Correlated Random Errors. Journal of the American Statistical Association 93, 341-348. · Zbl 1068.62512
[126] Wiggans, G. R., Misztal, I., and Van Vleck, L. D. (1988). Implementation of an Animal Model for Genetic Evaluation of Dairy Cattle in the United States. Journal of Dairy Science 71, 54-69.
[127] Wiggans, G. R., VanRaden, P. M., and Cooper, T. A. (2011). The genomic evaluation system in the United States: Past, present, future. Journal of Dairy Science 94, 3202-3211.
[128] ——- (2015). Technical note: Rapid calculation of genomic evaluations for new animals. Journal of Dairy Science 98, 2039-2042.
[129] Wimmer, V., Albrecht, T., Auinger, H.-J., and Schön, C.-C. (2012). synbreed: a framework for the analysis of genomic prediction data using R. Bioinformatics 28, 2086-2087.
[130] Wimmer, V., Lehermeier, C., Albrecht, T., Auinger, H.-J., Wang, Y., and Schön, C.-C. (2013). Genome-Wide Prediction of Traits with Different Genetic Architecture Through Efficient Variable Selection. Genetics 195, 573-587.
[131] Wu, X.-L., Sun, C., Beissinger, T. M., et al. (2012). Parallel Markov chain Monte Carlo-bridging the gap to high-performance Bayesian computation in animal breeding and genetics. Genetics Selection Evolution 44, 29.
[132] Yang, W., Chen, C., and Tempelman, R. J. (2015). Improving the computational efficiency of fully Bayes inference and assessing the effect of misspecification of hyperparameters in whole-genome prediction models. Genetics Selection Evolution 47, 13.
[133] Yang, W., and Tempelman, R. J. (2012). A Bayesian Antedependence Model for Whole Genome Prediction. Genetics 190, 1491-1501.
[134] Yi, N. J., and Xu, S. H. (2008). Bayesian LASSO for quantitative trait loci mapping. Genetics 179, 1045-1055.
[135] Yi, N. J., and Banerjee, S. (2009). Hierarchical Generalized Linear Models for Multiple Quantitative Trait Locus Mapping. Genetics 181, 1101-1113.
[136] Yi, N., Xu, S., Lou, X. Y., and Mallick, H. (2014). Multiple comparisons in genetic association studies: a hierarchical modeling approach. Statistical Applications in Genetics and Molecular Biology 13, 35-48. · Zbl 1296.92178
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.