Swift block-updating EM and pseudo-EM procedures for Bayesian shrinkage analysis of quantitative trait loci
- 522 Downloads
Virtually all existing expectation-maximization (EM) algorithms for quantitative trait locus (QTL) mapping overlook the covariance structure of genetic effects, even though this information can help enhance the robustness of model-based inferences.
Here, we propose fast EM and pseudo-EM-based procedures for Bayesian shrinkage analysis of QTLs, designed to accommodate the posterior covariance structure of genetic effects through a block-updating scheme. That is, updating all genetic effects simultaneously through many cycles of iterations.
Simulation results based on computer-generated and real-world marker data demonstrated the ability of our method to swiftly produce sensible results regarding the phenotype-to-genotype association. Our new method provides a robust and remarkably fast alternative to full Bayesian estimation in high-dimensional models where the computational burden associated with Markov chain Monte Carlo simulation is often unwieldy. The R code used to fit the model to the data is provided in the online supplementary material.
KeywordsQuantitative Trait Locus Genetic Effect Quantitative Trait Locus Mapping Genomic Breeding Value Estimation Posterior Covariance
The authors wish to thank Hanni Kärkkäinen, Zitong Li and two anonymous referees for their pertinent comments and suggestions. This work was supported by a research grants from the Academy of Finland and University of Helsinki’s research funds.
- Bishop CM, Tipping ME (2003) Bayesian regression and classification. In: Suykens J, Horvath G, Basu S, Micchelli C, Vandewalle J (eds) Advances in learning theory: methods, models and applications, vol 190. IOS Press, NATO Science, Amsterdam, pp 267–285Google Scholar
- Broman KW (2001) Review of statistical methods for QTL mapping in experimental crosses. Lab Anim 30:44–52Google Scholar
- Carlborg Ö, Andersson L (2002) Use of randomization testing to detect multiple epistatic QTLs. Genet Sel Evol 79:175–184Google Scholar
- Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc B 39:1–38Google Scholar
- Gelman A, Hill J (2007) Data analysis using regression and multilevel/hierarchical models. Cambridge University Press, New YorkGoogle Scholar
- Gelman A, Carlin JB, Stern HS, Rubin DB (2003) Bayesian data analysis, 2nd edn. Chapman and Hall, New YorkGoogle Scholar
- Gilks WR, Richardson S, Spiegelhalter DJ (eds) (1996) Markov Chain Monte Carlo in practice. Chapman and Hall, LondonGoogle Scholar
- Golub G, van Loan C (1996) Matrix computations, 3rd edn. The John Hopkins University Press, BaltimoreGoogle Scholar
- Heckerman D, Chickering DM, Meek C, Rounthwaite R, Kadie C (2000) Dependency network for inference, collaborative filtering, and data visualization. J Mach Learn Res 1:49–75Google Scholar
- Henderson CR (1950) Estimation of genetic parameters. Ann Math Stat 21:309–310Google Scholar
- Jeffreys H (1961) Theory of probability. Clarendon Press, OxfordGoogle Scholar
- Kärkkäinen HP, Sillanpää MJ (2012) Back to basics for Bayesian model building in genomic selection. Genetics 191:969–987Google Scholar
- Li Z, Sillanpää MJ (2012b) Overview of LASSO-related penalized regression methods for quantitative trait mapping and genomic selection. Theor Appl Genet 125:419–435Google Scholar
- Lowd D, Shamaei A (2011) Mean field inference in dependency networks: an empirical study. In: Proceedings of the 25th conference on artificial intelligence (AAAI-11), San Francisco, CAGoogle Scholar
- McLachlan GJ, Krishnan T (1997) The EM algorithm and extensions. Wiley, New YorkGoogle Scholar
- Myers RL (1992) Classical and modern regression analysis, 2nd edn. Wiley, New-YorkGoogle Scholar
- R Development Core Team (2011) R: A language and environment for statistical computing, reference index version 2.13.2. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. http://www.R-project.org
- Tibshirani R (1996) Regression shrinkage and selection via LASSO. J Roy Stat Soc B 58:267–288Google Scholar
- Tipping ME (2001) Sparse Bayesian learning and the relevance vector machine. J Mach Learn Res 1:211–244Google Scholar
- Wang S, Basten CJ, Zeng Z-B (2006) Windows QTL Cartographer 2.5. Department of Statistics, North Carolina State University, Raleigh, NCGoogle Scholar