title: A hybrid expectation maximisation and MCMC sampling algorithm to implement Bayesian mixture model based genomic prediction and QTL mapping.
abstract: BACKGROUND
  Bayesian mixture models in which the effects of SNP are assumed to come from normal distributions with different variances are attractive for simultaneous genomic prediction and QTL mapping. These models are usually implemented with Monte Carlo Markov Chain (MCMC) sampling, which requires long compute times with large genomic data sets. Here, we present an efficient approach (termed HyB_BR), which is a hybrid of an Expectation-Maximisation algorithm, followed by a limited number of MCMC without the requirement for burn-in.
  
  
  RESULTS
  To test prediction accuracy from HyB_BR, dairy cattle and human disease trait data were used. In the dairy cattle data, there were four quantitative traits (milk volume, protein kg, fat% in milk and fertility) measured in 16,214 cattle from two breeds genotyped for 632,002 SNPs. Validation of genomic predictions was in a subset of cattle either from the reference set or in animals from a third breeds that were not in the reference set. In all cases, HyB_BR gave almost identical accuracies to Bayesian mixture models implemented with full MCMC, however computational time was reduced by up to 1/17 of that required by full MCMC. The SNPs with high posterior probability of a non-zero effect were also very similar between full MCMC and HyB_BR, with several known genes affecting milk production in this category, as well as some novel genes. HyB_BR was also applied to seven human diseases with 4890 individuals genotyped for around 300 K SNPs in a case/control design, from the Welcome Trust Case Control Consortium (WTCCC). In this data set, the results demonstrated again that HyB_BR performed as well as Bayesian mixture models with full MCMC for genomic predictions and genetic architecture inference while reducing the computational time from 45 h with full MCMC to 3 h with HyB_BR.
  
  
  CONCLUSIONS
  The results for quantitative traits in cattle and disease in humans demonstrate that HyB_BR can perform equally well as Bayesian mixture models implemented with full MCMC in terms of prediction accuracy, but with up to 17 times faster than the full MCMC implementations. The HyB_BR algorithm makes simultaneous genomic prediction, QTL mapping and inference of genetic architecture feasible in large genomic data sets.
authors.affiliation: School of Engineering and Mathematical Sciences, La Trobe University, Melbourne, VIC, Australia. t22wang@students.latrobe.edu.au.|Biosciences Research, Department of Economic Development, Jobs, Transport and Resources, Bundoora, Melbourne, VIC, Australia. t22wang@students.latrobe.edu.au.|Dairy Futures Cooperative Research Centre, Melbourne, VIC, Australia. t22wang@students.latrobe.edu.au.
authors.forename: Tingting
authors.initials: T
authors.lastname: Wang
authors.affiliation: School of Engineering and Mathematical Sciences, La Trobe University, Melbourne, VIC, Australia.
authors.forename: Yi-Ping Phoebe
authors.initials: YP
authors.lastname: Chen
authors.affiliation: Biosciences Research, Department of Economic Development, Jobs, Transport and Resources, Bundoora, Melbourne, VIC, Australia.|Dairy Futures Cooperative Research Centre, Melbourne, VIC, Australia.|School of Applied Systems Biology, La Trobe University, Melbourne, VIC, Australia.
authors.forename: Phil J
authors.initials: PJ
authors.lastname: Bowman
authors.affiliation: Biosciences Research, Department of Economic Development, Jobs, Transport and Resources, Bundoora, Melbourne, VIC, Australia.|Dairy Futures Cooperative Research Centre, Melbourne, VIC, Australia.|Faculty of Veterinary and Agricultural Science, University of Melbourne, Melbourne, VIC, Australia.
authors.forename: Michael E
authors.initials: ME
authors.lastname: Goddard
authors.affiliation: Biosciences Research, Department of Economic Development, Jobs, Transport and Resources, Bundoora, Melbourne, VIC, Australia.|Dairy Futures Cooperative Research Centre, Melbourne, VIC, Australia.|Queensland Alliance for Agriculture and Food Innovation, Centre for Animal Science, University of Queensland, Queensland, Australia.
authors.forename: Ben J
authors.initials: BJ
authors.lastname: Hayes