ies have successfully identified genetic loci association with complex diseases and other traits. SNPs identified by traditional GWAS can only explain a small fraction of the heritability, due to the strict multiple-comparison significance requirement when testing each SNP individually. For Correspondence: [email protected] 1 Department of Statistics and Operation Research, University of North Carolina-Chapel Hill, 27514 Chapel Hill, USA Full list of author information is available at the end of the article example, Vissher discussed 54 loci associated with height which only explained 5% heritability; described 32 loci associated with Body Mass Index which explained 1.45% of the variance in BMI. More recently, used mixed linear models to simultaneously take into account all the SNPs, which is shown to alleviate the missing-heritability issue. In this study, we extend the work of to identify the subset of SNPs that are significantly associated with the phenotype of interest, instead of assuming all the SNPs are associative, through a Hierarchical Bayesian model 2015 PubMed ID:http://www.ncbi.nlm.nih.gov/pubmed/19801058 Wang et al.; licensee BioMed Central. This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. The Creative Commons Public Domain Dedication waiver applies to the data made available in this article, unless otherwise stated. Wang et al. BMC Genomics 2015, 16:3 http://www.biomedcentral.com/1471-2164/16/3 Page 2 of 11 . Similar to, all SNPs are considered simultaneously to estimate the heritability, instead of one by one as in the traditional GWAS, hence our HBM also helps to capture missing heritability. Different from the authors in, we assume that the SNP effects are distributed as the mixture of a point mass at zero, for those non-effective SNPs, 6 and a normal distribution for those associative SNPs. They adopted several strategies to improve order AZ-6102 computational performance, for example, they used marginal associations of the SNPs on the traits as the initial screen step for the latent indicator Ij in . This indicates that the distribution of the random effect bj is similar to the marginal estimates of the SNP effects on the traits. In this study, we modify the standard MCMC algorithm based on the stochastic search algorithm proposed by. The algorithm directly samples the parameters from their posterior distributions and obtain the inferences for the parameters. Because the number of SNPs is large, each iteration of the algorithm involves matrix inversion with the dimension being the number of SNPs. To reduce computation time, we modify the algorithm by sampling the random effects bj conditional on the indicator Ij. The modified algorithm significantly reduces computation time, especially when the number of SNPs is large and the mixture probability p is small, while is still able to identify the significant predictors accurately. Detailed description of the algorithm will be stated in Section “Methods”: Method. We also implement several computing tricks so that the algorithm can be used to estimate models with the number of SNPs in the order of 100,000. Our HBM is first applied to 
analyze simulated data sets in Section “Simulation studies” to show that the proposed algorithm is able to identify the SNPs that are significantly associated with the phenotype and correctly estimate the model parameters as wel
