An approximate Bayesian approach for quantitative trait loci estimation

Bayesian approaches have been widely used in quantitative trait locus (QTL) linkage analysis in experimental crosses, and have advantages in interpretability and in constructing parameter probability intervals. Most existing Bayesian linkage methods involve Monte Carlo sampling, which is computationally prohibitive for high-throughput applications such as eQTL analysis. In this paper, we present a Bayesian linkage model that offers directly interpretable posterior densities or Bayes factors for linkage. For our model, we employ the Laplace approximation for integration over nuisance parameters in backcross (BC) and F2 intercross designs. Our approach is highly accurate, and very fast compared with alternatives, including grid search integration, importance sampling, and Markov Chain Monte Carlo (MCMC). Our approach is thus suitable for high-throughput applications. Simulated and real datasets are used to demonstrate our proposed approach.