Graphical-model Based Multiple Testing under Dependence, with Applications to Genome-wide Association Studies

Large-scale multiple testing tasks often exhibit dependence, and leveraging the dependence between individual tests is still one challenging and important problem in statistics. With recent advances in graphical models, it is feasible to use them to perform multiple testing under dependence. We propose a multiple testing procedure which is based on a Markov-random-field-coupled mixture model. The ground truth of hypotheses is represented by a latent binary Markov random field, and the observed test statistics appear as the coupled mixture variables. The parameters in our model can be automatically learned by a novel EM algorithm. We use an MCMC algorithm to infer the posterior probability that each hypothesis is null (termed local index of significance), and the false discovery rate can be controlled accordingly. Simulations show that the numerical performance of multiple testing can be improved substantially by using our procedure. We apply the procedure to a real-world genome-wide association study on breast cancer, and we identify several SNPs with strong association evidence.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012

MLE-induced Likelihood for Markov Random Fields

Due to the intractable partition function, the exact likelihood function for a Markov random field (MRF), in many situations, can only be approximated. Major approximation approaches include pseudolikelihood and Laplace approximation. In this paper, we propose a novel way of approximating the likelihood function through first approximating the marginal likelihood functions of individual parameters and then reconstructing the joint likelihood function from these marginal likelihood functions. For approximating the marginal likelihood functions, we derive a particular likelihood function from a modified scenario of coin tossing which is useful for capturing how one parameter interacts with the remaining parameters in the likelihood function. For reconstructing the joint likelihood function, we use an appropriate copula to link up these marginal likelihood functions. Numerical investigation suggests the superior performance of our approach. Especially as the size of the MRF increases, both the numerical performance and the computational cost of our approach remain consistently satisfactory, whereas Laplace approximation deteriorates and pseudolikelihood becomes computationally unbearable

Graphical-model Based Multiple Testing under Dependence, with Applications to Genome-wide Association Studies

Large-scale multiple testing tasks often exhibit dependence, and leveraging the dependence between individual tests is still one challenging and important problem in statistics. With recent advances in graphical models, it is feasible to use them to perform multiple testing under dependence. We propose a multiple testing procedure which is based on a Markov-random-field-coupled mixture model. The ground truth of hypotheses is represented by a latent binary Markov random field, and the observed test statistics appear as the coupled mixture variables. The parameters in our model can be automatically learned by a novel EM algorithm. We use an MCMC algorithm to infer the posterior probability that each hypothesis is null (termed local index of significance), and the false discovery rate can be controlled accordingly. Simulations show that the numerical performance of multiple testing can be improved substantially by using our procedure. We apply the procedure to a real-world genome-wide association study on breast cancer, and we identify several SNPs with strong association evidence.