Title: Hidden Markov model in multiple testing on dependent data
Abstract: Multiple testing on dependent data needs to handle two basic modeling elements: the choice of distributions under the null and the non-null states and the modeling of the dependence structure across observations. A Bayesian hidden Markov model is constructed to handle these two issues. The proposed Bayesian method is based on the posterior probability of the null state and exhibits the property of an optimal test procedure, which has the lowest false negative rate with the false discovery rate under control. The model has either single or mixture distributions used under the nonnull state, which can be flexibly modeled by ad-hoc model selection or the nonparametric Bayesian method. The proposed method is applied to both continuous and count data. We compared the proposed method with a collection of commonly used testing procedures to show its performance under different scenarios.
Oct 23, Dr. Hyeongseon Jeon, University of Houston
Title: RNA-seq analysis with gene-specific covariates
Abstract: In this presentation, I will introduce a novel positive false discovery rate (pFDR) controlling method for testing gene-specific hypotheses using a gene-specific covariate variable, such as gene length. We suppose the null probability depends on the covariate variable. In this context, we propose a rejection rule that accounts for heterogeneity among tests by using two distinct types of null probabilities. We establish a pFDR estimator for a given rejection rule by following Storey’s q-value framework. A condition on a type 1 error posterior probability is provided that equivalently characterizes our rejection rule. We also present a suitable procedure for selecting a tuning parameter through cross-validation that maximizes the expected number of hypotheses declared significant. A simulation study demonstrates that our method is comparable to or better than existing methods across realistic scenarios. In data analysis, we find support for our method’s premise that the null probability varies with a gene-specific covariate variable.
Oct 30, Dr. Maoran Xu, Indiana University Bloomington
Title: Efficient Bayesian inference on sparse and low-rank covariance matrices via projection
Abstract: In covariance estimation for high-dimensional data, sparsity and low-rank assumptions are commonly used to reduce dimensionality. However, in a Bayesian paradigm, it is challenging to conduct posterior computation under priors that simultaneously impose sparsity and low-rank (SLR) structure. To bypass the usual challenges inherent in computation for orthogonal and sparse matrix factorizations, we propose a novel transformation-based approach. We project from a normal-inverse-Gamma prior to the SLR space by thresholding the row-norm and trace norm, leading to a projected SLR (PSLR) prior. Remarkably, we show that it is possible to conduct posterior computation under the PSLR prior by sampling from the conjugate normal-inverse-Gamma posterior and projecting the draws. This dramatically simplifies computation. The resulting posterior distribution is shown to satisfy frequentist optimality properties including adaptive posterior contraction rates. The approach is evaluated in simulation studies and applied to a gene expression data set.