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University of Edinburgh School of Mathematics and BioSS Date: Friday 25th Nov, 15:10pm Location: JCMB 5327 Speaker: Adrià Caballé Mestres, School of Mathematics, University of Edinburgh and BioSS Title: Testing and estimation of sparse precision matrices in paired gene expression data Abstract: We consider two related statistical problems that are motivated by genomic datasets in which genome profiles are observed for every individual in two different samples (i.e. tissues in two medical conditions). First, we present methodology related to hypothesis testing of the equality of two correlation matrices using two dependent high-dimensional datasets. We exploit average of squares, extreme value and a novel exceedances-based statistics to test the hypothesis of equal correlations and derive their limiting distribution. As second contribution, we study the estimation problem of two similar sparse precision matrices and the corresponding conditional dependence graphs for high dimensional data where observations of these matrices are dependent. We propose a new method to estimate simultaneously these precision matrices, a weighted fused graphical lasso estimator which encourages both sparsity and similarity in the estimated precision matrices. We apply the suggested approaches to high-dimensional case studies of gene expression data with samples in two medical conditions as healthy and colon (or lung) cancer as well as non-lesional and psoriasis lesional tissue with the aim of discovering pathway lists of genes that present different dependence structures between medical conditions. We find strong evidence for a large part of the pathway lists dependence's structures to change among the two medical conditions. Especially, we estimate denser graph structures for lesional (and tumor) samples than for healthy samples, with subgroups of genes interacting together. This is joint work with Natalia Bochkina (University of Edinburgh), Claus Mayer (Biomathematics and Statistics Scotland) and Ioannis Papastathopoulos (University of Edinburgh -- There will be tea and coffee after the seminar in the Mathematics Common Room. This seminar is a part of Maxwell Institute seminar series. -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336. You may leave the list at any time by sending the command SIGNOFF allstat to [log in to unmask], leaving the subject line blank.