Abstract:
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Large-scale inference involves estimating many parameters simultaneously, for example estimating group-wise differences in mean expression levels of thousands of genes. Genomics researchers have claimed that correlations among individuals may be present in such data, due to batch effects or latent variables, violating the traditional independent samples framework. Such correlations change the distribution of test statistics, leading to incorrect assessments of differential expression. In the setting of two-group hypothesis testing with correlated rows and columns, Allen and Tibshirani proposed a matrix-variate model in which the covariances have Kronecker product structure. Under this model, we propose a likelihood-based method for more accurate estimation of the mean structure. We assess the performance of the approach using simulations, and we apply our method to data from two genomic studies, one with only a few correlated samples, and one with heavier dependencies due to batch effects.
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