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Abstract:
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In a variety of application areas, there is a growing interest in analyzing high dimensional sparse count data. For example, in cancer genomic studies it is of interest to model the counts of mutated alleles across the genome. Existing approaches for analyzing multivariate count data via Poisson log-linear hierarchical models cannot flexibly adapt to the level and nature of sparsity in the data. We develop a new class of local-global shrinkage priors tailored for sparse counts. Theoretical properties are assessed, including posterior concentration, super-efficiency in estimating the sampling density, and robustness in posterior mean. Simulation studies illustrate excellent small sample properties relative to competitors, and we apply the method to model rare mutation data from the Exome Aggregation Consortium project.
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