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Bayesian regression analysis of skewed tensor responses
Authors:Inkoo Lee  Debajyoti Sinha  Qing Mai  Xin Zhang  Dipankar Bandyopadhyay
Institution:1. Department of Statistics, Rice University, Houston, Texas, USA;2. Department of Statistics, Florida State University, Tallahassee, Florida, USA;3. Department of Biostatistics, Virginia Commonwealth University, Richmond, Virginia, USA
Abstract:Tensor regression analysis is finding vast emerging applications in a variety of clinical settings, including neuroimaging, genomics, and dental medicine. The motivation for this paper is a study of periodontal disease (PD) with an order-3 tensor response: multiple biomarkers measured at prespecified tooth–sites within each tooth, for each participant. A careful investigation would reveal considerable skewness in the responses, in addition to response missingness. To mitigate the shortcomings of existing analysis tools, we propose a new Bayesian tensor response regression method that facilitates interpretation of covariate effects on both marginal and joint distributions of highly skewed tensor responses, and accommodates missing-at-random responses under a closure property of our tensor model. Furthermore, we present a prudent evaluation of the overall covariate effects while identifying their possible variations on only a sparse subset of the tensor components. Our method promises Markov chain Monte Carlo (MCMC) tools that are readily implementable. We illustrate substantial advantages of our proposal over existing methods via simulation studies and application to a real data set derived from a clinical study of PD. The R package BSTN available in GitHub implements our model.
Keywords:Markov chain Monte Carlo  periodontal disease  skewness  tensor regression
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