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Abstract:
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A substantial amount of work has been recently developed for tensor regression analysis in various applications such as neuroimaging, genomics, social network, and many others. Existing multivariate regression methods analyzing periodontal disease data ignore the tensor structure and do not accommodate skewness. To tackle the issues, we propose a new Bayesian tensor response regression method which allows highly skewness in tensor response. Unlike existing methods, we aim to regress moderate dimensional tensor response on vector covariate. We do not adopt either shrinkage prior or low-rank structure on the tensor coefficient. Our method is closed under marginalization to facilitate the interpretation of the covariate effects on marginal density. We handle missing data in a Bayesian fashion yielding valid inference by integrating missing values out. The proposed method promises MCMC tools are not computationally intense with easily implementable software. We illustrate substantial advantages over existing methods in terms of the estimation of parameters via simulation studies and periodontal disease data analysis.
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