  Modeling with multidimensional arrays, or tensors, often presents a problem
due to high dimensionality. In addition, these structures typically exhibit
inherent sparsity, requiring the use of regularization methods to properly
characterize an association between a tensor covariate and a scalar response.
We propose a Bayesian method to efficiently model a scalar response with a
tensor covariate using the Tucker tensor decomposition in order to retain the
spatial relationship within a tensor coefficient, while reducing the number of
parameters varying within the model and applying regularization methods.
Simulated data are analyzed to compare the model to recently proposed methods.
A neuroimaging analysis using data from the Alzheimer's Data Neuroimaging
Initiative is included to illustrate the benefits of the model structure in
making inference.
