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In this paper we present a Bayesian linear model for tensor variables, and make inference under the assumption of sparsity of the tensor coeffcient. We exploit the CONDECOMP/PARAFAC (CP) representation for the tensor of coeffcients in order to reduce the number of parameters and adopt a suitable hierarchical shrinkage prior for inducing sparsity. We apply a MCMC procedure for posterior approxiation and discuss the issues related to the initialisation of MCMC algorithm.