  We propose a Bayesian tensor regression model to accommodate the effect of
multiple factors on phenotype prediction. We adopt a set of prior distributions
that resolve identifiability issues that may arise between the parameters in
the model. Simulation experiments show that our method out-performs previous
related models and machine learning algorithms under different sample sizes and
degrees of complexity. We further explore the applicability of our model by
analysing real-world data related to wheat production across Ireland from 2010
to 2019. Our model performs competitively and overcomes key limitations found
in other analogous approaches. Finally, we adapt a set of visualisations for
the posterior distribution of the tensor effects that facilitate the
identification of optimal interactions between the tensor variables whilst
accounting for the uncertainty in the posterior distribution.
