  We present a method for modelling the covariance structure of tensor-variate
data, with the ulterior aim of learning an unknown model parameter vector using
such data. We express the high-dimensional observable as a function of this
sought model parameter vector, and attempt to learn such a high-dimensional
function given training data, by modelling it as a realisation from a
tensor-variate Gaussian Process (GP). The likelihood of the unknowns given
training data, is then tensor-normal. We choose vague priors on the unknown GP
parameters (mean tensor and covariance matrices) and write the posterior
probability density of these unknowns given the data. We perform posterior
sampling using Random-Walk Metropolis-Hastings. Thereafter we learn the
aforementioned unknown model parameter vector by performing posterior sampling
in two different ways, given test and training data, using MCMC, to generate
95$\%$ HPD credible region on each unknown. We make an application of this
method to the learning of the location of the Sun in the Milky Way disk.
