  Modelling noisy data in a network context remains an unavoidable obstacle;
fortunately, random matrix theory may comprehensively describe network
environments effectively. Thus it necessitates the probabilistic
characterisation of these networks (and accompanying noisy data) using matrix
variate models. Denoising network data using a Bayes approach is not common in
surveyed literature. This paper adopts the Bayesian viewpoint and introduces a
new matrix variate t-model in a prior sense by relying on the matrix variate
gamma distribution for the noise process, following the Gaussian graphical
network for the cases when the normality assumption is violated. From a
statistical learning viewpoint, such a theoretical consideration indubitably
benefits the real-world comprehension of structures causing noisy data with
network-based attributes as part of machine learning in data science. A full
structural learning procedure is provided for calculating and approximating the
resulting posterior of interest to assess the considered model's network
centrality measures. Experiments with synthetic and real-world stock price data
are performed not only to validate the proposed algorithm's capabilities but
also to show that this model has wider flexibility than originally implied in
Billio et al. (2021).
