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In this paper we develop an inverse Bayesian approach to find the value ofthe unknown model parameter vector that supports the real (or test) data, wherethe data comprises measurements of a matrix-variate variable. The method isillustrated via the estimation of the unknown Milky Way feature parametervector, using available test and simulated (training) stellar velocity datamatrices. The data is represented as an unknown function of the modelparameters, where this high-dimensional function is modelled using ahigh-dimensional Gaussian Process (${\cal GP}$). The model for this function istrained using available training data and inverted by Bayesian means, toestimate the sought value of the model parameter vector at which the test datais realised. We achieve a closed-form expression for the posterior of theunknown parameter vector and the parameters of the invoked ${\cal GP}$, giventest and training data. We perform model fitting by comparing the observed datawith predictions made at different summaries of the posterior probability ofthe model parameter vector. As a supplement, we undertake a leave-one-out crossvalidation of our method.

Bayesian Nonparametric Estimation of Milky Way Model Parameters Using a New Matrix-Variate Gaussian Process Based Method