Abstract

In this talk I will discuss a new Bayesian non-parametric method of predicting the value of the model parameter vector that supports real observed data, where this measured information is in the form of a matrix. The information is then expressed as an unknown, matrix-variate function of the model parameter vector and this unknown function is modelled using a high-dimensional Gaussian Process. The model is trained on a training data set that is generated (via simulations) at a chosen design set. In fact, in our treatment of the information as a vector of corresponding dimensions, this function is modelled as a vector-variate Gaussian Process leading to the likelihood being matrix-normal in nature, with mean and covariance matrices suggested by the structure of the Gaussian Process in question. In an effort to learn selected process parameters (such as the smoothness parameters) from the data, in addition to the unknown model parameter vector value that supports the real data, we write their joint posterior probability, given training as well as observed data. Inference is performed using Transformation-based MCMC . An application of this method is made to learn feature parameters of the Milky Way, using measured and simulated data of velocity vectors of stars that live in the vicinity of the Sun. Learning of the Galactic parameters with the real data is shown to produce a similar result to a comparator method that requires a much larger data set, in order to accomplish estimation.