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

TL;DR

This paper introduces a Bayesian nonparametric method using matrix-variate Gaussian processes to estimate Milky Way parameters from stellar velocity data, providing a closed-form posterior and validation techniques.

Contribution

It develops a novel inverse Bayesian approach with a matrix-variate Gaussian process model for high-dimensional data, enabling efficient parameter estimation in astrophysics.

Findings

Closed-form posterior for model parameters and GP hyperparameters.

Effective estimation of Milky Way features from stellar velocity data.

Validation through leave-one-out cross validation confirms method reliability.

Abstract

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