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Bayesian nonparametric estimation of Milky Way parameters using matrix-variate data in a new Gaussian Process-based method

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journal contribution
posted on 25.09.2017, 15:35 by Dalia Chakrabarty, Munmun Biswas, Sourabh Bhattacharya
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 (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 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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Electronic Journal of Statistics

Volume

9

Pages

1378 - 1403

Citation

CHAKRABARTY, D., BISWAS, M. and BHATTACHARYA, S., 2015. Bayesian nonparametric estimation of Milky Way parameters using matrix-variate data in a new Gaussian Process-based method. Electronic Journal of Statistics, 9 (1), pp.1378-1403.

Publisher

Project Euclid

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2015

ISSN

1935-7524

Language

en

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