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Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/26664

Title: Bayesian nonparametric estimation of Milky Way parameters using matrix-variate data in a new Gaussian Process-based method
Authors: Chakrabarty, Dalia
Biswas, Munmun
Bhattacharya, Sourabh
Issue Date: 2015
Publisher: Project Euclid
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.
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 (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.
Version: Accepted for publication
DOI: 10.1214/15-EJS1037
URI: https://dspace.lboro.ac.uk/2134/26664
Publisher Link: https://doi.org/10.1214/15-EJS1037
ISSN: 1935-7524
Appears in Collections:Published Articles (Maths)

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