文章基本信息

标题：Bayesian nonparametric estimation of Milky Way parameters using matrix-variate data, in a new Gaussian Process based method
本地全文：下载
作者：Dalia Chakrabarty ; Munmun Biswas ; Sourabh Bhattacharya 等
期刊名称：Electronic Journal of Statistics
印刷版ISSN：1935-7524
出版年度：2015
卷号：9
期号：1
页码：1378-1403
DOI：10.1214/15-EJS1037
语种：English
出版社：Institute of Mathematical Statistics
摘要：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 ($\mathcal{GP}$). 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 $\mathcal{GP}$, 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.