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Title: Inverse Bayesian Estimation of Gravitational Mass Density in Galaxies from Missing Kinematic Data
Authors: Chakrabarty, Dalia
Saha, P.
First Published: Feb-2014
Publisher: Scientific Research Publishing
Citation: D. Chakrabarty and P. Saha, "Inverse Bayesian Estimation of Gravitational Mass Density in Galaxies from Missing Kinematic Data," American Journal of Computational Mathematics, Vol. 4 No. 1, 2014, pp. 6-29.
Abstract: In this paper, we focus on a type of inverse problem in which the data are expressed as an unknown function of the sought and unknown model function (or its discretised representation as a model parameter vector). In particular, we deal with situations in which training data are not available. Then we cannot model the unknown functional relationship between data and the unknown model function (or parameter vector) with a Gaussian Process of appropriate dimensionality. A Bayesian method based on state space modelling is advanced instead. Within this framework, the likelihood is expressed in terms of the probability density function (pdf) of the state space variable and the sought model parameter vector is embedded within the domain of this pdf. As the measurable vector lives only inside an identified sub-volume of the system state space, the pdf of the state space variable is projected onto the space of the measurables, and it is in terms of the projected state space density that the likelihood is written; the final form of the likelihood is achieved after convolution with the distribution of measurement errors. Application motivated vague priors are invoked and the posterior probability density of the model parameter vectors, given the data are computed. Inference is performed by taking posterior samples with adaptive MCMC. The method is illustrated on synthetic as well as real galactic data.
DOI Link: 10.4236/ajcm.2014.41002
ISSN: 2161-1203
eISSN: 2161-1211
Version: Publisher Version
Status: Peer-reviewed
Type: Journal Article
Rights: Copyright © 2014 Dalia Chakrabarty, Prasenjit Saha. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In accordance of the Creative Commons Attribution License all Copyrights © 2014 are reserved for SCIRP and the owner of the intellectual property Dalia Chakrabarty, Prasenjit Saha. All Copyright © 2014 are guarded by law and by SCIRP as a guardian.
Appears in Collections:Published Articles, Dept. of Mathematics

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