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Title:  Minimum distance estimation of Milky Way model parameters and related inference 
Authors:  Banerjee, Sourabh Basu, Ayanendranath Bhattacharya, Sourabh Bose, Smarajit Chakrabarty, Dalia Mukherjee, Soumendu S. 
Issue Date:  2015 
Publisher:  Society for Industrial and Applied Mathematics 
Citation:  BANERJEE, S. ... et al., 2015. Minimum distance estimation of Milky Way model parameters and related inference. SIAM/ASA Journal on Uncertainty Quantification, 3 (1), pp.91115. 
Abstract:  We propose a method to estimate the location of the Sun in the disk of the Milky Way using a
method based on the Hellinger distance and construct confidence sets on our estimate of the unknown
location using a bootstrapbased method. Assuming the Galactic disk to be twodimensional, the
sought solar location then reduces to the radial distance separating the Sun from the Galactic center
and the angular separation of the Galactic center to Sun line, from a prefixed line on the disk. On
astronomical scales, the unknown solar location is equivalent to the location of us earthlings who
observe the velocities of a sample of stars in the neighborhood of the Sun. This unknown location
is estimated by undertaking pairwise comparisons of the estimated density of the observed set of
velocities of the sampled stars, with the density estimated using synthetic stellar velocity data
sets generated at chosen locations in the Milky Way disk. The synthetic data sets are generated
at a number of locations that we choose from within a constructed grid, at four different base
astrophysical models of the Galaxy. Thus, we work with one observed stellar velocity data and
four distinct sets of simulated data comprising a number of synthetic velocity data vectors, each
generated at a chosen location. For a given base astrophysical model that gives rise to one such
simulated data set, the chosen location within our constructed grid at which the estimated density
of the generated synthetic data best matches the density of the observed data is used as an estimate
for the location at which the observed data was realized. In other words, the chosen location
corresponding to the highest match offers an estimate of the solar coordinates in the Milky Way
disk. The “match” between the pair of estimated densities is parameterized by the affinity measure
based on the familiar Hellinger distance. We perform a novel crossvalidation procedure to establish
a desirable “consistency” property of the proposed method. 
Version:  Accepted for publication 
DOI:  10.1137/130935525 
URI:  https://dspace.lboro.ac.uk/2134/26666 
Publisher Link:  https://doi.org/10.1137/130935525 
Appears in Collections:  Published Articles (Maths)

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