Fast Bayesian Semiparametric Curve-Fitting and Clustering in Massive
  Data With Application to Cosmology
  Recent technological advances have led to a flood of new data on cosmology
rich in information about the formation and evolution of the universe, e.g.,
the data collected in Sloan Digital Sky Survey (SDSS) for more than 200 million
objects. The analyses of such data demand cutting edge statistical
technologies. Here, we have used the concept of mixture model within Bayesian
semiparametric methodology to fit the regression curve with the bivariate data
for the apparent magnitude and redshift for Quasars in SDSS (2007) catalogue.
Associated with the mixture modeling is a highly efficient curve-fitting
procedure, which is central to the application considered in this paper.
Moreover, we adopt a new method for analysing the posterior distribution of
clusterings, also generated as a by-product of our methodology. The results of
our analysis of the cosmological data clearly indicate the existence of four
change points on the regression curve andposssibiltiy of clustering of quasars
specially at high redshift. This sheds new light not only on the issue of
evolution, existence of acceleration or decceleration and environment around
quasars at high redshift but also help us to estimate thecosmological
parameters related to acceleration or decceleration.
