ASTROSTATISTICS - ANALYSIS OF GAMMA-RAY BURSTS DATA.
Professor G. Jogesh Babu
Department of Statistics
Pennsylvania State University
ABSTRACT
The interaction between astronomy and statistics benefited both fields
till the last century, leading to many foundations of mathematical
statistics such as least squares, theory of errors, curve fitting and
minimax theory. However, during the later half of the 19th century
astronomers have turned principally towards astrophysics, gaining insight
into the physical aspects of the universe.
During the last few years, a resurgence of interest in statistical
methods has emerged among astronomers, though with different emphases
than in the past. One major factor is the flood of data produced by
large astronomical surveys at many wavebands. The surveys present
a variety of challenging statistical problems: raw data processing,
source identification, source characterization and inter-relations
between multiwavelength properties. The multivariate databases from
astronomical surveys have complicated structure including heteroscedastic
measurement errors and censoring and truncation in one or more variables.
Some of these problems are illustrated in data from the 3rd BATSE (Burst
And Transient Source Experiment) catalog of gamma-ray bursts.
Gamma-ray bursts are astronomical events that are observed on average
once a day by the most sensitive gamma-ray burst experiment in operation
on the Compton Gamma-Ray Observatory (CGRO). These events, which
last from 10 milliseconds to 1000 seconds, are of unknown origin.
A multivariate analysis of gamma-ray burst (GRB) bulk properties is
presented to discriminate between distinct classes of GRBs. Several
variables representing burst duration, fluence and spectral hardness
are considered. Two multivariate clustering procedures are used:
a nonparametric average linkage hierarchical agglomerative clustering
procedure, and a parametric maximum likelihood model-based clustering
procedure.