Page 242 - Special Topic Session (STS) - Volume 1

STS426 Asis K.C.
Astrostatistics (or Statistical Astronomy) has emerged since 1980s. It is a
blending of statistical analysis of astronomical data along with the
development of new statistical techniques useful to analyze astrophysical
phenomenon. The target is not only to explore the formation and evolutionary
history of galaxies but also to uncover the unknown facts related to star
formation, gamma ray bursts, supernova and other intrinsic variable stars.
Gamma-ray bursts (GRBs), the brightest explosion in the universe, since
the Big Bang, show huge variation in their duration. This duration may vary
from ten milliseconds to several hours, indicating the variation in formation of
them. To explore the possible sources, clustering of GRBs is performed in
different ways (Chattopadhyay et al. (2007) and references therein). Among
the controversy that the number of natural groups in GRBs is 2 or 3, Modak
et.al. (2018) use kernel principal component analysis(KPCA) (Scholkopf &
Smola (2002), chapter 14) to GRB data set to perform clustering as well as
dimension and noise reduction. Previous work of kernel principal component
analysis on astronomical data includes supernovae (Ishida et al. (2013), (2012)),
image denoising, etc. Kernel principal component analysis is a nonlinear
transformation on raw data, where non-linear features are extracted from data
in terms of kernel principal components. It is a generalization of linear
transformation performed in standard principal component analysis, where
linear features are extracted from data in terms of principal components.
Statistical analysis with missing data is an important problem as the
problem of missing observation is very common in many situations. In
astrostatistics one should look at missing value problem from a different angle
(Chattopadhyay (2017)) since the causes of missing observation are
sometimes inherent in the process. The imputation method may not be
applicable to some astronomical data sets as the missing value may arise from
physical process and imputing missing values is likely to be misleading and
can skew subsequent analysis of data. For example, the Lyman break
technique (Giavalisco, M. (2002)) can identify high-redshift galaxies based on
the absence of detectable emissions in bands corresponding to the FUV rest
frame of the objects. Such high-redshift galaxies were previously
unobservable. De et al. (2016) has tackled the problem by including the
knowledge of missing proportion in a classification rule.
In the present work we have discussed about some of the above
mentioned applications of statistical methods.

2. Clustering Gamma Ray Bursts Data-methodology
Modak et al. (2018) retrieved a dataset from the fourth BATSE Gamma-Ray
Burst Catalog (revised) (Paciesas et al. (1999)), consists of information on 1972
GRBs for the following 9 variables. F1, F2, F3, F4 are time-integrated fluence in
20−50, 50−100, 100−300 and > 300 keV spectral channel, respectively; P64,

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