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MATHEMATICAL SCIENCES COLLOQUIUM

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.

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