Bookmakers' odds for the sky distribution of gamma-ray bursts

Details Bookmakers' odds for the sky distribution of gamma-ray bursts Bookmakers' odds for the sky distribution of gamma-ray bursts

Jun 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994apj...427..714s&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 427, no. 2, p. 714-717

Mathematics

Probability

3

Angular Distribution, Anisotropy, Astronomical Models, Gamma Ray Astronomy, Gamma Ray Bursts, Probability Theory, Statistical Analysis, Distribution Functions, Galactic Halos, Gamma Ray Observatory, Isotropy, Monte Carlo Method

Scientific paper

Given a set of data and two models which might describe them, bookmakers' odds represent an objective statement about how likely one model is relative to the other. We develop the necessary theory for computation of bookmakers' odds for models of the angular distribution of gamma-ray bursts; the models may contain parameters with initially unknown values. The theory applies equally to any situation involving a modeling a distribution function for discrete events. We then compute bookmakers' odds for models with anisotropic contributions (all directions for anisotropy being allowed) up to the order of an octupole, from the public Burst and Transient Source Experiment (BATSE) catalog (containing 260 bursts), allowing for the nonuniform sky coverage of the detector. This data set favors the isotropic model over any of these, but only weakly: a nonaxisymmetric quadrupole model is 70% as likely as the isotropic one, while the dipole model is less than 20% as likely. Obviously, the odds will change on including more data, admitting the possibility that the isotropic model might eventually become less compelling. However, we argue that with only a few hundred bursts, there may be little hope of strongly discriminating between isotropic and anisotropic models. For instance, moderately triaxial Galactic halo source models may be admissible.

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