From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics

Details From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics From Laplace to Supernova SN 1987A: Bayesian Inference in Astrophysics

Jan 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phdt.........9l&link_type=abstract

Thesis (PH.D.)--THE UNIVERSITY OF CHICAGO, 1995.Source: Dissertation Abstracts International, Volume: 56-05, Section: B, page: 2

Mathematics

Probability

1

Pierre Simon De Laplace

Scientific paper

This dissertation describes the Bayesian approach to general problems of statistical inference in astrophysics, and then describes in detail the application of such methods to the analysis of the neutrinos detected from supernova SN 1987A in the Large Magellanic Cloud. Part I presents the Bayesian approach to probability theory as an alternative to the currently used long-run relative frequency approach, which does not offer clear, compelling criteria for the design of statistical methods. Bayesian probability theory offers unique and demonstrably optimal solutions to well-posed statistical problems, and is historically the original approach to statistics. After a brief historical introduction, we outline the Bayesian approaches to parameter estimation and model comparison and illustrate them by application to simple problems based on the Gaussian distribution. As further illustrations of the Bayesian paradigm, we outline Bayesian solutions to some simple astrophysical problems. Finally, we present a brief bibliography of astrophysically interesting applications of Bayesian inference. Part II presents an analysis of the detected energies and arrival times of the neutrinos from supernova SN 1987A detected by the Kamiokande II, IMB, and Baksan detectors. This work improves on previous studies in several important respects, including use of a consistent and straightforward statistical methodology, proper treatment of background rates, and consideration of a wider variety of neutrino emission models than was explored previously. We show that the inferred neutrino emission model parameters are strongly correlated. Consequently, best fit values and one-dimensional confidence intervals for the individual parameters do not adequately summarize the implications of the data. Our analysis confirms that simple models of the neutrino cooling of the nascent neutron star formed by the supernova adequately explain the data. The inferred characteristics of these models are in spectacular agreement with the salient features of the theory of stellar collapse and neutron star formation that had developed over several decades in the absence of direct observational data. We discuss the technical and conceptual differences between our analysis and previous analyses.

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