Applications of Bayesian Probability Theory in Astrophysics

Bayesian Inference is a powerful approach to data analysis that is based almost entirely on probability theory. In this approach, probabilities model uncertainty rather than randomness or variability. This thesis is composed of a series of papers that have been published in various astronomical journals during the years 2005-2008. The unifying thread running through the papers is the use of Bayesian Inference to solve underdetermined inverse problems in astrophysics. Firstly, a methodology is developed to solve a question in gravitational lens inversion using the observed images of gravitational lens systems to reconstruct the undistorted source profile and the mass profile of the lensing galaxy. A similar technique is also applied to the task of inferring the number and frequency of modes of oscillation of a star from the time series observations that are used in the field of asteroseismology. For these complex problems, many of the required calculations cannot be done analytically, and so Markov Chain Monte Carlo algorithms have been used. Finally, probabilistic reasoning is applied to a controversial question in astrobiology: does the fact that life formed quite soon after the Earth constitute evidence that the formation of life is quite probable, given the right macroscopic conditions? Statement of Originality This thesis describes work carried out in the Institute of Astronomy, within the School of Physics, University of Sydney, between February 2005 and May 2008. This thesis contains no material that has been presented for a degree at this or any other university, and, to the best of my knowledge, contains no copy or paraphrase of work published by another person, except where duly acknowledged in the text. ................................... ......................... Brendon J. Brewer Date Publications Included in this Thesis Several chapters of this thesis have been published in peer-reviewed journals. Others are currently in the review process, and are listed as “submitted”. All of the first-author papers consist of research conducted by myself, in consultation with my supervisor Geraint Lewis, or other collaborators where applicable. The papers made use of astronomical data that were taken by others but provided to me in order to carry out this work. All of the text and figures of these papers were also written by me, with the exception of minor corrections and the occasional paragraph. For the paper on the radio Einstein Ring PSS2322+1944 (the only non-first author paper included in this thesis), the data were taken by Dominik Riechers and his team, who contacted us to undertake the gravitational lensing analysis. A significant fraction of the work contained in the paper (basically, everything related to lensing and Bayesian inference) was carried out by myself, producing Figures 4, 5 and 7 (and the results shown in Figure 6). The text describing the gravitational lens inversion was written by me, and forms a significant part of the paper. The other parts of the paper were predominantly written by Dominik Riechers. Strong Gravitational Lens Inversion: A Bayesian Approach. B. J. Brewer and G. F. Lewis, 2006, Astrophysical Journal 637, 608-619. The Einstein Ring 0047-2808 Revisited: A Bayesian Inversion. B. J. Brewer and G. F. Lewis, 2006, Astrophysical Journal 651, 8-13. Unlensing HST Observations of the Einstein Ring 1RXS J1131-1231: A Bayesian Analysis. B. J. Brewer and G. F. Lewis, Monthly Notices of the Royal Astronomical Society, in press. A Molecular Einstein Ring at z =4.12: Imaging the Quasar Host Galaxy of PSS2322+1944 Through a Cosmic Lens. D. A Riechers, F. Walter, B. J. Brewer, C. L. Carilli, G. F. Lewis, F. Bertoldi and P. Cox, the Astrophysical Journal, in press. Bayesian Inference from Observations of Solar-Like Oscillations. B. J. Brewer, T. R. Bedding, H. Kjeldsen and D. Stello, 2007, Astrophysical Journal 654, 551-557. Implications of the Early Formation of Life on Earth. B. J. Brewer, submitted to Astrobiology.