Journal Article

A Bayesian approach to the semi-analytic model of galaxy formation: methodology

Yu Lu, H. J. Mo, Martin D. Weinberg and Neal Katz

in Monthly Notices of the Royal Astronomical Society

Published on behalf of The Royal Astronomical Society

Volume 416, issue 3, pages 1949-1964
Published in print September 2011 | ISSN: 0035-8711
Published online September 2011 | e-ISSN: 1365-2966 | DOI: http://dx.doi.org/10.1111/j.1365-2966.2011.19170.x
A Bayesian approach to the semi-analytic model of galaxy formation: methodology

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We believe that a wide range of physical processes conspire to shape the observed galaxy population, but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multidimensional parametrizations of the physical processes of galaxy formation and provides a tool to constrain these underlying physical interactions. Because of the high dimensionality, the parametric problem of galaxy formation may be profitably tackled with a Bayesian-inference-based approach, which allows one to constrain theory with data in a statistically rigorous way. In this paper, we develop a SAM in the framework of Bayesian inference. We show that, with a parallel implementation of an advanced Markov chain Monte Carlo algorithm, it is now possible to rigorously sample the posterior distribution of the high-dimensional parameter space of typical SAMs. As an example, we characterize galaxy formation in the current Λ cold dark matter cosmology using the stellar mass function of galaxies as an observational constraint. We find that the posterior probability distribution is both topologically complex and degenerate in some important model parameters, suggesting that thorough explorations of the parameter space are needed to understand the models. We also demonstrate that because of the model degeneracy, adopting a narrow prior strongly restricts the model. Therefore, the inferences based on SAMs are conditional to the model adopted. Using synthetic data to mimic systematic errors in the stellar mass function, we demonstrate that an accurate observational error model is essential to meaningful inference.

Keywords: methods: numerical; methods: statistical; galaxies: evolution; galaxies: formation; galaxies: luminosity function, mass function

Journal Article.  12317 words.  Illustrated.

Subjects: Astronomy and Astrophysics

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