Astronomy and Astrophysics – Astrophysics – Instrumentation and Methods for Astrophysics
Scientific paper
2012-02-07
Astronomy and Astrophysics
Astrophysics
Instrumentation and Methods for Astrophysics
22 pages, 11 figures, submitted to MNRAS
Scientific paper
"Approximate Bayesian Computation" (ABC) represents a powerful methodology for the analysis of complex stochastic systems for which the likelihood of the observed data under an arbitrary set of input parameters may be entirely intractable-the latter condition rendering useless the standard machinery of tractable likelihood-based, Bayesian statistical inference (e.g. conventional Markov Chain Monte Carlo simulation; MCMC). In this article we demonstrate the potential of ABC for astronomical model analysis by application to a case study in the morphological transformation of high redshift galaxies. To this end we develop, first, a stochastic model for the competing processes of merging and secular evolution in the early Universe; and second, through an ABC-based comparison against the observed demographics of the first generation of massive (M_gal > 10^11 M_sun) galaxies (at 1.5 < z < 3) in the CANDELS/EGS dataset we derive posterior probability densities for the key parameters of this model. The "Sequential Monte Carlo" (SMC) implementation of ABC exhibited herein, featuring both a self-generating target sequence and self-refining MCMC kernel, is amongst the most efficient of contemporary approaches to this important statistical algorithm. We highlight as well through our chosen case study the value of careful summary statistic selection, and demonstrate two modern strategies for assessment and optimisation in this regard. Ultimately, our ABC analysis of the high redshift morphological mix returns tight constraints on the evolving merger rate in the early Universe and reveals merging, rather than secular evolution, as the most important mechanism for building up the first generation of bulges in early-type disks.
Cameron Ewan
Pettitt Anthony N.
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