E. Cameron, A. N. Pettitt
"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.
View original:
http://arxiv.org/abs/1202.1426
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