  "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 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 favours major merging (with disc survival
or rapid reformation) over secular evolution as the mechanism most responsible
for building up the first generation of bulges in early-type disks.
