  Testing theories of hierarchical structure formation requires estimating the
distribution of galaxy morphologies and its change with redshift. One aspect of
this investigation involves identifying galaxies with disturbed morphologies
(e.g., merging galaxies). This is often done by summarizing galaxy images
using, e.g., the CAS and Gini-M20 statistics of Conselice (2003) and Lotz et
al. (2004), respectively, and associating particular statistic values with
disturbance. We introduce three statistics that enhance detection of disturbed
morphologies at high-redshift (z ~ 2): the multi-mode (M), intensity (I), and
deviation (D) statistics. We show their effectiveness by training a
machine-learning classifier, random forest, using 1,639 galaxies observed in
the H band by the Hubble Space Telescope WFC3, galaxies that had been
previously classified by eye by the CANDELS collaboration (Grogin et al. 2011,
Koekemoer et al. 2011). We find that the MID statistics (and the A statistic of
Conselice 2003) are the most useful for identifying disturbed morphologies.
  We also explore whether human annotators are useful for identifying disturbed
morphologies. We demonstrate that they show limited ability to detect
disturbance at high redshift, and that increasing their number beyond
approximately 10 does not provably yield better classification performance. We
propose a simulation-based model-fitting algorithm that mitigates these issues
by bypassing annotation.
