New insight on galaxy structure from GALPHAT I. Motivation, methodology,
  and benchmarks for Sersic models
  We introduce a new galaxy image decomposition tool, GALPHAT (GALaxy
PHotometric ATtributes), to provide full posterior probability distributions
and reliable confidence intervals for all model parameters. GALPHAT is designed
to yield a high speed and accurate likelihood computation, using grid
interpolation and Fourier rotation. We benchmark this approach using an
ensemble of simulated Sersic model galaxies over a wide range of observational
conditions: the signal-to-noise ratio S/N, the ratio of galaxy size to the PSF
and the image size, and errors in the assumed PSF; and a range of structural
parameters: the half-light radius $r_e$ and the Sersic index $n$. We
characterise the strength of parameter covariance in Sersic model, which
increases with S/N and $n$, and the results strongly motivate the need for the
full posterior probability distribution in galaxy morphology analyses and later
inferences.
  The test results for simulated galaxies successfully demonstrate that, with a
careful choice of Markov chain Monte Carlo algorithms and fast model image
generation, GALPHAT is a powerful analysis tool for reliably inferring
morphological parameters from a large ensemble of galaxies over a wide range of
different observational conditions. (abridged)
