  Weak lensing by large-scale structure is a powerful probe of cosmology and of
the dark universe. This cosmic shear technique relies on the accurate
measurement of the shapes and redshifts of background galaxies and requires
precise control of systematic errors. The Monte Carlo Control Loops (MCCL) is a
forward modelling method designed to tackle this problem. It relies on the
Ultra Fast Image Generator (UFig) to produce simulated images tuned to match
the target data statistically, followed by calibrations and tolerance loops. We
present the first end-to-end application of this method, on the Dark Energy
Survey (DES) Year 1 wide field imaging data. We simultaneously measure the
shear power spectrum $C_{\ell}$ and the redshift distribution $n(z)$ of the
background galaxy sample. The method includes maps of the systematic sources,
Point Spread Function (PSF), an Approximate Bayesian Computation (ABC)
inference of the simulation model parameters, a shear calibration scheme, and
the fast estimation of the covariance matrix. We find a close statistical
agreement between the simulations and the DES Y1 data using an array of
diagnostics. In a non-tomographic setting, we derive a set of $C_\ell$ and
$n(z)$ curves that encode the cosmic shear measurement, as well as the
systematic uncertainty. Following a blinding scheme, we measure the combination
of $\Omega_m$, $\sigma_8$, and intrinsic alignment amplitude $A_{\rm{IA}}$,
defined as $S_8D_{\rm{IA}} = \sigma_8(\Omega_m/0.3)^{0.5}D_{\rm{IA}}$, where
$D_{\rm{IA}}=1-0.11(A_{\rm{IA}}-1)$. We find
$S_8D_{\rm{IA}}=0.895^{+0.054}_{-0.039}$, where systematics are at the level of
roughly 60\% of the statistical errors. We discuss these results in the context
of earlier cosmic shear analyses of the DES Y1 data. Our findings indicate that
this method and its fast runtime offer good prospects for cosmic shear
measurements with future wide-field surveys.
