  We present the methodology for and detail the implementation of the Dark
Energy Survey (DES) 3x2pt DES Year 1 (Y1) analysis, which combines
configuration-space two-point statistics from three different cosmological
probes: cosmic shear, galaxy-galaxy lensing, and galaxy clustering, using data
from the first year of DES observations. We have developed two independent
modeling pipelines and describe the code validation process. We derive
expressions for analytical real-space multi-probe covariances, and describe
their validation with numerical simulations. We stress-test the inference
pipelines in simulated likelihood analyses that vary 6-7 cosmology parameters
plus 20 nuisance parameters and precisely resemble the analysis to be presented
in the DES 3x2pt analysis paper, using a variety of simulated input data
vectors with varying assumptions.
  We find that any disagreement between pipelines leads to changes in assigned
likelihood $\Delta \chi^2 \le 0.045$ with respect to the statistical error of
the DES Y1 data vector. We also find that angular binning and survey mask do
not impact our analytic covariance at a significant level. We determine lower
bounds on scales used for analysis of galaxy clustering (8 Mpc$~h^{-1}$) and
galaxy-galaxy lensing (12 Mpc$~h^{-1}$) such that the impact of modeling
uncertainties in the non-linear regime is well below statistical errors, and
show that our analysis choices are robust against a variety of systematics.
These tests demonstrate that we have a robust analysis pipeline that yields
unbiased cosmological parameter inferences for the flagship 3x2pt DES Y1
analysis. We emphasize that the level of independent code development and
subsequent code comparison as demonstrated in this paper is necessary to
produce credible constraints from increasingly complex multi-probe analyses of
current data.
