  Density-estimation likelihood-free inference (DELFI) has recently been
proposed as an efficient method for simulation-based cosmological parameter
inference. Compared to the standard likelihood-based Markov Chain Monte Carlo
(MCMC) approach, DELFI has several advantages: it is highly parallelizable,
there is no need to assume a possibly incorrect functional form for the
likelihood and complicated effects (e.g the mask and detector systematics) are
easier to handle with forward models. In light of this, we present two DELFI
pipelines to perform weak lensing parameter inference with lognormal
realizations of the tomographic shear field -- using the C_l summary statistic.
The first pipeline accounts for the non-Gaussianities of the shear field,
intrinsic alignments and photometric-redshift error. We validate that it is
accurate enough for Stage III experiments and estimate that O(1000) simulations
are needed to perform inference on Stage IV data. By comparing the second DELFI
pipeline, which makes no assumption about the functional form of the
likelihood, with the standard MCMC approach, which assumes a Gaussian
likelihood, we test the impact of the Gaussian likelihood approximation in the
MCMC analysis. We find it has a negligible impact on Stage IV parameter
constraints. Our pipeline is a step towards seamlessly propagating all
data-processing, instrumental, theoretical and astrophysical systematics
through to the final parameter constraints.
