# Cosmic Shear: Inference from Forward Models

## TL;DR

This paper introduces two DELFI-based pipelines for weak lensing cosmological parameter inference using forward models, demonstrating their effectiveness and comparing them to traditional methods, with implications for future Stage IV experiments.

## Contribution

It develops and validates DELFI pipelines with forward modeling for weak lensing, assessing the Gaussian likelihood approximation's impact on parameter inference.

## Key findings

- DELFI pipelines accurately perform weak lensing inference for Stage III and IV.
- The Gaussian likelihood approximation has negligible impact on Stage IV constraints.
- Approximately 1000 simulations are needed for Stage IV data analysis.

## Abstract

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.