Sidestepping the inversion of the weak-lensing covariance matrix with Approximate Bayesian Computation

Weak gravitational lensing is one of the few direct methods to map dark-matter distribution on large scales in Universe, and estimate cosmological parameters. We study a Bayesian inference problem where data covariance C, estimated from number ns numerical simulations, singular. In context large-scale structure observations, creation such N-body simulations often prohibitively expensive. Inference based likelihood function includes precision matrix, Ψ=C−1. The matrix corresponding p-dimensional vector singular for p≥ns, which case unavailable. propose likelihood-free method Approximate Computation (ABC) as solution that circumvents inversion matrix. present examples increasing degree complexity, culminating realistic scenario determination weak-gravitational power spectrum upcoming European Space Agency satellite Euclid. While we found ABC parameter variances be mildly larger compared likelihood-based approaches, are restricted settings with p<ns, obtain unbiased estimates even extreme cases p/ns≫1. code has been made publicly available1 ensure reproducibility results.