• Corpus ID: 244908442

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

@inproceedings{Kilbinger2021SidesteppingTI,
  title={Sidestepping the inversion of the weak-lensing covariance matrix with Approximate Bayesian Computation},
  author={Martin Kilbinger and Emille E. O. Ishida and Jessi Cisewski-Kehe},
  year={2021}
}

• M. Kilbinger, E. Ishida, J. Cisewski-Kehe
• Published 6 December 2021
• Mathematics

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