# 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} }

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…

## References

SHOWING 1-10 OF 79 REFERENCES

### Precision matrix expansion – efficient use of numerical simulations in estimating errors on cosmological parameters

- Physics
- 2018

Computing the inverse covariance matrix (or precision matrix) of large data vectors is crucial in weak lensing (and multiprobe) analyses of the large-scale structure of the Universe. Analytically…

### CFHTLenS: a Gaussian likelihood is a sufficient approximation for a cosmological analysis of third-order cosmic shear statistics

- Physics
- 2015

We study the correlations of the shear signal between triplets of sources in the Canada–France–Hawaii Telescope Lensing Survey (CFHTLenS) to probe cosmological parameters via the matter bispectrum.…

### A Bayesian method for combining theoretical and simulated covariance matrices for large-scale structure surveys

- Computer ScienceMonthly Notices of the Royal Astronomical Society
- 2018

This work constructs a likelihood function conditioned on simulated and theoretical covariances, consistently propagating noise from the finite number of simulations and uncertainty in the theoretical model itself using an informative Inverse-Wishart prior.

### Karhunen-Loève Eigenvalue Problems in Cosmology: How Should We Tackle Large Data Sets?

- Physics
- 1996

Since cosmology is no longer “the data-starved science,” the problem of how to analyze large data sets best has recently received considerable attention, and Karhunen-Loève eigenvalue methods have…

### Accurate cosmic shear errors: do we need ensembles of simulations?

- Environmental ScienceJournal of Cosmology and Astroparticle Physics
- 2018

Accurate inference of cosmology from weak lensing shear requires an accurate shear power spectrum covariance matrix. Here, we investigate this accuracy requirement and quantify the relative…

### Performance of internal covariance estimators for cosmic shear correlation functions

- Mathematics
- 2016

Data re-sampling methods such as delete-one jackknife, bootstrap or the sub-sample covariance are common tools for estimating the covariance of large-scale structure probes. We investigate different…

### Weak Lensing and Cosmology

- Physics
- 1996

We explore the dependence of weak lensing phenomena on the background cosmology. We first generalize the relation between Pψ(ω), the angular power spectrum of the distortion, and the power spectrum…

### Monte Carlo control loops for cosmic shear cosmology with DES Year 1 data

- PhysicsPhysical Review D
- 2020

Weak lensing by large-scale structure is a powerful probe of cosmology and of the dark universe. This cosmic shear technique relies on the accurate measurement of the shapes and redshifts of…

### Cosmological parameters from weak lensing power spectrum and bispectrum tomography: including the non-Gaussian errors

- Physics
- 2013

We re-examine a genuine power of weak lensing bispectrum tomography for constraining cosmological parameters, when combined with the power spectrum tomography, based on the Fisher information matrix…

### Properties and use of CMB power spectrum likelihoods

- Mathematics
- 2009

Fast robust methods for calculating likelihoods from cosmic microwave background observations on small scales generally rely on approximations based on a set of power spectrum estimators and their…