# Sparse Bayesian mass-mapping with uncertainties: Full sky observations on the celestial sphere

@article{Price2020SparseBM, title={Sparse Bayesian mass-mapping with uncertainties: Full sky observations on the celestial sphere}, author={Matthew Alexander Price and Jason D. McEwen and Luke Pratley and Thomas D. Kitching}, journal={Monthly Notices of the Royal Astronomical Society}, year={2020} }

To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the flat-sky approximation has been sufficiently satisfied. However, with Stage IV surveys (e.g. LSST and Euclid) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian mass-mapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct maximum a…

## 11 Citations

Higher order statistics of shear field: a machine learning approach

- Computer Science
- 2020

This work investigates the development of a new method to treat weak lensing higher order statistics, which are known to break degeneracy among cosmological parameters thanks to their capability of probing the non-Gaussian properties of the shear field.

Sparse image reconstruction on the sphere: a general approach with uncertainty quantification

- MathematicsArXiv
- 2021

This article considers the Bayesian interpretation of the unconstrained problem which, combined with recent developments in probability density theory, permits rapid, statistically principled uncertainty quantification (UQ) in the spherical setting and linearity is exploited to significantly increase the computational efficiency of such UQ techniques.

Bayesian variational regularization on the ball

- Computer ScienceArXiv
- 2021

Variational regularization methods which leverage sparsity-promoting priors to solve severely illposed inverse problems defined on the 3D ball and thus does not suffer from discontinuities that plague alternate approaches where each spherical shell is considered independently.

Dark Energy Survey Year 3 results: Curved-sky weak lensing mass map reconstruction

- PhysicsMonthly Notices of the Royal Astronomical Society
- 2021

We present reconstructed convergence maps, mass maps, from the Dark Energy Survey (DES) third year (Y3) weak gravitational lensing data set. The mass maps are weighted projections of the density…

Posterior sampling for inverse imaging problems on the sphere

- Mathematics, Computer Science
- 2021

This work describes a framework that leverages a proximal Markov chain Monte Carlo algorithm to efficiently sample the highdimensional space of spherical inverse problems with a sparsitypromoting wavelet prior and finds that it is potentially useful for a wide range of applications at moderate resolutions.

Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs

- Environmental ScienceArXiv
- 2021

This work develops scattering networks constructed natively on the sphere that provide a powerful representational space for spherical data and shows how they can be leveraged to scale spherical CNNs to the high resolution data typical of many practical applications.

Weak Lensing Trispectrum and Kurt-Spectra

- Physics
- 2021

We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function…

Weak-lensing mass reconstruction using sparsity and a Gaussian random field

- Computer ScienceAstronomy & Astrophysics
- 2021

A novel approach to reconstructing dark matter mass maps from weak gravitational lensing measurements using an algorithm called MCALens based on an alternating minimisation incorporating both sparse recovery and proximal iterative Wiener filtering that exhibits improved estimation accuracy compared to customised mass-map reconstruction methods.

Cosmic shear cosmology beyond two-point statistics: a combined peak count and correlation function analysis of DES-Y1

- Physics
- 2020

We constrain cosmological parameters from a joint cosmic shear analysis of peak-counts and the two-point shear correlation function, as measured from the Dark Energy Survey (DES-Y1). We find the…

Higher-order statistics of shear field via a machine learning approach

- Computer Science
- 2020

This work investigates the development of a new method to treat weak lensing higher order statistics, which are known to break degeneracy among cosmological parameters thanks to their capability of probing the non-Gaussian properties of the shear field.

## References

SHOWING 1-10 OF 89 REFERENCES

Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations

- MathematicsMonthly Notices of the Royal Astronomical Society
- 2019

Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical…

Sparse Bayesian mass mapping with uncertainties: local credible intervals

- Computer Science
- 2019

This work draws on the concept of local credible intervals as an extension of the uncertainty quantification techniques previously detailed, and finds that, typically, its recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated with those recovered via Px-MALA.

Mapping dark matter on the celestial sphere with weak gravitational lensing

- Physics
- 2017

Convergence maps of the integrated matter distribution are a key science result from weak gravitational lensing surveys. To date, recovering convergence maps has been performed using a planar…

Hierarchical probabilistic inference of cosmic shear

- Physics
- 2014

Point estimators for the shearing of galaxy images induced by gravitational lensing involve a complex inverse problem in the presence of noise, pixelization, and model uncertainties. We present a…

KiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing

- Physics
- 2017

We present cosmological parameter constraints from a tomographic weak gravitational lensing analysis of ~450deg$^2$ of imaging data from the Kilo Degree Survey (KiDS). For a flat $\Lambda$CDM…

Improving weak lensing mass map reconstructions using Gaussian and Sparsity Priors: application to DES SV

- Geology
- 2018

Mapping the underlying density field, including non-visible dark matter, using weak gravitational lensing measurements is now a standard tool in cosmology. Due to its importance to the science…

Three-dimensional Reconstruction of the Density Field: An SVD Approach to Weak-lensing Tomography

- Geology
- 2010

We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the…

Full-sky Gravitational Lensing Simulation for Large-area Galaxy Surveys and Cosmic Microwave Background Experiments

- Physics
- 2017

We present 108 full-sky gravitational lensing simulation data sets generated by performing multiple-lens plane ray-tracing through high-resolution cosmological $N$-body simulations. The data sets…

Bayesian galaxy shape measurement for weak lensing surveys – III. Application to the Canada–France–Hawaii Telescope Lensing Survey

- Physics
- 2013

A likelihood-based method for measuring weak gravitational lensing shear in deep galaxy surveys is described and applied to the Canada–France–Hawaii Telescope (CFHT) Lensing Survey (CFHTLenS).…

ASKI: full-sky lensing map-making algorithms

- Physics
- 2010

Within the context of upcoming full-sky lensing surveys, the edge-preserving non-linear algorithm ASKI (All-Sky κ Inversion) is presented. Using the framework of Maximum A Posteriori inversion, it…