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… 

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References

SHOWING 1-10 OF 89 REFERENCES
Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations
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
TLDR
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
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
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
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
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
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
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
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
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
...
1
2
3
4
5
...