# Sparse Bayesian mass mapping with uncertainties: local credible intervals

@article{Price2019SparseBM, title={Sparse Bayesian mass mapping with uncertainties: local credible intervals}, author={Matthew A. Price and Xiaohao Cai and Jason D. McEwen and Marcelo Pereyra and Thomas D. Kitching}, journal={Monthly Notices of the Royal Astronomical Society}, year={2019}, volume={492}, pages={394-404} }

Until recently, mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work, we presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, we draw on the concept of local credible intervals (cf. Bayesian error bars) as an extension of the… Expand

#### 11 Citations

Probabilistic Mapping of Dark Matter by Neural Score Matching

- Physics, Computer Science
- 2020

This work presents a novel methodology for addressing inverse problems by combining elements of Bayesian statistics, analytic physical theory, and a recent class of Deep Generative Models based on Neural Score Matching, and presents an application on the first deep-learning-assisted Dark Matter map reconstruction of the Hubble Space Telescope COSMOS field. Expand

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

- Computer Science, Physics
- ArXiv
- 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. Expand

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

- Physics
- 2021

We introduce a novel approach to reconstruct dark matter mass maps from weak gravitational lensing measurements. The cornerstone of the proposed method lies in a new modelling of the matter density… Expand

Posterior sampling for inverse imaging problems on the sphere

- Physics
- 2021

Inverse problems defined on the sphere arise in many fields, and are generally high-dimensional and computationally very complex. As a result, sampling the posterior of spherical inverse problems is… Expand

Bayesian variational regularization on the ball

- Computer Science, Physics
- ArXiv
- 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. Expand

Langevin Monte Carlo without Smoothness

- Mathematics, Computer Science
- AISTATS
- 2020

This paper provides polynomial-time convergence guarantees for a variant of LMC in the setting of nonsmooth log-concave distributions, by leveraging the implicit smoothing of the log-density that comes from a small Gaussian perturbation that is added to the iterates of the algorithm. Expand

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

- Physics
- Monthly 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… Expand

Three-dimensional Reconstruction of Weak-lensing Mass Maps with a Sparsity Prior. I. Cluster Detection

- Physics
- 2021

We propose a novel method to reconstruct high-resolution three-dimensional mass maps using data from photometric weak-lensing surveys. We apply an adaptive LASSO algorithm to perform a sparsity-based… Expand

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

- Physics
- 2020

The unprecedented amount and the excellent quality of lensing data that the upcoming ground- and space-based surveys will produce represent a great opportunity to shed light on the questions that… Expand

Likelihood-free inference with neural compression of DES SV weak lensing map statistics

- Physics
- 2020

In many cosmological inference problems, the likelihood (the probability of the observed data as a function of the unknown parameters) is unknown or intractable. This necessitates approximations and… Expand

#### References

SHOWING 1-10 OF 48 REFERENCES

Uncertainty quantification for radio interferometric imaging: II. MAP estimation

- Physics, Computer Science
- Monthly Notices of the Royal Astronomical Society
- 2018

MAP-based techniques provide a means of quantifying uncertainties for radio interferometric imaging for realistic data volumes and practical use, and scale to the emerging big data era of radio astronomy. Expand

Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methods

- Physics, Computer Science
- Monthly Notices of the Royal Astronomical Society
- 2018

Three strategies to quantify uncertainties using the recovered posterior distribution are developed: local (pixel-wise) credible intervals to provide error bars for each individual pixel; highest posterior density credible regions; and hypothesis testing of image structure, which provide rich information for analysing radio interferometric observations in a statistically robust manner. Expand

Maximum-a-Posteriori Estimation with Bayesian Confidence Regions

- Mathematics, Computer Science
- SIAM J. Imaging Sci.
- 2017

A new general methodology for approximating Bayesian high-posterior-density credibility regions in inverse problems that are convex and potentially very high-dimensional and which can be computed very efficiently, even in large-scale problems, by using standard convex optimisation techniques. Expand

Efficient Bayesian Computation by Proximal Markov Chain Monte Carlo: When Langevin Meets Moreau

- Computer Science, Mathematics
- SIAM J. Imaging Sci.
- 2018

A new and highly efficient Markov chain Monte Carlo methodology to perform Bayesian computation for high-dimensional models that are log-concave and nonsmooth, a class of models that is central in imaging sciences. Expand

Scalable Bayesian Uncertainty Quantification in Imaging Inverse Problems via Convex Optimization

- Computer Science, Mathematics
- SIAM J. Imaging Sci.
- 2019

A main feature of this work is to leverage probability concentration phenomena and the underlying convex geometry to formulate the Bayesian hypothesis test as a convex problem, that is then efficiently solve by using scalable optimization algorithms. Expand

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

- Physics
- 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… Expand

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

- Physics
- 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… Expand

Bayesian Methods in Cosmology

- Physics, Mathematics
- 2017

These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide… Expand

Hierarchical cosmic shear power spectrum inference

- Physics
- 2016

We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear eld and its (tomographic) power… Expand

Mining weak lensing surveys

- Physics
- 2003

Abstract We present a survey of the cosmological applications of the next generation of weak lensing surveys, paying special attention to the computational challenges presented by the number of… Expand