Sparse Bayesian mass-mapping with uncertainties: local credible intervals

Abstract

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 uncertainty quantification techniques previously detailed. These uncertainty quantification techniques are benchmarked against those recovered via Px-MALA - a state of the art proximal Markov Chain Monte Carlo (MCMC) algorithm. We find that typically our recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient $\ge 0.85$) with those recovered via Px-MALA. Moreover, we demonstrate an increase in computational efficiency of $\mathcal{O}(10^6)$ when using our sparse Bayesian approach over MCMC techniques. This computational saving is critical for the application of Bayesian uncertainty quantification to large-scale stage IV surveys such as LSST and Euclid.

References in corpus (25)

• HEALPix -- a Framework for High Resolution Discretization, and Fast Analysis of Data Distributed on the Sphere
• Weak Gravitational Lensing
• Halos and galaxies in the standard cosmological model: results from the Bolshoi simulation
• Cosmology with Weak Lensing Surveys
• Sparsity Averaging Reweighted Analysis (SARA): a novel algorithm for radio-interferometric imaging
• Dark Energy Survey Year 1 Results: Curved-Sky Weak Lensing Mass Map
• Characterizing the non-linear growth of large-scale structure in the Universe
• Uncertainty quantification for radio interferometric imaging: I. proximal MCMC methods
• Hierarchical Cosmic Shear Power Spectrum Inference
• FASTLens (FAst STatistics for weak Lensing) : Fast method for Weak Lensing Statistics and map making
• Mining Weak Lensing Surveys
• High Resolution Weak Lensing Mass-Mapping Combining Shear and Flexion
• Improving Weak Lensing Mass Map Reconstructions using Gaussian and Sparsity Priors: Application to DES SV
• Uncertainty quantification for radio interferometric imaging: II. MAP estimation
• Testing the Cosmic Shear Spatially-Flat Universe Approximation with Generalized Lensing and Shear Spectra
• Bayesian Methods in Cosmology
• Efficient Optimal Reconstruction of Linear Fields and Band-powers from Cosmological Data
• 3D Reconstruction of the Density Field: An SVD Approach to Weak Lensing Tomography
• Weak lensing: Dark Matter, Dark Energy and Dark Gravity
• The Integrated Bispectrum and Beyond
• Sparse reconstruction of the merging A520 cluster system
• PRISM: Sparse Recovery of the Primordial Power Spectrum
• Mapping dark matter on the celestial sphere with weak gravitational lensing
• Efficient Bayesian computation by proximal Markov chain Monte Carlo: when Langevin meets Moreau
• Scalable Bayesian uncertainty quantification in imaging inverse problems via convex optimization

Cited by in corpus (16)

• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• Dark Energy Survey Year 3 results: curved-sky weak lensing mass map reconstruction
• Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere
• Weak lensing mass reconstruction using sparsity and a Gaussian random field
• Higher order statistics of shear field: a machine learning approach
• Mapping dark matter on the celestial sphere with weak gravitational lensing
• Langevin Monte Carlo without smoothness
• Posterior sampling for inverse imaging problems on the sphere in seismology and cosmology
• Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
• Uncertainty-Aware Blob Detection with an Application to Integrated-Light Stellar Population Recoveries
• Generative modelling for mass-mapping with fast uncertainty quantification
• Three-Dimensional Reconstruction of Weak Lensing Mass Maps with a Sparsity Prior. I. Cluster Detection
• Distribution-free uncertainty quantification for inverse problems: application to weak lensing mass mapping
• Sparse Bayesian mass-mapping using trans-dimensional MCMC
• Probabilistic Mapping of Dark Matter by Neural Score Matching
• Bayesian variational regularization on the ball