Title: Sparse Bayesian mass mapping with uncertainties: local credible intervals

Abstract

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 (never underestimate the uncertainty, yet the approximation error is bounded above), of similar magnitude and highly correlated 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.

Authors:

Price, M. A. ^[1]; Cai, X. ^[1]; McEwen, J. D. ^[1]; Pereyra, M. ^[2]; Kitching, T. D. ^[1]; LSST Dark Energy Science Collaboration

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+ Show Author Affiliations

1. Mullard Space Science Laboratory, University College London, Holmbury Hill Rd, Dorking RH5 6NT, UK
2. Maxwell Institute for Mathematical Sciences, Heriot-Watt University, Edinburgh EH14 4AS, UK

Publication Date:

2019-12-10

Sponsoring Org.:

USDOE

OSTI Identifier:

1581019

Grant/Contract Number:  

AC02-05CH11231; AC02-76SF00515

Resource Type:

Published Article

Journal Name:

Monthly Notices of the Royal Astronomical Society

Additional Journal Information:

Journal Name: Monthly Notices of the Royal Astronomical Society Journal Volume: 492 Journal Issue: 1; Journal ID: ISSN 0035-8711

Publisher:

Oxford University Press

Country of Publication:

United Kingdom

Language:

English