Sparse Bayesian mass mapping with uncertainties: Local credible intervals

M. A. Price, X. Cai, J. D. McEwen, M. Pereyra, T. D. Kitching

Research output: Contribution to journalArticle

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 O(106) 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.

Original languageEnglish
Pages (from-to)394-404
Number of pages11
JournalMonthly Notices of the Royal Astronomical Society
Volume492
Issue number1
Early online date10 Dec 2019
DOIs
Publication statusPublished - Feb 2020

Keywords

  • Gravitational lensing: weak
  • Methods: data analysis
  • Methods: statistical
  • Techniques: image processing

ASJC Scopus subject areas

  • Astronomy and Astrophysics
  • Space and Planetary Science

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