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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:
 [1];  [1];  [1];  [2];  [1];
  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:
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

Citation Formats

Price, M. A., Cai, X., McEwen, J. D., Pereyra, M., Kitching, T. D., and LSST Dark Energy Science Collaboration. Sparse Bayesian mass mapping with uncertainties: local credible intervals. United Kingdom: N. p., 2019. Web. doi:10.1093/mnras/stz3453.
Price, M. A., Cai, X., McEwen, J. D., Pereyra, M., Kitching, T. D., & LSST Dark Energy Science Collaboration. Sparse Bayesian mass mapping with uncertainties: local credible intervals. United Kingdom. doi:10.1093/mnras/stz3453.
Price, M. A., Cai, X., McEwen, J. D., Pereyra, M., Kitching, T. D., and LSST Dark Energy Science Collaboration. Tue . "Sparse Bayesian mass mapping with uncertainties: local credible intervals". United Kingdom. doi:10.1093/mnras/stz3453.
@article{osti_1581019,
title = {Sparse Bayesian mass mapping with uncertainties: local credible intervals},
author = {Price, M. A. and Cai, X. and McEwen, J. D. and Pereyra, M. and Kitching, T. D. and LSST Dark Energy Science Collaboration},
abstractNote = {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.},
doi = {10.1093/mnras/stz3453},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 1,
volume = 492,
place = {United Kingdom},
year = {2019},
month = {12}
}

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