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Sparse Bayesian mass mapping with uncertainties: local credible intervals

Sparse Bayesian mass mapping with uncertainties: local credible intervals
Sparse Bayesian mass mapping with uncertainties: local credible intervals
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.
Gravitational lensing: weak, Methods: data analysis, Methods: statistical, Techniques: image processing
0035-8711
394-404
Price, Matthew A.
4b9aaa38-54ba-436f-88da-bcf25c6375ea
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175
Pereyra, Marcelo
7ae249d9-94ea-4f67-a3ec-e2907665952e
Kitching, Thomas D.
ee37aa25-546f-4d80-bb83-495a4525da6d
Price, Matthew A.
4b9aaa38-54ba-436f-88da-bcf25c6375ea
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175
Pereyra, Marcelo
7ae249d9-94ea-4f67-a3ec-e2907665952e
Kitching, Thomas D.
ee37aa25-546f-4d80-bb83-495a4525da6d

Price, Matthew A., Cai, Xiaohao, McEwen, Jason D., Pereyra, Marcelo and Kitching, Thomas D. (2020) Sparse Bayesian mass mapping with uncertainties: local credible intervals. Monthly Notices of the Royal Astronomical Society, 492 (1), 394-404. (doi:10.1093/mnras/stz3453).

Record type: Article

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.

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More information

Accepted/In Press date: 4 December 2019
e-pub ahead of print date: 10 December 2019
Published date: 1 February 2020
Additional Information: Funding Information: This paper has undergone internal review in the LSST Dark Energy Science Collaboration. The internal reviewers were Chihway Chang, Tim Eifler, and Francois Lanusse. The authors thank the development teams of SOPT. MAP is supported by the Science and Technology Facilities Council (STFC). TDK is supported by a Royal Society University Research Fellowship (URF). This work was also supported by the Engineering and Physical Sciences Research Council (EPSRC) through grant EP/M011089/1 and by the Leverhulme Trust. The DESC acknowledges ongoing support Funding Information: from the Institut National de Physique Nucléaire et de Physique des Particules in France; the Science and Technology Facilities Council in the United Kingdom; and the Department of Energy, the National Science Foundation, and the LSST Corporation in the United States. The DESC uses resources of the IN2P3 Computing Center (CC-IN2P3–Lyon/Villeurbanne – France) funded by the Centre National de la Recherche Scientifique; the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231; STFC DiRAC HPC Facilities, funded by UK BIS National E-infrastructure capital grants; and the UK particle physics grid, supported by the GridPP Collaboration. This work was performed in part under DOE Contract DE-AC02-76SF00515. Publisher Copyright: © 2019 The Author(s).
Keywords: Gravitational lensing: weak, Methods: data analysis, Methods: statistical, Techniques: image processing

Identifiers

Local EPrints ID: 438782
URI: http://eprints.soton.ac.uk/id/eprint/438782
ISSN: 0035-8711
PURE UUID: 04ef08d7-282e-42fc-8740-a3a7348c5920
ORCID for Xiaohao Cai: ORCID iD orcid.org/0000-0003-0924-2834

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Date deposited: 24 Mar 2020 17:30
Last modified: 18 Oct 2022 01:58

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Contributors

Author: Matthew A. Price
Author: Xiaohao Cai ORCID iD
Author: Jason D. McEwen
Author: Marcelo Pereyra
Author: Thomas D. Kitching

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