The University of Southampton
University of Southampton Institutional Repository

Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure: hypothesis testing of structure

Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure: hypothesis testing of structure
Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure: hypothesis testing of structure

A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous 'dark core' - an overdense region with no optical counterpart - which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at 99 per cent confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

dark matter, gravitational lensing: weak, methods: data analysis, methods: statistical, techniques: image processing
0035-8711
3678-3690
Price, Matthew A
19d29708-961e-4104-81c4-8d37cdd2683e
McEwen, Jason D
6346d637-52cd-4533-a411-bd657d45ccc2
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Kitching, Thomas D
8ae1e9c5-5c49-42e6-bd23-bdb1b10f5656
Wallis, Christopher GR
4425567a-9485-493f-b8db-0a77045d40cb
LSST Dark Energy Science Collaboration
Price, Matthew A
19d29708-961e-4104-81c4-8d37cdd2683e
McEwen, Jason D
6346d637-52cd-4533-a411-bd657d45ccc2
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Kitching, Thomas D
8ae1e9c5-5c49-42e6-bd23-bdb1b10f5656
Wallis, Christopher GR
4425567a-9485-493f-b8db-0a77045d40cb

LSST Dark Energy Science Collaboration (2021) Sparse Bayesian mass mapping with uncertainties: hypothesis testing of structure: hypothesis testing of structure. Monthly Notices of the Royal Astronomical Society, 506 (3), 3678-3690. (doi:10.1093/mnras/stab1983).

Record type: Article

Abstract

A crucial aspect of mass mapping, via weak lensing, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. We present a new method to reconstruct maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type l1-norm sparsity-promoting priors, which we solve via convex optimization. Approaching mass mapping in this manner allows us to exploit recent developments in probability concentration theory to infer theoretically conservative uncertainties for our MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow us to perform hypothesis testing of structure, from which it is possible to distinguish between physical objects and artefacts of the reconstruction. Here, we present this new formalism, and demonstrate the method on simulations, before applying the developed formalism to two observational data sets of the Abell 520 cluster. Initial reconstructions of the Abell 520 catalogues reported the detection of an anomalous 'dark core' - an overdense region with no optical counterpart - which was taken to be evidence for self-interacting dark matter. In our Bayesian framework, it is found that neither Abell 520 data set can conclusively determine the physicality of such dark cores at 99 per cent confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

Text
1812.04014v1 - Author's Original
Restricted to Repository staff only
Request a copy
Text
stab1983 - Version of Record
Available under License Other.
Download (3MB)

More information

Accepted/In Press date: 6 July 2021
e-pub ahead of print date: 12 July 2021
Published date: September 2021
Keywords: dark matter, gravitational lensing: weak, methods: data analysis, methods: statistical, techniques: image processing

Identifiers

Local EPrints ID: 438769
URI: http://eprints.soton.ac.uk/id/eprint/438769
ISSN: 0035-8711
PURE UUID: 2bb67de4-4483-42e5-9231-33c873bf0713
ORCID for Xiaohao Cai: ORCID iD orcid.org/0000-0003-0924-2834

Catalogue record

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

Export record

Altmetrics

Contributors

Author: Matthew A Price
Author: Jason D McEwen
Author: Xiaohao Cai ORCID iD
Author: Thomas D Kitching
Author: Christopher GR Wallis
Corporate Author: LSST Dark Energy Science Collaboration

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×