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

Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
Sparse Bayesian mass-mapping with uncertainties: 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 results from a new method that reconstructs maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type $\ell_1$-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 artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on illustrative examples, before applying the developed formalism to two observational datasets of the Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of individual local massive substructure at significant confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.
astro-ph.CO
Price, Matthew A.
4b9aaa38-54ba-436f-88da-bcf25c6375ea
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Kitching, Thomas D.
ee37aa25-546f-4d80-bb83-495a4525da6d
Wallis, Christopher G.R.
3e91cdda-348c-426b-9e3b-ad522af106fa
Price, Matthew A.
4b9aaa38-54ba-436f-88da-bcf25c6375ea
McEwen, Jason D.
64c6269a-fe40-41d7-8b0c-d3c9ad920175
Cai, Xiaohao
de483445-45e9-4b21-a4e8-b0427fc72cee
Kitching, Thomas D.
ee37aa25-546f-4d80-bb83-495a4525da6d
Wallis, Christopher G.R.
3e91cdda-348c-426b-9e3b-ad522af106fa

Price, Matthew A., McEwen, Jason D., Cai, Xiaohao, Kitching, Thomas D. and Wallis, Christopher G.R. (2018) Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure. arXiv.

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 results from a new method that reconstructs maximum a posteriori (MAP) convergence maps by formulating an unconstrained Bayesian inference problem with Laplace-type $\ell_1$-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 artifacts of the reconstruction. Here we present this new formalism, demonstrate the method on illustrative examples, before applying the developed formalism to two observational datasets of the Abel-520 cluster. In our Bayesian framework it is found that neither Abel-520 dataset can conclusively determine the physicality of individual local massive substructure at significant confidence. However, in both cases the recovered MAP estimators are consistent with both sets of data.

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1812.04014v1
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Published date: 10 December 2018
Keywords: astro-ph.CO

Identifiers

Local EPrints ID: 438769
URI: http://eprints.soton.ac.uk/id/eprint/438769
PURE UUID: 2bb67de4-4483-42e5-9231-33c873bf0713

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Date deposited: 24 Mar 2020 17:30
Last modified: 24 Aug 2020 16:33

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Contributors

Author: Matthew A. Price
Author: Jason D. McEwen
Author: Xiaohao Cai
Author: Thomas D. Kitching
Author: Christopher G.R. Wallis

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