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Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations

Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations
Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations
Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.
0035-8711
3236-3250
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
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

Price, Matthew A., McEwen, Jason D., Cai, Xiaohao and Kitching, Thomas D. (2019) Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations. Monthly Notices of the Royal Astronomical Society, 489 (3), 3236-3250. (doi:10.1093/mnras/stz2373).

Record type: Article

Abstract

Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.

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More information

Accepted/In Press date: 23 August 2019
e-pub ahead of print date: 26 August 2019
Published date: November 2019

Identifiers

Local EPrints ID: 438781
URI: http://eprints.soton.ac.uk/id/eprint/438781
ISSN: 0035-8711
PURE UUID: c7fe2b97-ae57-4b35-89aa-61998fdcdb1b

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Date deposited: 24 Mar 2020 17:30
Last modified: 06 Oct 2020 18:43

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Contributors

Author: Matthew A. Price
Author: Jason D. McEwen
Author: Xiaohao Cai
Author: Thomas D. Kitching

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