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

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. Finally, 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.

Authors:
 [1];  [1];  [1];  [1]
  1. Univ. College London (United Kingdom)
Publication Date:
Research Org.:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); Engineering and Physical Sciences Research Council (EPSRC)
OSTI Identifier:
1577801
Alternate Identifier(s):
OSTI ID: 1561394
Grant/Contract Number:  
AC02-05CH11231; AC02-76SF00515; EP/M0110891
Resource Type:
Accepted Manuscript
Journal Name:
Monthly Notices of the Royal Astronomical Society
Additional Journal Information:
Journal Volume: 489; Journal Issue: 3; Journal ID: ISSN 0035-8711
Publisher:
Royal Astronomical Society
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; astronomy & astrophysics; gravitational lensing: weak; methods: statistical; techniques: image processing; cosmological parameters; dark matter

Citation Formats

Price, M. A., McEwen, J. D., Cai, X., and Kitching, T. D. Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations. United States: N. p., 2019. Web. doi:10.1093/mnras/stz2373.
Price, M. A., McEwen, J. D., Cai, X., & Kitching, T. D. Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations. United States. doi:10.1093/mnras/stz2373.
Price, M. A., McEwen, J. D., Cai, X., and Kitching, T. D. Mon . "Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations". United States. doi:10.1093/mnras/stz2373.
@article{osti_1577801,
title = {Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations},
author = {Price, M. A. and McEwen, J. D. and Cai, X. and Kitching, T. D.},
abstractNote = {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. Finally, 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.},
doi = {10.1093/mnras/stz2373},
journal = {Monthly Notices of the Royal Astronomical Society},
number = 3,
volume = 489,
place = {United States},
year = {2019},
month = {8}
}

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