1812.04014
Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
Price, et al
A crucial aspect of mass-mapping, via WL, is quantification of the uncertainty introduced during the reconstruction process. Properly accounting for these errors has been largely ignored to date. 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 is solved via convex optimization. Approaching mass-mapping in this manner allows exploitation of recent developments in probability concentration theory to infer theoretically conservative uncertainties for the MAP reconstructions, without relying on assumptions of Gaussianity. For the first time, these methods allow performing hypothesis testing of structure, from which it is possible to distinguish between physical objects and artifacts of the reconstruction. Present this new formalism, demonstrate the method on illustrative examples, before applying the developed formalism to two observational datasets o f the Abel-520 cluster. In the 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.
1812.04017
Sparse Bayesian mass-mapping with uncertainties: local credible intervals
Price et al.
Until recently mass-mapping techniques for WL convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work, presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, 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 MCMC algorithm. Find that typically the recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient >=0.85) with those recovered via Px-MALA. Moreover, demonstrate an increase in computational efficiency of O(1e6) when using the 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.
1812.04018
Sparse Bayesian mass-mapping with uncertainties: peak statistics and feature locations
Price, et al
WL 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, 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 SNR. 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. Demonstrate the uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.5 (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.
Until recently mass-mapping techniques for WL convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work, presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, 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 MCMC algorithm. Find that typically the recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient >=0.85) with those recovered via Px-MALA. Moreover, demonstrate an increase in computational efficiency of O(1e6) when using the 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.
1812.04018
Sparse Bayesian mass-mapping with uncertainties: peak statistics and feature locations
Price, et al
WL 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, 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 SNR. 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. Demonstrate the uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.5 (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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