arXiv subjects

Matthew A. Price

Publications and source records attributed to Matthew A. Price.

22 records · Page 2Linked to original sources

arXiv2021

Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere

To date weak gravitational lensing surveys have typically been restricted to small fields of view, such that the $\textit{flat-sky approximation}$ has been sufficiently satisfied. However, with Stage IV surveys ($\textit{e.g. LSST}$ and $\textit{Euclid}$) imminent, extending mass-mapping techniques to the sphere is a fundamental necessity. As such, we extend the sparse hierarchical Bayesian mass-mapping formalism presented in previous work to the spherical sky. For the first time, this allows us to construct $\textit{maximum a posteriori}$ spherical weak lensing dark-matter mass-maps, with principled Bayesian uncertainties, without imposing or assuming Gaussianty. We solve the spherical mass-mapping inverse problem in the analysis setting adopting a sparsity promoting Laplace-type wavelet prior, though this theoretical framework supports all log-concave posteriors. Our spherical mass-mapping formalism facilitates principled statistical interpretation of reconstructions. We apply our framework to convergence reconstruction on high resolution N-body simulations with pseudo-Euclid masking, polluted with a variety of realistic noise levels, and show a significant increase in reconstruction fidelity compared to standard approaches. Furthermore we perform the largest joint reconstruction to date of the majority of publicly available shear observational datasets (combining DESY1, KiDS450 and CFHTLens) and find that our formalism recovers a convergence map with significantly enhanced small-scale detail. Within our Bayesian framework we validate, in a statistically rigorous manner, the community's intuition regarding the need to smooth spherical Kaiser-Squires estimates to provide physically meaningful convergence maps. Such approaches cannot reveal the small-scale physical structures that we recover within our framework.

astro-ph.CO↗

arXiv2021

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.

astro-ph.CO↗

arXiv2021

Sparse Bayesian mass-mapping with uncertainties: local credible intervals

Until recently mass-mapping techniques for weak gravitational lensing convergence reconstruction have lacked a principled statistical framework upon which to quantify reconstruction uncertainties, without making strong assumptions of Gaussianity. In previous work we presented a sparse hierarchical Bayesian formalism for convergence reconstruction that addresses this shortcoming. Here, we 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 Markov Chain Monte Carlo (MCMC) algorithm. We find that typically our recovered uncertainties are everywhere conservative, of similar magnitude and highly correlated (Pearson correlation coefficient $\geq 0.85$) with those recovered via Px-MALA. Moreover, we demonstrate an increase in computational efficiency of $\mathcal{O}(10^6)$ when using our 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.

astro-ph.CO↗

arXiv2020

Scale-discretised ridgelet transform on the sphere

We revisit the spherical Radon transform, also called the Funk-Radon transform, viewing it as an axisymmetric convolution on the sphere. Viewing the spherical Radon transform in this manner leads to a straightforward derivation of its spherical harmonic representation, from which we show the spherical Radon transform can be inverted exactly for signals exhibiting antipodal symmetry. We then construct a spherical ridgelet transform by composing the spherical Radon and scale-discretised wavelet transforms on the sphere. The resulting spherical ridgelet transform also admits exact inversion for antipodal signals. The restriction to antipodal signals is expected since the spherical Radon and ridgelet transforms themselves result in signals that exhibit antipodal symmetry. Our ridgelet transform is defined natively on the sphere, probes signal content globally along great circles, does not exhibit blocking artefacts, supports spin signals and exhibits an exact and explicit inverse transform. No alternative ridgelet construction on the sphere satisfies all of these properties. Our implementation of the spherical Radon and ridgelet transforms is made publicly available. Finally, we illustrate the effectiveness of spherical ridgelets for diffusion magnetic resonance imaging of white matter fibers in the brain.

cs.IT↗