Sparse Bayesian mass-mapping using trans-dimensional MCMC by Augustin Marignier et al. on Sunday 27 November
Uncertainty quantification is a crucial step of cosmological mass-mapping
that is often ignored. Suggested methods are typically only approximate or make
strong assumptions of Gaussianity of the shear field. Probabilistic sampling
methods, such as Markov chain Monte Carlo (MCMC), draw samples form a
probability distribution, allowing for full and flexible uncertainty
quantification, however these methods are notoriously slow and struggle in the
high-dimensional parameter spaces of imaging problems. In this work we use, for
the first time, a trans-dimensional MCMC sampler for mass-mapping, promoting
sparsity in a wavelet basis. This sampler gradually grows the parameter space
as required by the data, exploiting the extremely sparse nature of mass maps in
wavelet space. The wavelet coefficients are arranged in a tree-like structure,
which adds finer scale detail as the parameter space grows. We demonstrate the
trans-dimensional sampler on galaxy cluster-scale images where the planar
modelling approximation is valid. In high-resolution experiments, this method
produces naturally parsimonious solutions, requiring less than 1% of the
potential maximum number of wavelet coefficients and still producing a good fit
to the observed data. In the presence of noisy data, trans-dimensional MCMC
produces a better reconstruction of mass-maps than the standard smoothed
Kaiser-Squires method, with the addition that uncertainties are fully
quantified. This opens up the possibility for new mass maps and inferences
about the nature of dark matter using the new high-resolution data from
upcoming weak lensing surveys such as Euclid.
arXiv: http://arxiv.org/abs/http://arxiv.org/abs/2211.13963v1
