Sparsity and the Bayesian Perspective

Abstract

Sparsity has been recently introduced in cosmology for weak-lensing and CMB data analysis for different applications such as denoising, component separation or inpainting (i.e. filling the missing data or the mask). Although it gives very nice numerical results, CMB sparse inpainting has been severely criticized by top researchers in cosmology, based on arguments derived from a Bayesian perspective. Trying to understand their point of view, we realize that interpreting a regularization penalty term as a prior in a Bayesian framework can lead to erroneous conclusions. This paper is by no means against the Bayesian approach, which has proven to be very useful for many applications, but warns about a Bayesian-only interpretation in data analysis, which can be misleading in some cases.

Accepted in A&A

References in corpus (5)

• Bayes in the sky: Bayesian inference and model selection in cosmology
• CMB data analysis and sparsity
• Bayesian component separation and CMB estimation for the 5-year WMAP temperature data
• Low-l CMB Analysis and Inpainting
• Local non-Gaussianity in the Cosmic Microwave Background the Bayesian way

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• WMAP 9-year CMB estimation using sparsity
• Semi-blind Bayesian inference of CMB map and power spectrum
• Bayesian $l_0$-regularized Least Squares
• Dealing with missing data: An inpainting application to the MICROSCOPE space mission
• Sparse point-source removal for full-sky CMB experiments: application to WMAP 9-year data
• Sparse Inpainting and Isotropy
• Sparse Isotropic Regularization for Spherical Harmonic Representations of Random Fields on the Sphere
• Solar multi-object multi-frame blind deconvolution with a spatially variant convolution neural emulator
• Distribution-free uncertainty quantification for inverse problems: application to weak lensing mass mapping
• Re-examining the Bayesian colour excess estimation for the local star-forming galaxies observed in the HETDEX Pilot Survey
• A plug-and-play approach with fast uncertainty quantification for weak lensing mass mapping