Hierarchical Cosmic Shear Power Spectrum Inference

Abstract

We develop a Bayesian hierarchical modelling approach for cosmic shear power spectrum inference, jointly sampling from the posterior distribution of the cosmic shear field and its (tomographic) power spectra. Inference of the shear power spectrum is a powerful intermediate product for a cosmic shear analysis, since it requires very few model assumptions and can be used to perform inference on a wide range of cosmological models \emph{a posteriori} without loss of information. We show that joint posterior for the shear map and power spectrum can be sampled effectively by Gibbs sampling, iteratively drawing samples from the map and power spectrum, each conditional on the other. This approach neatly circumvents difficulties associated with complicated survey geometry and masks that plague frequentist power spectrum estimators, since the power spectrum inference provides prior information about the field in masked regions at every sampling step. We demonstrate this approach for inference of tomographic shear $E$-mode, $B$-mode and $EB$-cross power spectra from a simulated galaxy shear catalogue with a number of important features; galaxies distributed on the sky and in redshift with photometric redshift uncertainties, realistic random ellipticity noise for every galaxy and a complicated survey mask. The obtained posterior distributions for the tomographic power spectrum coefficients recover the underlying simulated power spectra for both $E$- and $B$-modes.

16 pages, 8 figures, accepted by MNRAS

References in corpus (11)

• Cosmology with Weak Lensing Surveys
• Galaxy alignments: An overview
• Galaxy alignments: Observations and impact on cosmology
• Galaxy alignments: Theory, modelling and simulations
• Bayesian reconstruction of the cosmological large-scale structure: methodology, inverse algorithms and numerical optimization
• Measuring dark energy properties with 3D cosmic shear
• Cosmological constraints from COMBO-17 using 3D weak lensing
• Estimation of Polarized Power Spectra by Gibbs sampling
• Efficient Wiener filtering without preconditioning
• Hierarchical probabilistic inference of cosmic shear
• Bayesian Inference of Polarized CMB Power Spectra from Interferometric Data

Cited by in corpus (62)

• KiDS-450: Cosmological parameter constraints from tomographic weak gravitational lensing
• A unified pseudo-$C_{\ell }$ framework
• Weak lensing for precision cosmology
• Fast likelihood-free cosmology with neural density estimators and active learning
• Likelihood-free inference with neural compression of DES SV weak lensing map statistics
• The Limits of Cosmic Shear
• Bayesian optimisation for likelihood-free cosmological inference
• The Type Ia Supernova Color-Magnitude Relation and Host Galaxy Dust: A Simple Hierarchical Bayesian Model
• Cosmological parameters, shear maps and power spectra from CFHTLenS using Bayesian hierarchical inference
• Hierarchical Bayesian inference of galaxy redshift distributions from photometric surveys
• Lifting weak lensing degeneracies with a field-based likelihood
• Improving Weak Lensing Mass Map Reconstructions using Gaussian and Sparsity Priors: Application to DES SV
• 2dFLenS and KiDS: Determining source redshift distributions with cross-correlations
• The skewed weak lensing likelihood: why biases arise, despite data and theory being sound
• Consistent cosmic shear in the face of systematics: a B-mode analysis of KiDS-450, DES-SV and CFHTLenS
• Bayesian forward modelling of cosmic shear data
• A direct measurement of tomographic lensing power spectra from CFHTLenS
• Cosmic Shear: Inference from Forward Models
• Probabilistic Mass Mapping with Neural Score Estimation
• Flat-Sky Pseudo-Cls Analysis for Weak Gravitational Lensing
• Spherical Bayesian mass-mapping with uncertainties: full sky observations on the celestial sphere
• Parameter Inference for Weak Lensing using Gaussian Processes and MOPED
• Efficient Optimal Reconstruction of Linear Fields and Band-powers from Cosmological Data
• Weak lensing mass reconstruction using sparsity and a Gaussian random field
• Bayesian weak lensing tomography: Reconstructing the 3D large-scale distribution of matter with a lognormal prior
• KaRMMa -- Kappa Reconstruction for Mass Mapping
• Sparse Bayesian mass-mapping with uncertainties: local credible intervals
• Wiener filter reloaded: fast signal reconstruction without preconditioning
• Wiener filtering and pure E/B decomposition of CMB maps with anisotropic correlated noise
• Hierarchical inference of the relationship between Concentration and Mass in Galaxy Groups and Clusters
• The effect of detector nonlinearity on WFIRST PSF profiles for weak gravitational lensing measurements
• Designing and testing inflationary models with Bayesian networks
• Cluster mass profile reconstruction with size and flux magnification on the HST STAGES survey
• Bayesian power-spectrum inference with foreground and target contamination treatment
• Almanac: Weak Lensing power spectra and map inference on the masked sphere
• Mapping dark matter on the celestial sphere with weak gravitational lensing
• 3D cosmic shear: numerical challenges, 3D lensing random fields generation and Minkowski Functionals for cosmological inference
• Weak-lensing shear estimates with general adaptive moments, and studies of bias by pixellation, PSF distortions, and noise
• Sparse Bayesian mass-mapping with uncertainties: peak statistics and feature locations
• Fast Sampling from Wiener Posteriors for Image Data with Dataflow Engines
• Simulation-Based Inference Benchmark for Weak Lensing Cosmology
• Cosmological Parameters from CMB Maps without Likelihood Approximation
• Optimal and fast E/B separation with a dual messenger field
• Cosmic Microwave Background Mapmaking with a Messenger Field
• Euclid preparation. LIX. Angular power spectra from discrete observations
• Estimation of Full Sky Power Spectrum between Intermediate to Large Angular Scales from Partial Sky CMB Anisotropies using Artificial Neural Network
• An Unbiased Estimator of the Full-sky CMB Angular Power Spectrum at Large Scales using Neural Networks
• Almanac: MCMC-based signal extraction of power spectra and maps on the sphere
• Perturbative Gaussianizing transforms for cosmological fields
• Probabilistic Cosmological Mass Mapping from Weak Lensing Shear
• Preconditioner-free Wiener filtering with a dense noise matrix
• Accurate Kappa Reconstruction Algorithm for masked shear catalog (AKRA)
• Enhancing CMB map reconstruction and power spectrum estimation with convolutional neural networks
• A probabilistic framework for cosmological inference of peculiar velocities
• AKRA 2.0: Accurate Kappa Reconstruction Algorithm for masked shear catalog
• MADLens, a python package for fast and differentiable non-Gaussian lensing simulations
• Sparse Bayesian mass-mapping using trans-dimensional MCMC
• Probabilistic Mapping of Dark Matter by Neural Score Matching
• Fisher matrix for the angular power spectrum of multi-tracer galaxy surveys
• Sparse Bayesian mass-mapping with uncertainties: hypothesis testing of structure
• Diagnosing Systematic Effects Using the Inferred Initial Power Spectrum
• Generative modeling of convergence maps based on predicted one-point statistics