Maximal compression of the redshift space galaxy power spectrum and bispectrum

Abstract

We explore two methods of compressing the redshift space galaxy power spectrum and bispectrum with respect to a chosen set of cosmological parameters. Both methods involve reducing the dimension of the original data-vector ( e.g. 1000 elements ) to the number of cosmological parameters considered ( e.g. seven ) using the Karhunen-Loève algorithm. In the first case, we run MCMC sampling on the compressed data-vector in order to recover the one-dimensional (1D) and two-dimensional (2D) posterior distributions. The second option, approximately 2000 times faster, works by orthogonalising the parameter space through diagonalisation of the Fisher information matrix before the compression, obtaining the posterior distributions without the need of MCMC sampling. Using these methods for future spectroscopic redshift surveys like DESI, EUCLID and PFS would drastically reduce the number of simulations needed to compute accurate covariance matrices with minimal loss of constraining power. We consider a redshift bin of a DESI-like experiment. Using the power spectrum combined with the bispectrum as a data-vector, both compression methods on average recover the 68% credible regions to within 0.7% and 2% of those resulting from standard MCMC sampling respectively. These confidence intervals are also smaller than the ones obtained using only the power spectrum by (81%, 80%, 82%) respectively for the bias parameter b_1, the growth rate f and the scalar amplitude parameter A_s.

arXiv comment27 pages, 8 figures, 1 table, Accepted 2018 January 28. Received 2018 January 25; in original form 2017 September 11. Added clarifications in the text on the bias modelling and compression limits following referee's comments. Removed tetraspectrum term from the pk-bk cross covariance + correction in the appendix

References in corpus (66)

• emcee: The MCMC Hammer
• Planck 2015 results. XIII. Cosmological parameters
• Planck 2013 results. XVI. Cosmological parameters
• Efficient Computation of CMB anisotropies in closed FRW models
• SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way Galaxy, and Extra-Solar Planetary Systems
• Large-Scale Structure of the Universe and Cosmological Perturbation Theory
• The DESI Experiment Part I: Science,Targeting, and Survey Design
• The Large Scale Bias of Dark Matter Halos: Numerical Calibration and Model Tests
• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Euclid Definition Study Report
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Cosmic Growth History and Expansion History
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Biasing and Hierarchical Statistics in Large-scale Structure
• Baryon Acoustic Oscillations in 2D: Modeling Redshift-space Power Spectrum from Perturbation Theory
• Clustering of dark matter tracers: generalizing bias for the coming era of precision LSS
• The DESI Experiment, a whitepaper for Snowmass 2013
• Stochastic Nonlinear Galaxy Biasing
• Large-scale structure, the cosmic microwave background, and primordial non-gaussianity
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: RSD measurement from the power spectrum and bispectrum of the DR12 BOSS galaxies
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release
• Non-Linear Evolution of the Bispectrum of Cosmological Perturbations
• Gravity and Large-Scale Non-local Bias
• The Bispectrum as a Signature of Gravitational Instability in Redshift-Space
• Massive Lossless Data Compression and Multiple Parameter Estimation from Galaxy Spectra
• Cosmology and the Bispectrum
• Evidence for Quadratic Tidal Tensor Bias from the Halo Bispectrum
• Second Order Power Spectrum and Nonlinear Evolution at High Redshift
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure
• Large-scale bias in the Universe: bispectrum method
• The MICE Grand Challenge Lightcone Simulation II: Halo and Galaxy catalogues
• The Bispectrum: From Theory to Observations
• Skewness and Kurtosis in Large-Scale Cosmic Fields
• The nonlinear redshift-space power spectrum of galaxies
• The large-scale 3-point correlation function of the SDSS BOSS DR12 CMASS galaxies
• Non-local Lagrangian bias
• Signature of Primordial Non-Gaussianity on Matter Power Spectrum
• Estimating Cosmological Parameter Covariance
• Galaxy bispectrum, primordial non-Gaussianity and redshift space distortions
• Large-scale bias in the Universe II: redshift space bispectrum
• Near optimal bispectrum estimators for large-scale structure
• The Local Bias Model in the Large Scale Halo Distribution
• Massive data compression for parameter-dependent covariance matrices
• Halo bias in Lagrangian Space: Estimators and theoretical predictions
• Perturbative approach to covariance matrix of the matter power spectrum
• Testing Gravity Using Large-Scale Redshift-Space Distortions
• Information Content of the Angular Multipoles of Redshift-Space Galaxy Bispectrum
• Rapid Separable Analysis of Higher Order Correlators in Large Scale Structure
• Precision cosmology with redshift-space bispectrum: a perturbation theory based model at one-loop order
• Matter bispectrum of large-scale structure: Three-dimensional comparison between theoretical models and numerical simulations
• Towards optimal cosmological parameter recovery from compressed bispectrum statistics
• Relativistic wide-angle galaxy bispectrum on the light-cone
• Fast Estimation of Gravitational and Primordial Bispectra in Large Scale Structures
• Cosmology with anisotropic galaxy clustering from the combination of power spectrum and bispectrum
• A Prescription for Galaxy Biasing Evolution as a Nuisance Parameter
• Bispectrum covariance in the flat-sky limit
• Universal Non-Gaussian Initial Conditions for N-body Simulations
• A fitting formula for the non-Gaussian contribution to the lensing power spectrum covariance
• Three-Point Correlations in f(R) Models of Gravity
• Non-local bias contribution to third-order galaxy correlations
• Gaussianisation for fast and accurate inference from cosmological data
• Cosmological Large-scale Structures beyond Linear Theory in Modified Gravity
• Extreme data compression for the CMB
• Skewness as a probe of Baryon Acoustic Oscillations

Cited by in corpus (38)

• Weak lensing for precision cosmology
• Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology
• The galaxy power spectrum take on spatial curvature and cosmic concordance
• Cosmological information in the redshift-space bispectrum
• The High Latitude Spectroscopic Survey on the Nancy Grace Roman Space Telescope
• Constraining $M_{\nu }$ with the Bispectrum II: The Total Information Content of the Galaxy Bispectrum
• Generalized massive optimal data compression
• Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space
• Fewer Mocks and Less Noise: Reducing the Dimensionality of Cosmological Observables with Subspace Projections
• Dark Energy Survey Year 3 results: cosmology with moments of weak lensing mass maps -- validation on simulations
• Galaxy redshift-space bispectrum: the Importance of Being Anisotropic
• Toward a robust inference method for the galaxy bispectrum: likelihood function and model selection
• Cosmological parameters from the likelihood analysis of the galaxy power spectrum and bispectrum in real space
• Cosmology Without Window Functions: Cubic Estimators for the Galaxy Bispectrum
• Enhancing BOSS bispectrum cosmological constraints with maximal compression
• Matter trispectrum: theoretical modelling and comparison to N-body simulations
• ENCORE: An $\mathcal{O}(N_{\mathrm{g}}^2)$ Estimator for Galaxy $N$-Point Correlation Functions
• Quijote-PNG: Simulations of primordial non-Gaussianity and the information content of the matter field power spectrum and bispectrum
• The Covariance of Squeezed Bispectrum Configurations
• Geometrical compression: a new method to enhance the BOSS galaxy bispectrum monopole constraints
• Beyond two-point statistics: using the minimum spanning tree as a tool for cosmology
• Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data
• Quijote-PNG: Quasi-maximum likelihood estimation of Primordial Non-Gaussianity in the non-linear dark matter density field
• Modal compression of the redshift-space galaxy bispectrum
• Towards cosmological constraints from the compressed modal bispectrum: a robust comparison of real-space bispectrum estimators
• Extreme data compression while searching for new physics
• Testing the consistency of three-point halo clustering in Fourier and configuration space
• GEOMAX: beyond linear compression for 3pt galaxy clustering statistics
• On the Fast Random Sampling and Other Properties of the Three Point Correlation Function in Galaxy Surveys
• Constraining the growth rate of structure with phase correlations
• A Model for the Redshift-Space Galaxy 4-Point Correlation Function
• Data Compression and Covariance Matrix Inspection: Cosmic Shear
• Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements
• Projected two- and three-point statistics: Forecasts and mitigation of non-linear RSDs
• Speeding up the detectability of the harmonic-space galaxy bispectrum
• New tests of dark sector interactions from the full-shape galaxy power spectrum
• Quijote PNG: The information content of the halo power spectrum and bispectrum
• Dark Energy Survey Year 3 results: Cosmology with peaks using an emulator approach