GEOMAX: beyond linear compression for 3pt galaxy clustering statistics

Abstract

We present the GEOMAX algorithm and its Python implementation for a two-step compression of bispectrum measurements. The first step groups bispectra by the geometric properties of their arguments; the second step then maximises the Fisher information with respect to a chosen set of model parameters in each group. The algorithm only requires the derivatives of the data vector with respect to the parameters and a small number of mock data, producing an effective, non-linear compression. By applying GEOMAX to bispectrum monopole measurements from BOSS DR12 CMASS redshift-space galaxy clustering data, we reduce the $68\%$ credible intervals for the inferred parameters $\left(b_1,b_2,f,{\sigma }_8\right)$ by $\left(50.4\%,56.1\%,33.2\%,38.3\%\right)$ with respect to standard MCMC on the full data vector. We run the analysis and comparison between compression methods over one hundred galaxy mocks to test the statistical significance of the improvements. On average GEOMAX performs $\sim 15\%$ better than geometrical or maximal linear compression alone and is consistent with being lossless. Given its flexibility, the GEOMAX approach has the potential to optimally exploit three-point statistics of various cosmological probes like weak lensing or line-intensity maps from current and future cosmological data-sets such as DESI, Euclid, PFS and SKA.

arXiv comment17 pages, 9 figures, accepted version by MNRAS

References in corpus (60)

• emcee: The MCMC Hammer
• The NumPy array: a structure for efficient numerical computation
• SDSS-III: Massive Spectroscopic Surveys of the Distant Universe, the Milky Way Galaxy, and Extra-Solar Planetary Systems
• The Baryon Oscillation Spectroscopic Survey of SDSS-III
• Non-Gaussianity from Inflation: Theory and Observations
• Karhunen-Loeve eigenvalue problems in cosmology: how should we tackle large data sets?
• Why your model parameter confidences might be too optimistic -- unbiased estimation of the inverse covariance matrix
• Extragalactic Science, Cosmology and Galactic Archaeology with the Subaru Prime Focus Spectrograph (PFS)
• The Cosmological Analysis of the SDSS/BOSS data from the Effective Field Theory of Large-Scale Structure
• Cosmological parameters from lensing power spectrum and bispectrum tomography
• 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
• Large-scale structure, the cosmic microwave background, and primordial non-gaussianity
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: mock galaxy catalogues for the BOSS Final Data Release
• Massive Lossless Data Compression and Multiple Parameter Estimation from Galaxy Spectra
• The power spectrum and bispectrum of SDSS DR11 BOSS galaxies I: bias and gravity
• Fast likelihood-free cosmology with neural density estimators and active learning
• Probing Primordial Non-Gaussianity with Large-Scale Structure
• Large-scale Bias and Efficient Generation of Initial Conditions for Non-Local Primordial Non-Gaussianity
• Review of local non-Gaussianity from multi-field inflation
• Massive optimal data compression and density estimation for scalable, likelihood-free inference in cosmology
• Primordial non-Gaussianity, scale-dependent bias, and the bispectrum of galaxies
• Constraining Primordial non-Gaussianity with Bispectrum and Power Spectum from Upcoming Optical and Radio Surveys
• Constraining $M_{\nu }$ with the Bispectrum I: Breaking Parameter Degeneracies
• Detection of Baryon Acoustic Oscillation Features in the Large-Scale 3-Point Correlation Function of SDSS BOSS DR12 CMASS Galaxies
• Cosmological information in the redshift-space bispectrum
• Information content of weak lensing power spectrum and bispectrum: including the non-Gaussian error covariance matrix
• Automatic physical inference with information maximising neural networks
• The large-scale 3-point correlation function of the SDSS BOSS DR12 CMASS galaxies
• Generalized massive optimal data compression
• An improved fitting formula for the dark matter bispectrum
• 1-loop Perturbative Corrections to the Matter and Galaxy Bispectrum with non-Gaussian Initial Conditions
• The Galaxy Power Spectrum and Bispectrum in Redshift Space
• Cosmological parameters from combined second- and third-order aperture mass statistics of cosmic shear
• A complete FFT-based decomposition formalism for the redshift-space bispectrum
• Estimating Cosmological Parameter Covariance
• Bias Loop Corrections to the Galaxy Bispectrum
• Comparing approximate methods for mock catalogues and covariance matrices III: Bispectrum
• A Detection of the Baryon Acoustic Oscillation Features in the SDSS BOSS DR12 Galaxy Bispectrum
• The 21cm bispectrum as a probe of non-Gaussianities due to X-ray heating
• Constraining Neutrino Mass with the Tomographic Weak Lensing Bispectrum
• DEMNUni: Massive neutrinos and the bispectrum of large scale structures
• Toward a robust inference method for the galaxy bispectrum: likelihood function and model selection
• Maximal compression of the redshift space galaxy power spectrum and bispectrum
• The Halo Bispectrum in N-body Simulations with non-Gaussian Initial Conditions
• Enhancing BOSS bispectrum cosmological constraints with maximal compression
• Precision cosmology with redshift-space bispectrum: a perturbation theory based model at one-loop order
• The one-loop matter bispectrum as a probe of gravity and dark energy
• Relativistic wide-angle galaxy bispectrum on the light-cone
• The dipole of the galaxy bispectrum
• The Full-Sky Angular Bispectrum in Redshift Space
• Geometrical compression: a new method to enhance the BOSS galaxy bispectrum monopole constraints
• The squeezed matter bispectrum covariance with responses
• Graph Database Solution for Higher Order Spatial Statistics in the Era of Big Data
• Extracting bias using the cross-bispectrum: An EoR and 21 cm-[CII]-[CII] case study
• Signatures of Cosmic Reionization on the 21cm 2- and 3-point Correlation Function I: Quadratic Bias Modeling
• Relativistic cosmological large scale structures at one-loop
• Bispectrum as Baryon Acoustic Oscillation Interferometer
• Higher multipoles of the galaxy bispectrum in redshift space
• An analytic halo approach to the bispectrum of galaxies in redshift space
• The gravitational and lensing-ISW bispectrum of 21cm radiation

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• Matter trispectrum: theoretical modelling and comparison to N-body simulations
• The Covariance of Squeezed Bispectrum Configurations
• The Halo Bispectrum Multipoles in Redshift Space
• Modal compression of the redshift-space galaxy bispectrum
• Integrated trispectrum detection from BOSS DR12 NGC CMASS
• Towards cosmological constraints from the compressed modal bispectrum: a robust comparison of real-space bispectrum estimators
• The halo 3-point correlation function: a methodological analysis
• GEO-FPT: a model of the galaxy bispectrum at mildly non-linear scales
• Updated neutrino mass constraints from galaxy clustering and CMB lensing-galaxy cross-correlation measurements
• Speeding up the detectability of the harmonic-space galaxy bispectrum