Indicator Functions: Distilling the Information from Gaussian Random Fields

Abstract

A random Gaussian density field contains a fixed amount of Fisher information on the amplitude of its power spectrum. For a given smoothing scale, however, that information is not evenly distributed throughout the smoothed field. We investigate which parts of the field contain the most information by smoothing and splitting the field into different levels of density (using the formalism of indicator functions), deriving analytic expressions for the information content of each density bin in the joint-probability distribution (given a distance separation). When we choose one particular distance regime (i.e., cells separated by $60$-$80h^{-1}$ Mpc), we find that the information in that range peaks at moderately rare densities (where the number of smoothed survey cells is roughly of order of magnitude 100). Counter-intuitively, we find that, for a finite survey volume (again at a particular distance range), indicator function analysis can outperform conventional two-point statistics while using only a fraction of the total survey cells, and we explain why. In light of recent developments in marked statistics (such as the indicator power spectrum and density-split clustering), this result elucidates how to optimize sampling for effective extraction of cosmological information.

Corrected slight error in Figure 1 (from inadvertently omitting exponent on prefactor 1/A_z^2 [Eqns 39, 41]). 10 pages, 2 figures; published in MNRAS

References in corpus (44)

• The DESI Experiment Part I: Science,Targeting, and Survey Design
• CMB-S4 Science Case, Reference Design, and Project Plan
• How to measure redshift-space distortions without sample variance
• The Wide Field Infrared Survey Telescope: 100 Hubbles for the 2020s
• Rejuvenating the matter power spectrum: restoring information with a logarithmic density mapping
• Line-Intensity Mapping: 2017 Status Report
• The Luminosity-Weighted or `Marked' Correlation Function
• Density split statistics: Cosmological constraints from counts and lensing in cells in DES Y1 and SDSS data
• Using the Marked Power Spectrum to Detect the Signature of Neutrinos in Large-Scale Structure
• Optimal Constraints on Local Primordial Non-Gaussianity from the Two-Point Statistics of Large-Scale Structure
• Luminosity- and morphology-dependent clustering of galaxies
• Density split statistics: joint model of counts and lensing in cells
• A marked correlation function for constraining modified gravity models
• Redshift-space distortions with split densities
• Galaxy and Mass Assembly (GAMA): Redshift Space Distortions from the Clipped Galaxy Field
• Strong clustering of underdense regions and the environmental dependence of clustering from Gaussian initial conditions
• Calibrating CHIME, A New Radio Interferometer to Probe Dark Energy
• Cosmic web dependence of galaxy clustering and quenching in SDSS
• Cosmology without cosmic variance
• Clipping the Cosmos: The Bias and Bispectrum of Large Scale Structure
• Breaking Halo Occupation Degeneracies with Marked Statistics
• Information content in the halo-model dark-matter power spectrum II: Multiple cosmological parameters
• Optimal linear reconstruction of dark matter from halo catalogs
• Unscreening Modified Gravity in the Matter Power Spectrum
• Accurate Analytic Model for the Weak Lensing Convergence One-Point Probability Distribution Function and its Auto-Covariance
• Information Content in the Galaxy Angular Power Spectrum from the Sloan Digital Sky Survey and Its Implication on Weak Lensing Analysis
• Position-dependent correlation function from the SDSS-III Baryon Oscillation Spectroscopic Survey Data Release 10 CMASS Sample
• The environmental dependence of clustering in hierarchical models
• The luminosity dependence of clustering and higher order correlations in the PSCz survey
• Dependence of halo bias on mass and environment
• Optimal non-linear transformations for large scale structure statistics
• The dependence of galaxy clustering on tidal environment in the Sloan Digital Sky Survey
• Clipping the Cosmos II: Cosmological information from non-linear scales
• KiDS-450: Enhancing cosmic shear with clipping transformations
• The large-scale correlations of multi-cell densities and profiles, implications for cosmic variance estimates
• Density-dependent clustering: I. Pulling back the curtains on motions of the BAO peak
• Precision Prediction of the Log Power Spectrum
• It takes two to know one: Computing accurate one-point PDF covariances from effective two-point PDF models
• On the equivalence between the effective cosmology and excursion set treatments of environment
• Beyond Kaiser bias: mildly non-linear two-point statistics of densities in distant spheres
• On the total cosmological information in galaxy clustering: an analytical approach
• The Variance and Covariance of Counts-in-Cells Probabilities
• Covariances of density probability distribution functions. Lessons from hierarchical models
• Baryon Acoustic Oscillations analyses with Density-Split Statistics