Simulations and cosmological inference: A statistical model for power spectra means and covariances

Abstract

We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate Normal distribution for the power spectrum band powers, but takes full account of the (parameter dependent) power spectrum covariance. The model is calibrated using an extension of the framework in Habib et al. (2007) to train Gaussian processes for the power spectrum mean and covariance given a set of simulation runs over a hypercube in parameter space. We demonstrate the performance of this machinery by estimating the parameters of a power-law model for the power spectrum. Within this framework, our calibrated sample variance distribution is robust to errors in the estimated covariance and shows rapid convergence of the posterior parameter constraints with the number of training simulations.

14 pages, 3 figures, matches final version published in PRD

References in corpus (20)

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Cited by in corpus (22)

• The Coyote Universe I: Precision Determination of the Nonlinear Matter Power Spectrum
• The Coyote Universe II: Cosmological Models and Precision Emulation of the Nonlinear Matter Power Spectrum
• The Effect of Covariance Estimator Error on Cosmological Parameter Constraints
• Dark Quest. I. Fast and Accurate Emulation of Halo Clustering Statistics and Its Application to Galaxy Clustering
• The Coyote Universe III: Simulation Suite and Precision Emulator for the Nonlinear Matter Power Spectrum
• Mock galaxy catalogs using the quick particle mesh method
• Determining Fundamental Properties of Matter Created in Ultrarelativistic Heavy-Ion Collisions
• The Mira-Titan Universe: Precision Predictions for Dark Energy Surveys
• Constraint on neutrino masses from SDSS-III/BOSS Ly$\alpha$ forest and other cosmological probes
• The Parameter Space of Galaxy Formation
• Cosmic Shear Covariance Matrix in $w$CDM: Cosmology Matters
• On the road to percent accuracy II: calibration of the non-linear matter power spectrum for arbitrary cosmologies
• Sample variance in weak lensing: how many simulations are required?
• PkANN - I. Non-linear matter power spectrum interpolation through artificial neural networks
• Fast generation of ensembles of cosmological N-body simulations via mode-resampling
• Constraining cosmology with weak lensing voids
• On estimating cosmology-dependent covariance matrices
• Intelligent Design: On the Emulation of Cosmological Simulations
• Identifying Tools for Comparing Simulations and Observations of Spectral-line Data Cubes
• Cosmological forecasts with the clustering of weak lensing peaks
• Keeping It Real: Revisiting a Real-Space Approach to Running Ensembles of Cosmological N-body Simulations
• The Parameter-Level Performance of Covariance Matrix Conditioning in Cosmic Microwave Background Data Analyses