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

TL;DR

This paper introduces a statistical model for the distribution of the non-linear matter power spectrum's sample variance, calibrated with limited simulations, enabling efficient cosmological inference with robust parameter estimation.

Contribution

The paper presents a novel Gaussian process-based model that accounts for parameter-dependent covariance in power spectrum analysis, improving inference from limited simulation data.

Findings

Model accurately estimates power spectrum parameters

Robust to covariance estimation errors

Rapid convergence with fewer simulations

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.