Including parameter dependence in the data and covariance for cosmological inference

TL;DR

This paper introduces an efficient interpolation method to incorporate parameter dependence into data and covariance matrices in cosmological analyses, improving accuracy with modest computational costs.

Contribution

It presents a simple interpolation scheme for including parameter dependence in covariance matrices, enhancing the accuracy of cosmological inferences.

Findings

Interpolation scheme effectively includes parameter dependence

Geometric structure-based scheme outperforms simpler methods

Both schemes perform well in practical tests

Abstract

The final step of most large-scale structure analyses involves the comparison of power spectra or correlation functions to theoretical models. It is clear that the theoretical models have parameter dependence, but frequently the measurements and the covariance matrix depend upon some of the parameters as well. We show that a very simple interpolation scheme from an unstructured mesh allows for an efficient way to include this parameter dependence self-consistently in the analysis at modest computational expense. We describe two schemes for covariance matrices. The scheme which uses the geometric structure of such matrices performs roughly twice as well as the simplest scheme, though both perform very well.