Bayesian and frequentist investigation of prior effects in EFTofLSS analyses of full-shape BOSS and eBOSS data

TL;DR

This paper compares Bayesian and frequentist methods in analyzing cosmological data with EFTofLSS, revealing prior dependence issues and emphasizing the importance of combining approaches for accurate inference.

Contribution

It introduces a frequentist profile likelihood approach to assess prior effects in EFTofLSS analyses, providing a more prior-independent perspective on cosmological parameter constraints.

Findings

Bayesian constraints depend on priors and show volume effects.

Frequentist intervals are wider and prior-independent.

Future data will reconcile Bayesian and frequentist results.

Abstract

Previous studies based on Bayesian methods have shown that the constraints on cosmological parameters from the Baryonic Oscillation Spectroscopic Survey (BOSS) full-shape data using the Effective Field Theory of Large Scale Structure (EFTofLSS) depend on the choice of prior on the EFT nuisance parameters. In this work, we explore this prior dependence by adopting a frequentist approach based on the profile likelihood method, which is inherently independent of priors, considering data from BOSS, eBOSS and Planck. We find that the priors on the EFT parameters in the Bayesian inference are informative and that prior volume effects are important. This is reflected in shifts of the posterior mean compared to the maximum likelihood estimate by up to 1.0 {\sigma} (1.6 {\sigma}) and in a widening of intervals informed from frequentist compared to Bayesian intervals by factors of up to 1.9 (1.6) for BOSS (eBOSS) in the baseline configuration, while the constraints from Planck are unchanged. Our frequentist confidence intervals give no indication of a tension between BOSS/eBOSS and Planck. However, we find that the profile likelihood prefers extreme values of the EFT parameters, highlighting the importance of combining Bayesian and frequentist approaches for a fully nuanced cosmological inference. We show that the improved statistical power of future data will reconcile the constraints from frequentist and Bayesian inference using the EFTofLSS.