Reducing nuisance prior sensitivity via non-linear reparameterization, with application to EFT analyses of large-scale structure

TL;DR

This paper introduces a non-linear reparameterization technique using GAMs to decorrelate nuisance parameters from parameters of interest in EFT analyses of large-scale structure, improving the robustness of cosmological inferences.

Contribution

The authors develop a novel reparameterization method that reduces prior sensitivity by decorrelating nuisance and target parameters in complex models.

Findings

Reduces dependence of posterior on nuisance priors

Improves robustness of cosmological parameter inference

Applicable to non-linear relationships in EFT models

Abstract

Many physical models contain nuisance parameters that quantify unknown properties of an experiment that are not of primary relevance. Typically, these cannot be measured except by fitting the models to the data from the experiment, requiring simultaneous measurement of interesting parameters that are our target of inference and nuisance terms that are not directly of interest. A recent example of this is fitting Effective Field Theory (EFT) models to large-scale structure (LSS) data to make cosmological inferences. These models have a large number of nuisance parameters that are typically correlated with cosmological parameters in the posterior, leading to strong dependence on the nuisance parameter priors. We introduce a reparametrization method that leverages Generalized Additive Models (GAMs) to decorrelate nuisance parameters from the parameters of interest in the likelihood, even in the presence of non-linear relationships. This reparametrization forms a natural basis within which to define priors that are independent between nuisance and target parameters: the separation means that the marginal posterior for cosmological parameters does not depend on simple priors placed on nuisance terms. In application to EFT models using LSS data, we demonstrate that the proposed approach leads to robust cosmological inference.