The EFT Likelihood for Large-Scale Structure

TL;DR

This paper develops a rigorous theoretical framework for the likelihood function in large-scale structure Bayesian inference, incorporating non-Gaussian stochasticity and higher-derivative corrections to improve modeling accuracy.

Contribution

It derives the EFT-based conditional likelihood for tracers given matter fields, including corrections beyond previous Gaussian assumptions.

Findings

Derived the conditional likelihood using functional methods and bias expansion.

Identified and quantified corrections from non-Gaussian stochasticity and higher-derivative terms.

Discussed implications for Bayesian inference and potential extensions to primordial non-Gaussianity.

Abstract

We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all stochastic terms apart from the ones appearing in the auto two-point function of tracers, we recover the result of Schmidt et al., 2018. We then rigorously derive the corrections to this result, such as those coming from a non-Gaussian stochasticity (which include the stochastic corrections to the tracer bispectrum) and higher-derivative terms. We discuss how these corrections can affect current applications of Bayesian inference. We comment on possible extensions to our result, with a particular eye towards primordial non-Gaussianity. This work puts on solid theoretical grounds the EFT-based approach to Bayesian forward modeling.