Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation

TL;DR

TMNRE is a novel simulation-based inference method that significantly improves efficiency, scalability, and trustworthiness in cosmological data analysis, especially for high-dimensional problems with many nuisance parameters.

Contribution

The paper introduces Truncated Marginal Neural Ratio Estimation (TMNRE), a new approach that overcomes limitations of traditional sampling methods in cosmology, enabling faster and more reliable inference.

Findings

TMNRE achieves converged posteriors with far fewer simulator calls than MCMC.

The number of samples needed is effectively independent of nuisance parameters.

TMNRE allows rigorous statistical consistency checks not possible with sampling-based methods.

Abstract

Sampling-based inference techniques are central to modern cosmological data analysis; these methods, however, scale poorly with dimensionality and typically require approximate or intractable likelihoods. In this paper we describe how Truncated Marginal Neural Ratio Estimation (TMNRE) (a new approach in so-called simulation-based inference) naturally evades these issues, improving the $(i)$ efficiency, $(ii)$ scalability, and $(iii)$ trustworthiness of the inferred posteriors. Using measurements of the Cosmic Microwave Background (CMB), we show that TMNRE can achieve converged posteriors using orders of magnitude fewer simulator calls than conventional Markov Chain Monte Carlo (MCMC) methods. Remarkably, the required number of samples is effectively independent of the number of nuisance parameters. In addition, a property called \emph{local amortization} allows the performance of rigorous statistical consistency checks that are not accessible to sampling-based methods. TMNRE promises to become a powerful tool for cosmological data analysis, particularly in the context of extended cosmologies, where the timescale required for conventional sampling-based inference methods to converge can greatly exceed that of simple cosmological models such as $\Lambda$CDM. To perform these computations, we use an implementation of TMNRE via the open-source code \texttt{swyft}.