Fast and Credible Likelihood-Free Cosmology with Truncated Marginal Neural Ratio Estimation (2111.08030v2)

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}.

• The paper presents TMNRE, a novel simulation-based inference method that drastically reduces simulation counts compared to traditional MCMC.
• It introduces a truncated marginal approach to efficiently focus on high-density, scientifically relevant parameter regions amid numerous nuisance parameters.
• The method employs local amortization for credible statistical checks, ensuring robust and reliable posterior inferences in complex cosmological data.

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

The paper introduces and validates a novel simulation-based inference (SBI) methodology called Truncated Marginal Neural Ratio Estimation (TMNRE) that is specifically tailored to improve cosmological data analysis. The challenges intrinsic to cosmological inference often involve approximations or intractable likelihoods combined with computational complexities that scale poorly with increasing parameters. The paper aims to ameliorate these issues through efficient and scalable inference techniques while maintaining statistical robustness, offering an alternative to traditional sampling-based approaches, such as Markov Chain Monte Carlo (MCMC).

TMNRE capitalizes on the statistical innovations presented by SBI methods, which use neural networks to interpret data from stochastic simulators, bypassing the need for explicitly defined likelihood functions. Among SBI techniques, TMNRE presents a unique focus on marginalized posteriors, particularly useful in scenarios where a multitude of nuisance parameters are present yet only a subset of parameters hold primary scientific interest.

The numerical experiments conducted within the paper demonstrate TMNRE's efficacy through cosmo-simulators such as Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations (BAO) setups. A notable result revealed that TMNRE requires significantly fewer simulations—scaling efficiently regardless of the dimensionality and complexity of the parameter space—compared to conventional methods like MCMC. Indeed, TMNRE achieves orders of magnitude reduction in the number of necessary simulations while producing converged posteriors, highlighting its scalability advantage in scenarios inclusive of extensive nuisance parameters.

One of the defining characteristics of TMNRE is its ability to perform credible statistical consistency checks through a process termed "local amortization." This capability empowers rigorous testing of posterior estimates' reliability, something notoriously challenging for traditional sampling-based methods. Such local amortization is pivotal in maintaining trust in the statistical properties of the inference outputs.

Significantly, the paper elucidates TMNRE’s potential to adaptively and dynamically focus computations on regions in parameter space that are most informative given the observed data. Through an iterative truncation process, TMNRE hones in on parameters likely to produce high-density posteriors, efficiently discarding less probable regions, thereby enhancing computational efficiency.

In summary, this research acknowledges TMNRE as an influential and robust tool in the field of cosmology. As an efficient alternative that complements the limitations of MCMC, TMNRE could set the groundwork for broader application in scenarios where high dimensionality and computational expense are critical bottlenecks. As cosmological data sets expand, with upcoming surveys promising revolutionary insights, methodologies like TMNRE are poised to become indispensable, unlocking full potential from extensive, complex, and parameter-rich data environments. Future work may involve adapting TMNRE to different models and exploring broader implications in cosmology and astrophysics to further enhance its practicality and applicability.