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Sampling-based inference techniques are central to modern cosmological dataanalysis; these methods, however, scale poorly with dimensionality andtypically require approximate or intractable likelihoods. In this paper wedescribe how Truncated Marginal Neural Ratio Estimation (TMNRE) (a new approachin so-called simulation-based inference) naturally evades these issues,improving the $(i)$ efficiency, $(ii)$ scalability, and $(iii)$ trustworthinessof the inferred posteriors. Using measurements of the Cosmic MicrowaveBackground (CMB), we show that TMNRE can achieve converged posteriors usingorders of magnitude fewer simulator calls than conventional Markov Chain MonteCarlo (MCMC) methods. Remarkably, the required number of samples is effectivelyindependent of the number of nuisance parameters. In addition, a propertycalled \emph{local amortization} allows the performance of rigorous statisticalconsistency checks that are not accessible to sampling-based methods. TMNREpromises to become a powerful tool for cosmological data analysis, particularlyin the context of extended cosmologies, where the timescale required forconventional sampling-based inference methods to converge can greatly exceedthat of simple cosmological models such as $\Lambda$CDM. To perform thesecomputations, we use an implementation of TMNRE via the open-source code\texttt{swyft}.

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