**T**he next One World ABC seminar is on Thursday 24 Feb, with Rafael Izbicki talking on Likelihood-Free Frequentist Inference – Constructing Confidence Sets with Correct Conditional Coverage. It will take place at 14:30 CET (GMT+1).

*Many areas of science make extensive use of computer simulators that implicitly encode **likelihood functions of complex systems. Classical statistical methods are poorly suited* *for these so-called likelihood-free inference (LFI) settings, outside the asymptotic and low-**dimensional regimes. Although new machine learning methods, such as normalizing flows,* *have revolutionized the sample efficiency and capacity of LFI methods, it remains an open* *question whether they produce reliable measures of uncertainty. We present a statistical* *framework for LFI that unifies classical statistics with modern machine learning to: (1)* *efficiently construct frequentist confidence sets and hypothesis tests with finite-sample guar**antees of nominal coverage (type I error control) and power; (2) provide practical diagnostics*

*for assessing empirical coverage over the entire parameter space. We refer to our framework **as likelihood-free frequentist inference (LF2I). Any method that estimates a test statistic,* *like the likelihood ratio, can be plugged into our framework to create valid confidence sets* *and compute diagnostics, without costly Monte Carlo samples at fixed parameter settings.* *In this work, we specifically study the power of two test statistics (ACORE and BFF),* *which, respectively, maximize versus integrate an odds function over the parameter space.* *Our study offers multifaceted perspectives on the challenges in LF2I. This is joint work with* *Niccolo Dalmasso, David Zhao and Ann B. Lee.*

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