**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 encodelikelihood functions of complex systems. Classical statistical methods are poorly suitedfor 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 openquestion whether they produce reliable measures of uncertainty. We present a statisticalframework for LFI that unifies classical statistics with modern machine learning to: (1)efficiently construct frequentist confidence sets and hypothesis tests with finite-sample guarantees of nominal coverage (type I error control) and power; (2) provide practical diagnosticsfor assessing empirical coverage over the entire parameter space. We refer to our frameworkas 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 setsand 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 withNiccolo Dalmasso, David Zhao and Ann B. Lee.