text: 79,49,1508407909155278848,13800042,Lukas Heinrich,"Short new paper on lhood-free inference:We use the profile lhood ratio b/c of its asymptotically optimal properties but often need to approximate p(x|θ) to compute it. But if we take its properties seriously, we can find it in a fully likelihood-free way: <LINK> <LINK> As in the likelihood ratio trick, the idea is simple: if we use a test stat because it's optimal, that just means we can find it through optimization. The LRT is (asymptotically) optimal is various ways e.g. has best average power in a certain sense The idea is to optimizing a neural network-based statistic for best average power - this will generally give you a good test statistic. If the underlying model behaves asymptotically, this recovers the profile likelihood ratio without ever having to evaluate or fit p(x|θ)",http://arxiv.org/abs/2203.13079,"The design of optimal test statistics is a key task in frequentist statistics and for a number of scenarios optimal test statistics such as the profile-likelihood ratio are known. By turning this argument around we can find the profile likelihood ratio even in likelihood-free cases, where only samples from a simulator are available, by optimizing a test statistic within those scenarios. We propose a likelihood-free training algorithm that produces test statistics that are equivalent to the profile likelihood ratios in cases where the latter is known to be optimal. ",Learning Optimal Test Statistics in the Presence of Nuisance Parameters,3,"['Short new paper on lhood-free inference:We use the profile lhood ratio b/c of its asymptotically optimal properties but often need to approximate p(x|θ) to compute it. But if we take its properties seriously, we can find it in a fully likelihood-free way: <LINK> <LINK>', ""As in the likelihood ratio trick, the idea is simple: if we use a test stat because it's optimal, that just means we can find it through optimization. The LRT is (asymptotically) optimal is various ways e.g. has best average power in a certain sense"", 'The idea is to optimizing a neural network-based statistic for best average power - this will generally give you a good test statistic. If the underlying model behaves asymptotically, this recovers the profile likelihood ratio without ever having to evaluate or fit p(x|θ)']",22,03,792