Monte Carlo Tests with Nuisance Parameters: A General Approach to Finite-Sample Inference and Nonstandard Asymptotics

"Green's relation" results in a larger variance of the average energy so convergence is not as rapid but the method permits the use of a scaling rela- tion so that

This approach can be generalized to obtain a continuous CDF estimator and then an unbiased density estimator, via the likelihood ratio (LR) simulation-based derivative estimation

Keywords: Auxiliary information; Conditional inference; Finite population; Inclu- sion probabilities; Monte Carlo methods; Sampling weights..

• In Section ??, we propose the use of classifier two-sample tests to evaluate the sample quality of generative models with intractable likelihoods, such as Generative

Sample average approximation; multilevel Monte Carlo; vari- ance reduction; uniform strong large law of numbers; central limit theorem; importance Sampling..

While we confine ourselves to the MMD in this paper, we emphasize that the block approach applies to a much broader variety of test situations where the null distribution cannot

By considering the ratio of each partial variance to the total variance, we obtain a measure of importance for each input variable that is called the Sobol index or sensitivity index

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