Approximating Likelihood Ratios with Calibrated Discriminative Classifiers

In particle physics likelihood ratio tests are established tools for statistical inference. These tests are complicated by the fact that computer simulators are used as a generative model for the data, but they do not provide a way to evaluate the likelihood function. We demonstrate how discriminative classifiers can be used to approximate the likelihood function when a generative model for the data is available for training and calibration. This offers an approach to parametric inference when simulators are used that is complementary to approximate Bayesian computation.