Robust Simulation Based Inference

Simulation-Based Inference (SBI) is an approach to statistical inference where simulations from an assumed model are used to construct estimators and confidence sets. SBI is often used when the likelihood is intractable and to construct confidence sets that do not rely on asymptotic methods or regularity conditions. Traditional SBI methods assume that the model is correct, but, as always, this can lead to invalid inference when the model is misspecified. This paper introduces robust methods that allow for valid frequentist inference in the presence of model misspecification. We propose a framework where the target of inference is a projection parameter that minimizes a discrepancy between the true distribution and the assumed model. The method guarantees valid inference, even when the model is incorrectly specified and even if the standard regularity conditions fail. Alternatively, we introduce model expansion through exponential tilting as another way to account for model misspecification. We also develop an SBI based goodness-of-fit test to detect model misspecification. Finally, we propose two ideas that are useful in the SBI framework beyond robust inference: an SBI based method to obtain closed form approximations of intractable models and an active learning approach to more efficiently sample the parameter space.