Approximate Bayesian Inference by Density Ratio Estimation

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Since it's inception, simulation-based inference has become an increasingly important area of statistics for a variety of reasons: as these methods become more sophisticated they become increasingly accessible to scientists and further there are copious amounts of existing and previously collected data yet untapped. Simulation based inference methods are one of the few techniques for performing inference with intractable likelihoods - a situation encountered in a diverse range of scientific fields, from cosmology to population genetics. In practical settings, simulations are often expensive and thus algorithms that make use of them must be efficient. We aim to provide new innovations to this field, specifically, to extend the existing methodologies by integrating techniques from emerging paradigms of machine learning. These new ideas will allow us to decrease the number of simulations required and therefore increase efficiency. Not only do we intend to produce novel algorithms, but we also seek to provide theoretical guarantees of our techniques such as convergence and robustness properties. These techniques will then be applied to real-world data to explore their empirical performance.