Approximate Bayesian Inference by Density Ratio Estimation

从一开始，基于模拟的推理已经成为统计学中越来越重要的领域，原因有很多：随着这些方法变得越来越复杂，科学家们越来越容易使用它们，而且还有大量现有的和以前收集的数据尚未开发。基于模拟的推理方法是执行难以处理的可能性推理的少数技术之一，这种情况在从宇宙学到种群遗传学的各种科学领域中都会遇到。在实际设置中，模拟通常是昂贵的，因此利用它们的算法必须是高效的。我们的目标是为这一领域提供新的创新，特别是通过整合新兴机器学习范式的技术来扩展现有的方法。这些新想法将使我们能够减少所需的模拟次数，从而提高效率。我们不仅打算产生新颖的算法，而且还寻求为我们的技术提供理论保证，例如收敛性和鲁棒性。然后将这些技术应用于现实世界的数据，以探索其经验性能。

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.