Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap
Robust Bayesian Inference for Simulator-based Models via the MMD Posterior Bootstrap
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发表时间：
2022-02
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通讯作者：
Charita Dellaporta;Jeremias Knoblauch;T. Damoulas;F. Briol
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作者：
Charita Dellaporta;Jeremias Knoblauch;T. Damoulas;F. Briol
基于模拟器的模型是可能性难以处理但模拟合成数据是可能的模型。它们通常用于描述复杂的现实世界现象，因此在实践中经常被错误指定。不幸的是，现有的贝叶斯方法的模拟器是众所周知的，在这些情况下表现不佳。在本文中，我们提出了一种新的算法的基础上的后验自助和最大平均差异估计。这导致了具有强鲁棒性的高度并行化的贝叶斯推理算法。这是证明通过深入的理论研究，其中包括概括界和证明的频率一致性和鲁棒性，我们的后验。然后评估的方法，包括一个g和k分布和切换开关模型的例子范围。
Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in those cases. In this paper, we propose a novel algorithm based on the posterior bootstrap and maximum mean discrepancy estimators. This leads to a highly-parallelisable Bayesian inference algorithm with strong robustness properties. This is demonstrated through an in-depth theoretical study which includes generalisation bounds and proofs of frequentist consistency and robustness of our posterior. The approach is then assessed on a range of examples including a g-and-k distribution and a toggle-switch model.