PhD position on model misspecification sponsored by Microsoft Research

机械或基于模拟的模型在科学研究中用于理解复杂的自然现象。机制模型可以采用常/偏/随机微分方程（O/P/SDEs）的形式，可以是刚性的，但对科学家来说有可解释和可测试的参数设置。部分由于模型形式的不灵活性，模型的错误说明可能导致计算上昂贵的推理过程，更重要的是，误导性的结论，由此参数估计肯定是不正确的。越来越多的证据表明，与其他推理方法相比，近似贝叶斯计算（ABC）的推理框架对模型错误规范的鲁棒性更强。我们建议研究这种鲁棒性的数学和统计性质，并探索当前处理模型错误规范的方法的改进。研究将是务实的，将理论与实际例子相结合（领域知识被理解，因此可以发现错误的说明），包括使用在公共卫生领域使用的半机械模型。

Mechanistic or simulation-based models are used in scientific research to understand complex natural phenomena. A mechanistic model can take the form of ordinary/partial/stochastic differential equations (O/P/SDEs) and can be rigid in form but have the benefit to the scientist of having interpretable and testable parameter settings. In part due to the inflexibility of the model forms, misspecification of the model can lead to computationally expensive inference procedures, and more importantly, misleading conclusions, whereby the parameter estimates are confidently incorrect. There is increasing evidence that the inference framework called approximate Bayesian computation (ABC) is more robust to model misspecification than other inferential approaches. We propose to study the mathematical and statistical properties of this robustness, and explore improvements of current approaches for dealing with model misspecification. The research will be pragmatic, embedding the theory with practical examples (where domain knowledge is understood, and hence misspecification can be detected), including using semi-mechanistic models that are used in the public health domain.