PhD position on model misspecification sponsored by Microsoft Research

机械或基于模拟的模型用于科学研究，以了解复杂的自然现象。机械模型可以采用普通/偏/随机微分方程（O/P/SDEs）的形式，并且可以是严格的形式，但对科学家来说具有可解释和可测试的参数设置的好处。部分由于模型形式的可验证性，模型的错误指定可能导致计算上昂贵的推理程序，更重要的是，误导性的结论，从而参数估计值肯定是不正确的。越来越多的证据表明，推理框架称为近似贝叶斯计算（ABC）是更强大的模型误指定比其他推理方法。我们建议研究这种鲁棒性的数学和统计特性，并探索改进目前的方法来处理模型误指定。该研究将是务实的，嵌入的理论与实际的例子（领域知识的理解，因此可以检测到错误的规格），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.