Nudging is a popular algorithmic strategy in numerical filtering to deal with the problem of inference in high-dimensional dynamical systems. We demonstrate in this paper that general nudging techniques can also tackle another crucial statistical problem in filtering, namely the misspecification of the transition model. Specifically, we rely on the formulation of nudging as a general operation increasing the likelihood and prove analytically that, when applied carefully, nudging techniques implicitly define state-space models (SSMs) that have higher marginal likelihoods for a given (fixed) sequence of observations. This provides a theoretical justification of nudging techniques as data-informed algorithmic modifications of SSMs to obtain robust models under misspecified dynamics. To demonstrate the use of nudging, we provide numerical experiments on linear Gaussian SSMs and a stochastic Lorenz 63 model with misspecified dynamics and show that nudging offers a robust filtering strategy for these cases.

翻译：微调是数值滤波中处理高维动态系统推断问题的一种常用算法策略。本文证明，广义的微调技术同样能够应对滤波中的另一个关键统计问题，即转移模型的误设。具体而言，我们基于将微调表述为一种提升似然性的广义操作，并通过解析证明：当谨慎应用时，微调技术隐式地定义了对于给定（固定）观测序列具有更高边缘似然的状态空间模型。这为微调技术提供了理论依据，即将其视为基于数据的状态空间模型算法修正，从而在动态模型误设下获得鲁棒模型。为展示微调的应用，我们在线性高斯状态空间模型及动态误设的随机Lorenz 63模型上进行了数值实验，结果表明微调为这些情形提供了鲁棒的滤波策略。