Quantification of model uncertainty on path-space via goal-oriented relative entropy
Quantification of model uncertainty on path-space via goal-oriented relative entropy
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DOI：
10.1051/m2an/2020070
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发表时间：
2019-06
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影响因子：
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通讯作者：
Jeremiah Birrell;M. Katsoulakis;Luc Rey-Bellet
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文献类型：
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作者：
Jeremiah Birrell;M. Katsoulakis;Luc Rey-Bellet
在许多应用中，量化参数和模型形式不确定性对随机模型预测的影响是一个关键挑战。前人的工作表明，相对熵率是推导遍历平均上的路径空间不确定性量化(UQ)界的有效工具。在这项工作中，我们为路径空间上更大范围的兴趣量识别合适的信息论对象，例如命中时间和指数折扣的可观测值，并给出相应的UQ界。此外，我们的方法产生了更紧的Uq界限，即使在以前基于相对熵的方法也适用的情况下，例如，对于遍历平均。我们用期权定价、不可逆扩散过程、随机控制、半马尔可夫排队模型以及到达时间的期望和分布的例子来说明这些结果。
Quantifying the impact of parametric and model-form uncertainty on the predictions of stochastic models is a key challenge in many applications. Previous work has shown that the relative entropy rate is an effective tool for deriving path-space uncertainty quantification (UQ) bounds on ergodic averages. In this work we identify appropriate information-theoretic objects for a wider range of quantities of interest on path-space, such as hitting times and exponentially discounted observables, and develop the corresponding UQ bounds. In addition, our method yields tighter UQ bounds, even in cases where previous relative-entropy-based methods also apply, e.g., for ergodic averages. We illustrate these results with examples from option pricing, non-reversible diffusion processes, stochastic control, semi-Markov queueing models, and expectations and distributions of hitting times.