Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling
Markov chain Monte Carlo for a hyperbolic Bayesian inverse problem in traffic flow modeling
复制标题
DOI：
10.1017/dce.2022.3
复制
发表时间：
2022-02
期刊：
影响因子：
--
通讯作者：
Jeremie Coullon;Y. Pokern
中科院分区：
文献类型：
--
作者：
Jeremie Coullon;Y. Pokern
摘要由于用贝叶斯方法来拟合高速公路交通流模型在文献中还很少见，我们从经验上探讨了这种方法所带来的抽样挑战，它与后验分布的强相关性和多模式性有关。特别是，我们提供了一个统一的统计模型，利用高速公路数据估计由于Lighthill，Whitham和Richards被称为LWR的高速公路交通流模型中的边界条件和基本图表参数。这使得我们能够提供一种交通流密度估计方法，该方法被证明优于在交通流文献中找到的两种方法。为了从这种具有挑战性的后验分布中进行采样，我们使用了一种最先进的无梯度函数空间采样器，并增加了并行回火。
Abstract As a Bayesian approach to fitting motorway traffic flow models remains rare in the literature, we empirically explore the sampling challenges this approach offers which have to do with the strong correlations and multimodality of the posterior distribution. In particular, we provide a unified statistical model to estimate using motorway data both boundary conditions and fundamental diagram parameters in a motorway traffic flow model due to Lighthill, Whitham, and Richards known as LWR. This allows us to provide a traffic flow density estimation method that is shown to be superior to two methods found in the traffic flow literature. To sample from this challenging posterior distribution, we use a state-of-the-art gradient-free function space sampler augmented with parallel tempering.