Parameter estimation for Gipps’ car following model in a Bayesian framework

Samson Ting, Thomas Lymburn, Thomas Stemler, Yuchao Sun and Michael Small

Physica A: Statistical Mechanics and its Applications, 2024, vol. 639, issue C

Abstract: Car following model is an important part in traffic modelling and has attracted a lot of attentions in the literature. As the proposed car following models become more complex with more components, reliably estimating their parameters becomes crucial to enhance model predictive performance. While most studies adopt an optimisation-based approach for parameters estimation, we present a statistically rigorous method that quantifies uncertainty of the estimates. We present a Bayesian approach to estimate parameters using the popular Gipps’ car following model as demonstration, which allows proper uncertainty quantification and propagation. Since the parameters of the car following model enter the statistical model through the solution of a delay-differential equation, the posterior is analytically intractable so we implemented an adaptive Markov Chain Monte Carlo algorithm to sample from it. Our results show that predictive uncertainty using a point estimator versus a full Bayesian approach are similar with sufficient data. In the absence of adequate data, the former can make over-confident predictions while such uncertainty is more appropriately incorporated in a Bayesian framework. Furthermore, we found that the congested flow parameters in the Gipps’ car following model are strongly correlated in the posterior, which not only causes issues for sampling efficiency but more so suggests the potential ineffectiveness of a point estimator in an optimisation-based approach. Lastly, an application of the Bayesian approach to a car following episode in the NGISM dataset is presented.

Keywords: Model calibration and validation; Bayesian inference; Uncertainty quantification; Adaptive Markov chain Monte Carlo (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:639:y:2024:i:c:s0378437124001808

DOI: 10.1016/j.physa.2024.129671

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