Strengthening the Case for a Bayesian Approach to Car-following Model Calibration and Validation using Probabilistic Programming

Abstract

Compute and memory constraints have historically prevented traffic simulation software users from fully utilizing the predictive models underlying them. When calibrating car-following models, particularly, accommodations have included 1) using sensitivity analysis to limit the number of parameters to be calibrated, and 2) identifying only one set of parameter values using data collected from multiple car-following instances across multiple drivers. Shortcuts are further motivated by insufficient data set sizes, for which a driver may have too few instances to fully account for the variation in their driving behavior. In this paper, we demonstrate that recent technological advances can enable transportation researchers and engineers to overcome these constraints and produce calibration results that 1) outperform industry standard approaches, and 2) allow for a unique set of parameters to be estimated for each driver in a data set, even given a small amount of data. We propose a novel calibration procedure for car-following models based on Bayesian machine learning and probabilistic programming, and apply it to realworld data from a naturalistic driving study. We also discuss how this combination of mathematical and software tools can offer additional benefits such as more informative model validation and the incorporation of true-to-data uncertainty into simulation traces.

A Probabilistic Approach for the Calibration of Incomplete Microscopic Traffic Models

“…∀i ∈ D, t ∈ T , where u 0 is the desired speed, s 0 is the minimum gap of vehicle i and the precending vehicle, T safe is the minimum travel time interval between vehicle i and the leading vehicle, a max is the maximum vehicle acceleration, β the comfortable breaking deceleration and δ a constant that represents the rate at which a vehicle's acceleration is changing when the vehicle is approaching the desired velocity [13].…”

“…More recently, the Bayesian inference paradigm was used as an alternative, aiming to derive the probability density function of the unknown parameters [11], [12]. To improve the estimation accuracy of the Bayesian framework, [13] used a hierarchical model formulation for multiple individual vehicles, while [14] extended this hierarchical framework to take into account the autocorrelation per individual driver.…”

Identifiability of car-following dynamic

“…The differential geometry framework [68] considers identifiability as an augmented observability property for a general nonlinear system of ODEs such as (1), and it can be evaluated in the same manner. In general, observability is checked by looking at the rank of the observability matrix O(x) that links the model output y with the state x and contains the partial derivatives of the output with respect to the states.…”

“…Studies of car-following models and calibration of such models have mostly been focused on data-fitting quality. Model calibration is usually posed as an optimization problem such that the best fit parameters are found by minimizing the error between the model prediction and corresponding measurement data [29,58], or through probabilistic approaches to find the most likely parameter candidate [1,78]. Although the approaches report good accuracy of the estimated parameters, they lack a theoretical guarantee that a unique parameter set can be recovered, which is provided by an identifiability analysis of the evolution-observation system [7,40].…”

Probabilistic programming with densities in SlicStan: efficient, flexible, and deterministic

“…Edward2 (Tran et al, 2018) is a deep probabilistic programming language embedded into Python and built on top of TensorFlow (Abadi et al, 2015). It has found several applications in fields that require processing large amounts of data, such as intelligent transportation systems (Abodo et al, 2019), recommendation systems (Mladenov et al, 2020), and biological sequence models (Weinstein and Marks, 2021). Edward2 uses effect handlers (referred to in the language as interceptors or tracers) to change the meaning of probabilistic assignment at runtime.…”