用于随机跟驰模型校准的严格适当评分规则理论
A Strictly Proper Scoring-Rule Theory for Calibrating Stochastic Car-Following Models
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中文总结 AI 辅助
该研究建立随机跟驰模型校准的严格适当评分规则理论，明确不同评分指标的特性，推荐合适的估计方法，验证其适用于随机交通模拟器的向量值输出。
中文摘要 AI 辅助
问题定义：随机模拟器中的固定参数和输入会产生完整轨迹的分布，而非单一轨迹；校准必须评估该分布（包括变异性和时间依赖性）与观测值的契合度，但随机跟驰模型通常沿用确定性建模的轨迹误差目标进行校准。方法与结果：我们建立了随机校准的评分规则理论，严格适当性要求数据生成分布能唯一最小化期望评分；MRMean-I（按运行平均的误差）可驱动可分离的随机散布趋于零，MRMean-II（集合平均轨迹的误差）无法识别仅改变散布的参数，MRMin（最接近模拟运行的误差）的总体目标随集合规模变化；这些结果在带有加性加速度噪声和随机期望车头时距的随机智能驾驶员模型扩展中得到验证。我们建议在可获得正确转移密度时使用精确最大似然，否则采用基于模拟的严格适当评分的无偏估计量；能量评分满足该要求，在评估的基于模拟的目标中给出最佳的保留分布预测，尽管两个模型均保留过窄的区间且遗漏持续干扰。意义：严格适当性将有效校准目标与参数可识别性及模型充分性分离，该理论适用于随机交通模拟器的向量值输出，跟驰实验说明了其适用范围。
英文摘要
Problem definition: Fixed parameters and inputs in a stochastic simulator induce a distribution over complete trajectories, not one trajectory. Calibration must assess this distribution, including variability and temporal dependence, against observations. Yet stochastic car-following models are commonly calibrated with trajectory-error objectives inherited from deterministic modelling. Methodology/results: We establish a scoring-rule theory of stochastic calibration. Strict propriety requires the data-generating distribution to uniquely minimise expected score. MRMean-I, the average run-wise error, drives separable stochastic spread to zero; MRMean-II, the error of the ensemble-mean trajectory, cannot identify a parameter that changes only spread; and MRMin, the error of the closest simulated run, has a population target that changes with ensemble size. These results are confirmed for stochastic Intelligent Driver Model extensions with additive acceleration noise and random desired headway. We recommend exact maximum likelihood when the correct transition density is available; otherwise, an unbiased simulation-based estimator of a strictly proper score. The energy score meets this requirement and gives the best held-out distributional prediction among the evaluated simulation-based objectives, although both models retain too-narrow bands and miss persistent disturbances. Implications:Strict propriety separates a valid calibration target from parameter identifiability and model adequacy. The theory applies to vector-valued outputs from stochastic transportation simulators; the car-following experiments illustrate its scope.
