This paper presents the first application of Gaussian Mixture Copula Models to the statistical modeling of driving scenarios for the safety validation of automated driving systems. Knowledge of the joint probability distribution of scenario parameters is essential for scenario-based safety assessment, where risk quantification depends on the likelihood of concrete parameter combinations. Gaussian Mixture Copula Models bring together the multimodal expressivity of Gaussian Mixture Models and the flexibility of copulas, enabling separate modeling of marginal distributions and dependence. We benchmark Gaussian Mixture Copula Models against previously proposed approaches - Gaussian Mixture Models and Gaussian Copula Models - using real-world driving data drawn from two scenarios defined in United Nations Regulation No. 157. Our evaluation on approximately 18 million instances of these two scenarios demonstrates that Gaussian Mixture Copula Models consistently surpass Gaussian Copula Models and perform competitively with Gaussian Mixture Models, as measured by both log-likelihood and Sinkhorn distance, with relative performance depending on the scenario. The results are promising for the adoption of Gaussian Mixture Copula Models as a statistical foundation for future scenario-based validation frameworks.

翻译：本文首次将高斯混合Copula模型应用于驾驶场景的统计建模，以支持自动驾驶系统的安全验证。在基于场景的安全评估中，场景参数的联合概率分布知识至关重要，因为风险量化依赖于具体参数组合的出现概率。高斯混合Copula模型融合了高斯混合模型的多模态表达能力与Copula函数的灵活性，实现了边缘分布与相关结构的分离建模。我们使用联合国第157号法规中定义的两个场景的真实驾驶数据，将高斯混合Copula模型与先前提出的方法——高斯混合模型和高斯Copula模型——进行基准比较。基于约1800万条场景实例的评估表明，在对数似然与Sinkhorn距离两项指标上，高斯混合Copula模型始终优于高斯Copula模型，并与高斯混合模型表现相当，其相对性能依具体场景而定。这些结果为采用高斯混合Copula模型作为未来基于场景的验证框架的统计基础提供了有力支持。