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 dependencies. We benchmark Gaussian Mixture Copula Models against previously proposed approaches - Gaussian Mixture Models and Gaussian Copula Models - using real-world driving data drawn from scenarios defined in United Nations Regulation No. 157. Our evaluation across approximately 18 million scenario instances demonstrates that Gaussian Mixture Copula Models consistently surpass Gaussian Copula Models and perform better than, or at least comparably to, Gaussian Mixture Models, as measured by both log-likelihood and Sinkhorn distance. These 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模型应用于自动驾驶系统安全验证的驾驶场景统计建模。场景参数联合概率分布的认知对于基于场景的安全评估至关重要，其中风险量化取决于具体参数组合的可能性。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的灵活性，实现了边缘分布与依赖关系的分离建模。我们使用联合国第157号法规所定义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。基于对数似然与Sinkhorn距离的评估结果表明，在大约1800万个场景实例的测试中，高斯混合Copula模型始终优于高斯Copula模型，且性能优于或至少不亚于高斯混合模型。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展现了良好前景。