Estimating the Joint Probability of Scenario Parameters with Gaussian Mixture Copula Models

• URL: http://arxiv.org/abs/2506.10098v2
• Date: Wed, 08 Oct 2025 09:26:20 GMT
• Title: Estimating the Joint Probability of Scenario Parameters with Gaussian Mixture Copula Models
• Authors: Christian Reichenbächer, Philipp Rank, Jochen Hipp, Oliver Bringmann,
• Abstract summary: 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.<n>We benchmark the two approaches against each other using real-world driving data drawn from scenarios defined in United Nations Regulation No. 157.
• Score: 0.8851061118021407
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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