Estimating the Joint Probability of Scenario Parameters with Gaussian Mixture Copula Models
This work addresses the need for accurate statistical modeling in scenario-based safety assessment for automated driving systems, representing an incremental improvement by combining existing techniques.
The paper tackles the problem of estimating the joint probability distribution of driving scenario parameters for safety validation of automated driving systems by applying Gaussian Mixture Copula Models, which outperform or match previous methods like Gaussian Mixture Models and Gaussian Copula Models on real-world data from approximately 18 million scenario instances as measured by log-likelihood and Sinkhorn distance.
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.