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Uncertainty-Aware Measurement of Scenario Suite Representativeness for Autonomous Systems

Robab Aghazadeh Chakherlou, Siddartha Khastgir, Xingyu Zhao, Jerein Jeyachandran, Shufeng Chen

TL;DR

This work addresses how to quantify representativeness of scenario data for autonomous systems when the Target Operational Domain $TOD$ is unknown and must be inferred from data. It introduces an imprecise Bayesian framework that models the TOD as an uncertain categorical distribution and propagates prior imprecision through Dirichlet posteriors to yield interval estimates of representativeness. Representativeness is quantified via two distributional distances, $D_{TV}$ and $D_{JS}$, which become interval-valued under epistemic uncertainty, providing transparent bounds on alignment between the scenario suite and TOD. The numerical example demonstrates strong global representativeness despite deliberate oversampling of safety-critical conditions and shows how prior strength and dependencies influence the uncertainty bounds, supporting auditable safety arguments and potential Integration into Assurance 2.0.

Abstract

Assuring the trustworthiness and safety of AI systems, e.g., autonomous vehicles (AV), depends critically on the data-related safety properties, e.g., representativeness, completeness, etc., of the datasets used for their training and testing. Among these properties, this paper focuses on representativeness-the extent to which the scenario-based data used for training and testing, reflect the operational conditions that the system is designed to operate safely in, i.e., Operational Design Domain (ODD) or expected to encounter, i.e., Target Operational Domain (TOD). We propose a probabilistic method that quantifies representativeness by comparing the statistical distribution of features encoded by the scenario suites with the corresponding distribution of features representing the TOD, acknowledging that the true TOD distribution is unknown, as it can only be inferred from limited data. We apply an imprecise Bayesian method to handle limited data and uncertain priors. The imprecise Bayesian formulation produces interval-valued, uncertainty-aware estimates of representativeness, rather than a single value. We present a numerical example comparing the distributions of the scenario suite and the inferred TOD across operational categories-weather, road type, time of day, etc., under dependencies and prior uncertainty. We estimate representativeness locally (between categories) and globally as an interval.

Uncertainty-Aware Measurement of Scenario Suite Representativeness for Autonomous Systems

TL;DR

This work addresses how to quantify representativeness of scenario data for autonomous systems when the Target Operational Domain is unknown and must be inferred from data. It introduces an imprecise Bayesian framework that models the TOD as an uncertain categorical distribution and propagates prior imprecision through Dirichlet posteriors to yield interval estimates of representativeness. Representativeness is quantified via two distributional distances, and , which become interval-valued under epistemic uncertainty, providing transparent bounds on alignment between the scenario suite and TOD. The numerical example demonstrates strong global representativeness despite deliberate oversampling of safety-critical conditions and shows how prior strength and dependencies influence the uncertainty bounds, supporting auditable safety arguments and potential Integration into Assurance 2.0.

Abstract

Assuring the trustworthiness and safety of AI systems, e.g., autonomous vehicles (AV), depends critically on the data-related safety properties, e.g., representativeness, completeness, etc., of the datasets used for their training and testing. Among these properties, this paper focuses on representativeness-the extent to which the scenario-based data used for training and testing, reflect the operational conditions that the system is designed to operate safely in, i.e., Operational Design Domain (ODD) or expected to encounter, i.e., Target Operational Domain (TOD). We propose a probabilistic method that quantifies representativeness by comparing the statistical distribution of features encoded by the scenario suites with the corresponding distribution of features representing the TOD, acknowledging that the true TOD distribution is unknown, as it can only be inferred from limited data. We apply an imprecise Bayesian method to handle limited data and uncertain priors. The imprecise Bayesian formulation produces interval-valued, uncertainty-aware estimates of representativeness, rather than a single value. We present a numerical example comparing the distributions of the scenario suite and the inferred TOD across operational categories-weather, road type, time of day, etc., under dependencies and prior uncertainty. We estimate representativeness locally (between categories) and globally as an interval.

Paper Structure

This paper contains 29 sections, 1 theorem, 24 equations, 2 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Comparison with Existing Methods on Representativeness
  4. Imprecise Probability
  5. A metric for quantifying the representativeness
  6. Estimating the Posterior Distribution Envelopes of TOD
  7. Representativeness Metric under Uncertainty
  8. Total Variation Distance (TVD)
  9. Jensen-Shannon Divergence (JSD)
  10. Propagating Epistemic Uncertainty
  11. Numerical Example
  12. Problem Setting: Common Cases
  13. Problem Setting: Scenario Suite
  14. Problem Setting: TOD
  15. Posterior inference
  16. ...and 14 more sections

Key Result

Theorem 1

Let the Target Operational Domain (TOD) be represented by a categorical random variable $Z \in \{1,\ldots,K\}$ with unknown probability vector $\boldsymbol{\theta}_{\text{TOD}} = (\theta_1,\ldots,\theta_K) \in \Delta_{K-1}$ where, $\Delta_{K-1}$ is the probability simplex as follows: Given observed category counts $\mathbf{k}=(k_1,\ldots,k_K)$ from $n$ i.i.d. samples, the likelihood is multinomia

Figures (2)

  • Figure 1: Schematic illustration of the representativeness evaluation process. The true population of TOD scenarios is unknown, and sampling from it introduces uncertainty, represented by imprecise probability envelopes around the estimated distribution. Representativeness is then assessed by comparing this uncertain TOD distribution with the known distribution of the scenario test suite.
  • Figure 2: Comparison between the empirical scenario suite distribution and the posterior mean of the TOD distribution.

Theorems & Definitions (1)

  • Theorem 1: Posterior inference for the TOD distribution