Sampling-Based Possibility Theory for Engineering Analysis Under Uncertainty: Inference, Prediction and Optimization

This contribution is a response to the 2025 NASA and DNV challenge on optimization under uncertainty. Three typical engineering problems in the form of parameter identification, forward propagation of uncertainty, and optimization are addressed. The framework of possibility theory is outlined and applied to the problems of the challenge. Given the nature of possibility theory, the results provide a rigorous and deliberately cautious perspective on the challenge problems. Accordingly, this approach is expected to be among the more conservative responses, offering a robust and well-substantiated analysis of uncertainty. The analysis is implemented through a samplingbased approach, returning statistically valid confidence distributions with all prior information explicitly stated.

Keywords: Uncertainty quantification, Imprecise probabilities, Possibility theory, Sampling, Statistical inference, Confidence, Forward propagation, Optimization.