A Proposal for Computing With Imprecise Probabilities: A Framework for Multiple Representations of Uncertainty in Simulation Software

We propose the design and construction of a programming language for the formal representation of uncertainty in modeling and simulation. Modeling under uncertainty has been of paramount importance in the past half century, as quantitative methods of analysis have been developed to take advantage of computational resources. Simulation is gaining prominence as the proper tool of scientific analysis under circumstances where it is infeasible or impractical to directly study the system in question. This programming language will be built as an extension to the Modelica programming language, which is an acausal object-oriented language for hybrid continuous and discrete-event simulations [22]. Our language extensions will serve as a platform for the research into representation and calibration of imprecise probabilities in quantitative risk analysis simulations. Imprecise probability is used a generic term for any mathematical model which measures chance or uncertainty without crisp numerical probabilities. The explicit representation of imprecise probability theories in a domain-specific programming language will facilitate the development of efficient algorithms for expressing, computing, and calibrating imprecise probability structures. Computation with imprecise probability structures will lead to quantitative risk analyses that are more informative than analyses using traditional probability theory. We have three primary research objectives: (i) the exploration of efficient representational structures and computational algorithms of Dempster-Shafer belief structures; (ii) the application of the imprecise probabilities to representing variable dependence; and (iii) the exploration of various Dempster-Shafer combination rules for model calibration. At the completion of this dissertation, we will have produced the end-to-end design, implementation, and analysis of a programming language that will facilitate the future exploration of algorithms, software, and theory for quantitative uncertainty analysis in computer science.