Numerical Probabilistic Analysis under Aleatory and Epistemic Uncertainty

This paper discusses Numerical Probabilistic Analysis (NPA) for problems under aleatory and epistemic uncertainty. The basis of NPA are numerical operations on probability density functions of the random values and probabilistic extensions. The numerical operations of the histogram arithmetic constitute the major component of NPA. The concepts of natural, probabilistic and histogram extensions of a function are considered. Using NPA approach, we construct numerical methods that enable us to solve systems of linear and nonlinear algebraic equations with stochastic parameters. To facilitate a more detailed description of the epistemic uncertainty, we introduce the concept of second order histograms. Relying on specific practical examples, we show that using second order histograms may prove helpful in decision making. In particular, we consider risk assessment of investment projects, where histograms of factors such as Net Present Value (NPV) and Internal Rate of Return (IRR) are computed. ∗Submitted: February 23, 2013; Revised: March 8, 2014; Accepted: April 15, 2014.