Mathematical Modeling and Analysis
Mathematical Modeling and Analysis
Computational uncertainties are unavoidable in numerical calculations. The generation and propagation of uncertainties in the initial conditions, data and the constants in mathematical model can have serious implications in the reliability of the simulation and the decisions being made based on the simulation. These uncertainties can be quantified by probability distributions and the correlations between the variables. We have extended the standard computer arithmetic operations to include a probability distribution variable (PDV) as a basic data type. A PDV is a random variable that is usually characterized by its generalized probabilistic discretization. The computer arithmetic operations between the PDVs are deterministic rules that do not require multiple stochastic simulations and are designed based on rigorous mathematical analysis to obtain the tight probability distribution bounds for the results. The correlations and dependencies between PDVs arising in a computation are automatically calculated and tracked to give sharp bounds in quantifying the uncertainties in predictive models.
