Parameter Estimation Using Interval Computations

Abstract

Parameter estimation is the problem of finding the values of the unknowns of a mathematical model for simulating a complex system. A model is generally given by differential equations or systems of equations or inequalities. Interval computations are numerical computations over sets of real numbers. In this paper intervals are used to model uncertainty in parameter estimation problems---for instance, some noise associated with measured data. Interval-based algorithms using consistency techniques and local search are developed. The goal is to reliably approximate the set of consistent values of parameters by inner and outer intervals. Such computations allow one to take into account all possible decisions. Applications for pharmacokinetics, biology, and census are described. Finally, a set of experimental results is discussed.