An inverse method for bounded error parameter identification

Abstract

In this paper we present an algorithm to bound parameters estimated from very small data sets and use this method to suggest optimal times for data collection. The method is deterministic in that we assume that one has error bars on the data. The basic idea is based on bounded error parameter identification methods and we use this framework to assign a measure of quality to the estimated parameter. Exploiting the dynamics of the underlying mathematical model allows us to describe the quality of the estimated parameter in a way that, due to the small number of data points, is not appropriate for traditional statistical techniques. The algorithm in this paper differs from traditional bounded error parameter identification techniques in that one computes the membership set by solving an inverse problem rather than a forward interval problem.