Confidence interval estimation using polynomial chaos theory

This paper proposes an analytical method to estimate the confidence interval of a measurement using polynomial chaos theory (PCT). In previous work, the authors proposed an approach based on polynomial chaos theory (PCT) to evaluate the worst-case in an indirect measurement process, which in some cases can be considered as 100% confidence interval estimate. In many practical cases though, it is important to be able to determine the confidence intervals. The confidence interval computed as the integral the probability density function (PDF), the cumulative distribution function (CDF), requires the availability of the PDF. An analytical approach to calculate of the PDF associated to a PCT polynomial has been previously proposed in literature. This analytical approach based on a regularized estimation of the joint PDF, yields a well-defined and well shaped PDF. The method proposed in this paper is based on the analytical reconstruction of PDF from the polynomial structure of the PCT expansion. Once the PDF is obtained, the integral can be calculated and an estimation of the confidence interval can be derived. This methodology is demonstrated using an indirect loop impedance measurement as an example.