Statistical Engineering Division
Seminar Series

Maurice Cox
National Physical Laboratory, UK
Statistical Engineering Division, NIST
Lecture Room A
Friday, August 5, 2005, 10:30 AM

Abstract

Determining the definite integral I of a function f over an interval is a basic concept in mathematics. For cases that cannot be treated analytically, quadrature rules are applied to obtain I numerically, ideally to within a user-prescribed accuracy. Typically, f is evaluated at stipulated points in order to implement the rule.

What can be done (a) if f is given by measurement at a number of points, (b) if these points are arbitrarily spaced, (c) about the measurement uncertainties? An approach is described based on (1) regarding the measurement points as representing a curve, the area under which is sought, (2) representing each interval between adjacent points by a polynomial piece, (3) forming the definite integral of each such piece, (4) summing these integrals to approximate the required area, (5) comparing the results obtained using polynomials of different orders, (6) propagating the measurement uncertainties to evaluate the uncertainties associated with the approximations.

An application to climate change is presented, viz., quantifying the component of the Earth's Radiation Budget relating to the incoming radiation from the sun.

Speaker Bio

Dr. Cox is a Senior Fellow at the National Physical Laboratory (NPL), where he is a consultant mathematician. He is leader of the BIPM Director's Advisory Group on Uncertainties, Convenor of ISO Working Group ISO/TC 69/SC 6/WC 7 on Statistical Methods to Support Measurement Uncertainty Evaluation, Convenor of British Standards Panel SS/6/-/3 on Measurement Uncertainty, Convenor of British Standards Committee SS/6 on Precision of Test Methods, lead author of Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. Dr. Cox received a BSc in Applied Mathematics and a PhD in numerical analysis, from City University, London, UK. His research interests include mathematical modelling (especially applied to measurement problems), statistical modelling (especially applied to inter-laboratory comparisons), uncertainty evaluation, numerical analysis, mathematical algorithms, software validation.