Monte Carlo evaluation of the uncertainty associated with the construction and use of a fitted curve. http://dx.doi.org/10.1016/j.measurement.2011.07.021

Abstract

A Monte Carlo procedure is presented for computing the joint state-of-knowledge probability distribution to be assigned to the coefficients of a curve fitted to a set of points in a two-dimensional coordinate system. Experimental data about this set may be available, but other relevant information may also be taken into account. The procedure is fully in line with the approach in Supplement 1 to the Guide to the Expression of Uncertainty in Measurement. It consists of propagating the joint probability distribution of the input quantities through the mathematical model of the measurement by which the coefficients are defined. The model is usually obtained by least-squares adjustment, which is here interpreted differently than in the conventional formulation. However, applying other fitting criteria is also possible. Examples illustrate the application of the procedure.