Monte Carlo evaluation of the uncertainty associated with the construction and use of a fitted curve

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.

► The problem of fitting a curve to a set of points in a two-dimensional coordinate system recurs throughout science and technology.
► In general, the coefficients of the adjusted curve will not be perfectly known.
► In this paper, a Monte Carlo procedure is presented for computing the joint state-of-knowledge probability distribution to be assigned to these coefficients.
► From this distribution, the best estimates of the coefficients can then be found, together with their associated standard uncertainties.