Copulas for Uncertainty Analysis

Applying the Monte Carlo method for propagation of measurement uncertainty described in the GUM Supplement 1, when the input quantities are correlated, involves the specification of a joint probability distribution for these quantities.

In practice, however, all that typically is available are probability distributions for the individual input quantities (their marginal distributions), and estimates of the correlations between them. Therefore, a method is needed to manufacture that joint distribution.

This seminar reviews the guidance in the GUM Supplement 1 regarding a Monte Carlo method for propagation of distributions, and extends the method by employing copulas that may be used to manufacture joint probability distributions consistent with given margins and correlations.

The presentation consists mostly of simple practical examples that are worked out in detail and that illustrate and contrast all the techniques, old and new, that are discussed.

Dr. Antonio Possolo
Division Chief
Statistical Engineering Division
NIST