This paper presents the probabilistic collocation method as a computationally efficient method for performing uncertainty analysis on large complex models such as those used in global climate change research. The collocation method is explained, and then the results of its application to a box model of ocean thermohaline circulation are presented. A comparison of the results of the collocation method with a traditional Monte Carlo simulation show that the collocation method gives a better approximation for the probability density function of the model's response with less than 20 model runs as compared with a Monte Carlo simulation of 5000 model runs. / Includes bibliographical references (p. 21). / Abstract in HTML and technical report in HTML and PDF available on the Massachusetts Institute of Technology Joint Program on the Science and Policy of Global Change website (http://mit.edu/globalchange/www/).