Modified PERT versus fractile assessment of subjective probability distributions

Abstract

A technique of subjective probability distribution assessment of uncertain quantities based on a most likely, optimistic, and pessimistic estimate as used in PERT (Program Evaluation and Review Technique) to manage large-scale projects, was compared to five direct fractile assessments. A beta probability density function was also fitted to each of the assessed distributions, compared, and then its parameters manipulated simultaneously using a scaling constant, to improve external calibration and accuracy. PERT assessments yielded somewhat looser subjective probability distributions than direct fractile assessments, and therefore fewer “surprises.” Beta density functions fit to tail fractiles were considerably tighter than beta densities fit to central fractiles. Tail fractile beta fits were also tighter than the assessed distributions, while central fractile beta fits were looser. For group generated proportions, the average underestimation bias of high valued uncertain quantities and overestimation bias of low valued uncertain quantities appeared to be reasonably well behaved. This suggested that each beta parameter might be manipulated separately using individual scaling constants as a method of recalibrating the assessor, to mitigate both the inherent biases of overconfidence (second moment bias) and departure of the .50 fractile from the true value (first moment bias). Further implications with respect to subjective probability distribution assessment and future research are discussed.