The effectiveness of imprecise probability forecasts

In this paper the authors investigate the feasibility of algorithmically deriving precise probability forecasts from imprecise forecasts. They provide an empirical evaluation of precise probabilities that have been derived from two types of imprecise probability forecasts: probability intervals and probability intervals with second-order probability distributions. The minimum cross-entropy (MCE) principle is applied to the former to derive precise (i.e. additive) probabilities; expectation (EX) is used to derive precise probabilities in the latter case. Probability intervals that were constructed without second-order probabilities tended to be narrower than and contained in those that were amplified by second-order probabilities. Evidence that this narrowness is due to motivational bias is presented. Analysis of forecasters’ mean Probability Scores for the derived precise probabilities indicates that it is possible to derive precise forecasts whose external correspondence is as good as directly assessed precise probability forecasts. The forecasts of the EX method, however, are more like the directly assessed precise forecasts than those of the MCE method.