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Most subjective probability aggregation procedures use a single probabilityjudgment from each expert, even though it is common for experts studying realproblems to update their probability estimates over time. This paper advancesinto unexplored areas of probability aggregation by considering a dynamiccontext in which experts can update their beliefs at random intervals. Theupdates occur very infrequently, resulting in a sparse data set that cannot bemodeled by standard time-series procedures. In response to the lack ofappropriate methodology, this paper presents a hierarchical model that takesinto account the expert's level of self-reported expertise and producesaggregate probabilities that are sharp and well calibrated both in- andout-of-sample. The model is demonstrated on a real-world data set that includesover 2300 experts making multiple probability forecasts over two years ondifferent subsets of 166 international political events.

Probability aggregation in time-series: Dynamic hierarchical modeling of sparse expert beliefs