Kairosis: A method for dynamical probability forecast aggregation informed by Bayesian change point detection

We present a new method, "kairosis", for aggregating probability forecasts made over a time period of a single outcome determined at the end of that period. Informed by work on Bayesian change-point detection, we begin by constructing for each time during the period a posterior probability that the forecasts before and after this time are distributed differently. The resulting posterior probability mass function is integrated to give a cumulative mass function, which is used to create a weighted median forecast. The effect is to construct an aggregate in which the most heavily weighted forecasts are those which have been made since the probable most recent change in the forecasts' distribution. Kairosis outperforms standard methods, and is especially suitable for geopolitical forecasting tournaments because it is observed to be robust across disparate questions and forecaster distributions.