Combination and selection of binary forecasts

Binary yes-no forecasts are used to indicate whether a particular set of events will or will not occur. A mechanism for combining independent binary forecasts for the case where likelihood functions are available is given. The decision maker (DM) has to assume a priori from the natural conjugate family of distributions, and uses the forecasts as data points. The assumptions of this model are examined, and some statistical properties are developed. These properties are used to provide a dynamic programming procedure for a priori and sequential selection of an optimal subset of the forecast set when they are costly