Aggregating point estimates: a flexible modeling approach

Article Abstract:

The use of a flexible modeling approach in aggregating point estimates in decision-making problems is examined. In such situations information from various sources may be available, but aggregating such data results in statistical difficulties that heretofore had been solved using historical data.Alternatively, a Bayesian framework is proposed that aggregates point estimatesof unknown variables by encoding subjective knowledge about the sources of information. This is accomplished through modeling of the sources' conditional distributions, which already capture dependence. Traditional decision-analysis assessment methods are used to formulate subjective judgements. Application to ozone-exposure health risks illustrates use of this model, which produces a posterior distribution for the variable in question.

Usage

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Calibration and the aggregation of probabilities

Article Abstract:

Morris details an axiomatic technique used to formulate a multiplicative regulation for aggregating the decision maker's and the expert's probabilities, in the effort to keep from examining a complicated likelihood element. The multiplicative regulation has a basic problem in that it does not enable the decision maker to model his opinions on the dependence between the expert's data and his own assessment. If the calculation is done correctly, the decision maker has to deal with the task which Morris plans to avoid.

Methods, Management science, Probabilities, Probability theory, Axioms

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Unanimity and compromise among probability forecasters

Article Abstract:

Several Bayesian probability-aggregation consensus models were examined to determine whether the models conformed to the principles of unanimity and compromise. The data were obtained from the precipitation probability forecasts of the US National Weather Service Techniques Development Laboratory between Apr 1972 and Sep 1983. The models were fit to the data, and the Log-odds II and Genest and Schervish-II models, which allowed forecast dependence, offered the best fit.

Mathematical models, Probability forecasts (Meteorology)

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