6533b7d2fe1ef96bd125e9a0
RESEARCH PRODUCT
Optimal Reporting of Predictions
Maria J. BayarriMorris H. Degrootsubject
Statistics and ProbabilityMathematical optimizationExpert opinionStatisticsGaining weightStatistics Probability and UncertaintyDecision makerBayesian inferenceFinite setRandom variableValue (mathematics)WeightingMathematicsdescription
Abstract Consider a problem in which you and a group of other experts must report your individual predictive distributions for an observable random variable X to some decision maker. Suppose that the report of each expert is assigned a prior weight by the decision maker and that these weights are then updated based on the observed value of X. In this situation you will try to maximize your updated, or posterior, weight by appropriately choosing the distribution that you report, rather than necessarily simply reporting your honest predictive distribution. We study optimal reporting strategies under various conditions regarding your knowledge and beliefs about X and the reports of the other experts, and under various utility functions for your posterior weight. We present the only utility functions for which it is always optimal to report your honest predictive distribution. Attention is restricted to problems in which X can take only a finite number of values.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 1989-03-01 | Journal of the American Statistical Association |