Distributions Agreeing With Exchangeable Sequential Forecasting
| Autor: | Frank Lad, Romano Scozzafava |
|---|---|
| Rok vydání: | 2001 |
| Předmět: |
Statistics and Probability
General Mathematics Statistical parameter Conditional probability Coherence (philosophical gambling strategy) Function (mathematics) Combinatorics Statistics Probability mass function Statistics Probability and Uncertainty Statistical theory Sufficient statistic Event (probability theory) Mathematics |
| Zdroj: | The American Statistician. 55:131-139 |
| ISSN: | 1537-2731 0003-1305 |
| Popis: | We follow the lines of Bruno de Finetti's “fundamental theorem of prevision” to characterize a very large family of distributions that agree with exchangeable forecasts conditioned only on the sum of successes in a sequence of events. This agreement is despite the fact that the sum is not a sufficient statistic for the entire family of distributions. After some introductory exposition on exchangeability and sufficiency, we first derive the most general relation that coherency requires of the simultaneous assertion of a probability mass function for the sum of N + 1 ordered events, and a conditional probability function for the final event given each possible value of the sum of the first N events. We then apply this relation to characterize the family of all distributions on N + 1 events that agree with the exchangeable sequential forecasting equations. Surprisingly, this agreeing family is much larger than the family of exchangeable distributions, but is included within the family of all pairwise exchang... |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|