Beschreibung
The quality of forecasts is commonly assessed in terms of loss functions. We review the paradigm that these loss functions should incentivise truthful forecasts in that they are minimised in expectation by an optimal forecast. Optimality is specified in terms of a functional of the underlying probability distribution, such as the mean, the variance, or the whole probability distribution itself.Many interesting functionals are non-unique or set-valued, such as prediction intervals. There are typically multiple intervals obtaining a pre-specified coverage, say 95%.
We argue that in such situations one must thoroughly distinguish the possible form of forecasts: Exhaustive ones, being set-valued and aiming at correctly specifying the entire functional, and selective forecasts, content with solely specifying a single point in the correct functional.
This distinction leads to two different types of loss functions. We show a mutual exclusivity result: A set-valued functional can admit incentive compatible forecasts either for selective forecasts, or for exhaustive forecasts, or not at all.
These concepts are illustrated in terms of the class of prediction intervals.
The presentation is based on the recent preprint https://arxiv.org/abs/1910.07912v2.
| Zeitraum | 26 Okt. 2020 → 28 Okt. 2020 |
|---|---|
| Ereignistitel | 40th International Symposium on Forecasting |
| Veranstaltungstyp | Keine Angaben |
| Bekanntheitsgrad | International |