Efficient testing of forecasts
Journal
International Journal of Foundations of Computer Science
Journal Volume
21
Journal Issue
1
Pages
61-72
Date Issued
2010
Author(s)
Chang, C.-L.
Abstract
Each day a weather forecaster predicts a probability for each type of weather for the next day. After n days, all the predicted probabilities and the real weather data are sent to a test which decides whether to accept the forecaster as having prior knowledge about the distribution of nature. Consider tests that accept with high probability forecasters who know the distribution of nature. Sandroni shows that any such test can be passed with high probability by a forecaster who has no prior knowledge about the distribution of nature, provided that the duration n is revealed to the forecaster in advance [14]. However, Fortnow and Vohra show that Sandroni's result requires forecasters with high computational complexity [6]. Consider the family F of forecasters who select a deterministic Turing-machine forecaster according to an arbitrary distribution and then use that machine for all future forecasts. We show that Sandroni's result requires forecasters even more powerful than those in F. We also show that Sandroni's result does not apply when the duration n is not revealed to the forecaster in advance. © 2010 World Scientific Publishing Company.
SDGs
Type
journal article