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Efficient testing of forecasts. (English) Zbl 1206.62156
Lin, Guohui (ed.), Computing and combinatorics. 13th annual international conference, COCOON 2007, Banff, Canada, July 16–19, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-73544-1/pbk). Lecture Notes in Computer Science 4598, 285-295 (2007).
Summary: Each day a weather forecaster predicts a probability of 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 possessing predicting power. Consider tests such that forecasters who know the distribution of nature are passed with high probability. A. Sandroni showed that any such test can be passed by a forecaster who has no prior knowledge of nature [Int. J. Game Theory 32, No. 1, 151–159 (2003; Zbl 1071.62084)], provided that the duration \(n\) is known to the forecaster in advance. On the other hand, L. Fortnow and F. V. Vohra [Econometrica 77, No. 1, 93–105 (2009; Zbl 1160.91396)] show that Sandroni’s result may require forecasters with high computational complexity and is thus of little practical relevance in some cases. We consider 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 forecasters even more powerful than the above ones are required for Sandroni’s result. Also, we show that Sandroni’s result does not apply when the duration \(n\) is not known to the forecaster in advance.
For the entire collection see [Zbl 1119.68012].
MSC:
62M20 Inference from stochastic processes and prediction
62P12 Applications of statistics to environmental and related topics
68U99 Computing methodologies and applications
91A99 Game theory
62A01 Foundations and philosophical topics in statistics
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