Prequential Probability: Principles and Properties

Prequential Probability: Principles and Properties

Forcaster has to predict, sequentially, a string of uncertain quantities (X1,X2,... ), whose values are determined and revealed, one by one, by Nature. Various criteria may be proposed to assess Forecaster's empirical performance. The weak prequential principle requires that such a criterion sh...

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Veröffentlicht in:Bernoulli. - International Statistical Institute and Bernoulli Society for Mathematical Statistics and Probability, 1995. - 5(1999), 1, Seite 125-162
1. Verfasser: Dawid, A. Philip (VerfasserIn)
Weitere Verfasser: Vovk, Vladimir G.
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1999
Zugriff auf das übergeordnete Werk:Bernoulli
Schlagworte:Farthingale Forecasting Goodness of fit Limit theorems of probability theory Martingale Perfect-information game Strong prequential principle Weak prequential principle Mathematics Environmental studies Behavioral sciences
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520 |a Forcaster has to predict, sequentially, a string of uncertain quantities (X1,X2,... ), whose values are determined and revealed, one by one, by Nature. Various criteria may be proposed to assess Forecaster's empirical performance. The weak prequential principle requires that such a criterion should depend on Forecaster's behaviour or strategy only through the actual forecasts issued. A wide variety of appealing criteria are shown to respect this principle. We further show that many such criteria also obey the strong prequential principle, which requires that, when both Nature and Forecaster make their choices in accordance with a common joint distribution P for (X1,X2,... ), certain stochastic properties, underlying and justifying the criterion and inferences based on it, hold regardless of the detailed specification of P. In order to understand further this compliant behaviour, we introduce the prequential framework, a game-theoretic basis for probability theory in which it is impossible to violate the prequential principles, and we describe its connections with classical probability theory. In this framework, in order to show that some criterion for assessing Forecaster's empirical performance is valid, we have to exhibit a winning strategy for a third player, Statistician, in a certain perfect-information game. We demonstrate that many performance criteria can be formulated and are valid in this framework and, therefore, satisfy both prequential principles. 
540 |a Copyright 1999 International Statistical Institute/Bernoulli Society 
650 4 |a Farthingale 
650 4 |a Forecasting 
650 4 |a Goodness of fit 
650 4 |a Limit theorems of probability theory 
650 4 |a Martingale 
650 4 |a Perfect-information game 
650 4 |a Strong prequential principle 
650 4 |a Weak prequential principle 
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650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Applied statistics  |x Statistical results  |x Statistical forecasts 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Probabilities 
650 4 |a Environmental studies  |x Atmospheric sciences  |x Meteorology  |x Meteorological research  |x Weather forecasting 
650 4 |a Mathematics  |x Applied mathematics  |x Analytics  |x Predictive analytics  |x Analytical forecasting  |x Forecasting models 
650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables  |x Stochastic processes  |x Martingales 
650 4 |a Mathematics  |x Mathematical expressions  |x Mathematical functions  |x Transcendental functions  |x Logarithms 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Statistical theories 
650 4 |a Mathematics  |x Applied mathematics  |x Statistics  |x Statistical theories  |x Law of large numbers 
650 4 |a Behavioral sciences  |x Leisure studies  |x Recreation  |x Games 
655 4 |a research-article 
700 1 |a Vovk, Vladimir G.  |e verfasserin  |4 aut 
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773 1 8 |g volume:5  |g year:1999  |g number:1  |g pages:125-162 
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856 4 0 |u https://doi.org/10.2307/3318616  |3 Volltext 
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