**Prequential probability: game-theoretic = measure theoretic.** / Vovk, Vladimir.

Research output: Working paper

Published

**Prequential probability: game-theoretic = measure theoretic.** / Vovk, Vladimir.

Research output: Working paper

@techreport{3b0701ba020f4b33b593bf88f45eac3c,

title = "Prequential probability: game-theoretic = measure theoretic",

abstract = "This article continues study of the prequential framework for evaluating aprobability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using prequential notions of probability. It turns out that there are two natural notions of probability in the prequential framework: game-theoretic, whose idea goes back to von Mises and Ville, and measure-theoretic, whose idea goes back to Kolmogorov. The main result of this article is that, in the caseof predicting binary outcomes, the two notions of probability in fact coincide on the analytic sets (in particular, on the Borel sets).",

keywords = "math.ST, stat.TH",

author = "Vladimir Vovk",

note = "16 pages",

year = "2009",

month = may,

day = "11",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Prequential probability: game-theoretic = measure theoretic

AU - Vovk, Vladimir

N1 - 16 pages

PY - 2009/5/11

Y1 - 2009/5/11

N2 - This article continues study of the prequential framework for evaluating aprobability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using prequential notions of probability. It turns out that there are two natural notions of probability in the prequential framework: game-theoretic, whose idea goes back to von Mises and Ville, and measure-theoretic, whose idea goes back to Kolmogorov. The main result of this article is that, in the caseof predicting binary outcomes, the two notions of probability in fact coincide on the analytic sets (in particular, on the Borel sets).

AB - This article continues study of the prequential framework for evaluating aprobability forecaster. Testing the hypothesis that the sequence of forecasts issued by the forecaster is in agreement with the observed outcomes can be done using prequential notions of probability. It turns out that there are two natural notions of probability in the prequential framework: game-theoretic, whose idea goes back to von Mises and Ville, and measure-theoretic, whose idea goes back to Kolmogorov. The main result of this article is that, in the caseof predicting binary outcomes, the two notions of probability in fact coincide on the analytic sets (in particular, on the Borel sets).

KW - math.ST

KW - stat.TH

M3 - Working paper

BT - Prequential probability: game-theoretic = measure theoretic

ER -