## Good randomized sequential probability forecasting is always possible (2005)

Citations: | 23 - 12 self |

### BibTeX

@MISC{Vovk05goodrandomized,

author = {Vladimir Vovk and Glenn Shafer},

title = {Good randomized sequential probability forecasting is always possible },

year = {2005}

}

### Years of Citing Articles

### OpenURL

### Abstract

### Citations

1688 | An Introduction to Kolmogorov Complexity and Its Applications
- Li, Vitányi
- 1997
(Show Context)
Citation Context ...fails, whether on the entire sequence or on a subsequence, a statistical test has been failed. But as Ville (1939) demonstrated, there are other statistical tests that go beyond calibration (see also =-=Li and Vitányi 1997-=-, p. 313). We can check, for example, whether the convergence required by calibration is at the rate required the law of the iterated logarithm In the measure-theoretic framework, violation of the law... |

332 |
The definition of random sequences
- Martin-Löf
- 1966
(Show Context)
Citation Context ...t. In the usual measure-theoretic framework for probability, an asymptotic statistical test can be defined by specifying an event of probability zero; the test is passed if the event does not happen (=-=Martin-Löf 1966-=-). In our framework, a statistical test is a betting strategy for the sceptic; the test is passed if the sceptic does not become infinitely rich. Because we consider any betting strategy for sceptic (... |

171 |
Statistical theory: the prequential approach
- Dawid
- 1984
(Show Context)
Citation Context ...ssertion can be refuted when the sequence is observed, and if it is not refuted then Forecaster can avoid refutation himself only by agreeing with P ’s predictions in the limit (Vovk and Shafer 2004; =-=Dawid 1984-=-, p. 281). But there seems to be very little content in the assertion that a sequence is governed by a completely unknown probability distribution. When he follows the strategy suggested by the proof ... |

155 | Kolmogoroff): Grundbegriffe der Wahrscheinlichkeitsrechnung - Kolmogorov - 1933 |

136 | Probability and Finance: It’s Only a Game
- Shafer, Vovk
- 2001
(Show Context)
Citation Context ...uence of von Neumann’s minimax theorem, simplifies and generalizes work by earlier authors. Keywords: probability forecasting; calibration; game-theoretic probability 1 Introduction In a recent book (=-=Shafer and Vovk, 2001-=-), we introduced a purely game-theoretic framework for probability theory. In this article, we build on that framework to demonstrate the possibility of good probability forecasting. In Section 2, we ... |

106 | Étude Critique de la Notion de Collectif - Ville - 1939 |

70 | Asymptotic calibration
- Foster, Vohra
- 1998
(Show Context)
Citation Context ... So far as mathematical technique is concerned, this article holds little novelty, for our argument from the minimax theorem was already used by some of the authors concerned with proper calibration (=-=Foster and Vohra 1998-=-, Fudenberg 1999, Sandroni et al. 2003). Our contribution is to put the argument in our game-theoretic framework and to show that it can lead to forecasts with stochastic properties going beyond calib... |

32 | The Reproducible Properties of Correct Forecasts - Sandroni - 2003 |

20 | An Easier Way to Calibrate - Fudenberg, Levine - 1999 |

16 | Any inspection is manipulable - Lehrer - 2001 |

14 |
On logical foundations of probability theory
- Kolmogorov
- 1983
(Show Context)
Citation Context ...em descriptions of the past rather than predictions of the future. 16sKolmogorov once expressed puzzlement about the appearance in the real world of the kind of irregularity described by probability (=-=Kolmogorov 1983-=-, p. 1): In everyday language we call random those phenomena where we cannot find a regularity allowing us to predict precisely their results. Generally speaking there is no ground to believe that ran... |

13 | Defensive forecasting - Vovk, Takemura, et al. - 2005 |

12 | Grundlagen der Wahrscheinlichkeitsrechnung - MISES - 1919 |

11 | Self-calibrating priors do not exist (with discussion - Oakes - 1985 |

10 | Die Widerspruchfreiheit des Kollectivbegriffes der Wahrscheinlichkeitsrechnung. Ergebnisse eines Mathematischen Kolloquiums - Wald - 1937 |

8 |
The origins and legacy of Kolmogorov’s Grundbegriffe. The Game-Theoretic Probability and Finance project, http://probabilityandfinance.com, Working Paper 4, October 2005. Part of this technical report (covering the Grundbegriffe and the period before its
- Shafer, Vovk
(Show Context)
Citation Context ...mall or zero probability will not happen has been considered fundamental to the interpretation of probability by many authors, including Kolmogorov (1933). It is sometimes called Cournot’s principle (=-=Shafer and Vovk 2004-=-). Within our game-theoretic framework, we use Cournot’s principle as another name for our hypothesis of the excluded gambling system. We conclude this brief review of the game-theoretic framework wit... |

7 | 2nd edn - Shiryaev, Probability - 1996 |

6 | Degree of Confirmation’ and Inductive Logic”. The Philosophy of Rudolf Carnap - Putnam - 1963 |

3 |
Good sequential probability forecasting is always possible
- Vovk, Shafer
- 2005
(Show Context)
Citation Context ...any observation. The assertion can be refuted when the sequence is observed, and if it is not refuted then Forecaster can avoid refutation himself only by agreeing with P ’s predictions in the limit (=-=Vovk and Shafer 2004-=-; Dawid 1984, p. 281). But there seems to be very little content in the assertion that a sequence is governed by a completely unknown probability distribution. When he follows the strategy suggested b... |

1 | Probability forecasting. Encyclopaedia of Statistical Sciences (eds - Dawid - 1986 |

1 | Calibration with many checking rules - V - 2003 |

1 | Non-asymptotic calibration and resolution. Working Paper #13, www.probabilityandfinance.com - Vovk - 2005 |

1 | Forecasting under stochasticity Suppose we fix a horizon N and a function T - unknown authors |