Good sequential probability forecasting is always possible

Building on the game-theoretic framework for probability, we show that it is possible, using randomization, to make sequential probability forecasts that will pass any given battery of statistical tests. This result, an easy consequence of von Neumann’s minimax theorem, simplifles and generalizes work by earlier authors.

[1]  Vladimir Vovk,et al.  The game-theoretic capital asset pricing model , 2008, Int. J. Approx. Reason..

[2]  Per Martin-Löf,et al.  The Literature on von Mises' Kollektivs Revisited , 2008 .

[3]  Vladimir Vovk,et al.  Leading strategies in competitive on-line prediction , 2006, Theor. Comput. Sci..

[4]  Vladimir Vovk,et al.  Continuous and randomized defensive forecasting: unified view , 2007, ArXiv.

[5]  Vladimir Vovk,et al.  Defensive forecasting for optimal prediction with expert advice , 2007, ArXiv.

[6]  Peter,et al.  Game-theoretic probability and its uses , especially defensive forecasting , 2007 .

[7]  G. Shafer,et al.  The Sources of Kolmogorov’s Grundbegriffe , 2006, math/0606533.

[8]  Vladimir Vovk,et al.  On-Line Regression Competitive with Reproducing Kernel Hilbert Spaces , 2005, TAMC.

[9]  G. Shafer,et al.  Good randomized sequential probability forecasting is always possible , 2005 .

[10]  Vladimir Vovk.  Competitive on-line learning with a convex loss function , 2005, ArXiv.

[11]  Akimichi Takemura,et al.  Defensive Forecasting for Linear Protocols , 2005, ALT.

[12]  Vladimir Vovk,et al.  Non-asymptotic calibration and resolution , 2005, Theor. Comput. Sci..

[13]  Akimichi Takemura,et al.  Defensive Forecasting , 2005, AISTATS.

[14]  Sham M. Kakade,et al.  Deterministic calibration and Nash equilibrium , 2004, J. Comput. Syst. Sci..

[15]  Alvaro Sandroni,et al.  The reproducible properties of correct forecasts , 2003, Int. J. Game Theory.

[16]  Richard B. Scherl,et al.  A new understanding of subjective probability and its generalization to lower and upper prevision , 2003, Int. J. Approx. Reason..

[17]  Alvaro Sandroni,et al.  Calibration with Many Checking Rules , 2003, Math. Oper. Res..

[18]  Vladimir Vovk,et al.  A Game-Theoretic Explanation of the √(dt) Effect , 2003 .

[19]  Vladimir Vovk,et al.  Kolmogorov's Contributions to the Foundations of Probability , 2003, Probl. Inf. Transm..

[20]  Vladimir Vovk,et al.  Game-Theoretic Capital Asset Pricing in Continuous Time , 2001 .

[21]  E. Lehrer.  Any Inspection is Manipulable , 2001 .

[22]  G. Shafer,et al.  Probability and Finance: It's Only a Game! , 2001 .

[23]  D. Fudenberg,et al.  An Easier Way to Calibrate , 1999 .

[24]  David Oakes,et al.  Self-Calibrating Priors Do Not Exist , 1985 .

[25]  A. Kolmogorov.  On Logical Foundations of Probability Theory , 1983 .

[26]  Yu. A. Gur'yan,et al.  Parts I and II , 1982 .

[27]  R Š Lipcer,et al.  ON THE QUESTION OF ABSOLUTE CONTINUITY AND SINGULARITY OF PROBABILITY MEASURES , 1977 .

[28]  Claus-Peter Schnorr,et al.  Zufälligkeit und Wahrscheinlichkeit - Eine algorithmische Begründung der Wahrscheinlichkeitstheorie , 1971, Lecture Notes in Mathematics.

[29]  Claus Peter Schnorr.  über die Definition von effektiven Zufallstests , 1970 .

[30]  Andrei N. Kolmogorov,et al.  Logical basis for information theory and probability theory , 1968, IEEE Trans. Inf. Theory.

[31]  J. Curtiss.  An Elementary Mathematical Model for the Interpretation of Precipitation Probability Forecasts , 1968 .

[32]  A. Kolmogorov.  Three approaches to the quantitative definition of information , 1968 .

[33]  Per Martin-Löf,et al.  The Definition of Random Sequences , 1966, Inf. Control..

[34]  L. Schmetterer.  Zeitschrift fur Wahrscheinlichkeitstheorie und Verwandte Gebiete. , 1963 .

[35]  D. Blackwell,et al.  Merging of Opinions with Increasing Information , 1962 .

[36]  A. N. Kolmogorov,et al.  Foundations of the theory of probability , 1960 .

[37]  Karl R. Popper,et al.  Degree of Confirmation , 1954 .

[38]  J. Doob.  Stochastic processes , 1953 .

[39]  G. Brier.  VERIFICATION OF FORECASTS EXPRESSED IN TERMS OF PROBABILITY , 1950 .

[40]  A. Church.  On the concept of a random sequence , 1940 .

[41]  Jean-Luc Ville.  Étude critique de la notion de collectif , 1939 .

[42]  A. Kolmogoroff.  Grundbegriffe der Wahrscheinlichkeitsrechnung , 1933 .

[43]  A. Kolmogoroff.  Über das Gesetz des iterierten Logarithmus , 1929 .

[44]  R. Mises.  Grundlagen der Wahrscheinlichkeitsrechnung , 1919 .