Prequential Randomness

This paper studies Dawid’s prequential framework from the point of view of the algorithmic theory of randomness. The main result is that two natural notions of randomness coincide. One notion is the prequential version of the standard definition due to Martin-L¨of, and the other is the prequential version of the martingale definition of randomness due to Schnorr. This is another manifestation of the close relation between the two main paradigms of randomness, typicalness and unpredictability. The algorithmic theory of randomness can be stripped of the algorithms and still give meaningful results; the typicalness paradigm then corresponds to Kolmogorov’s measure-theoretic probability and the unpredictability paradigm corresponds to game-theoretic probability. It is an open problem whether the main result of this paper continues to hold in the stripped version of the theory.

• Type: Conference
• Year: 2008
• Where: ALT
• Authors: Vladimir Vovk, Alexander Shen
• Keywords: Algorithmic Theory, ALT 2008, Machine Learning, Randomness Coincide, Unpredictability Paradigm Corresponds