Related papers: Prequential probability: game-theoretic = measure …
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
It is well known that a Bayesian probability forecast for all future observations should be a probability measure in order to satisfy a natural condition of coherence. The main topics of this paper are the evolution of the Bayesian…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to…
Game-theoretic upper expectations are joint (global) probability models that mathematically describe the behaviour of uncertain processes in terms of supermartingales; capital processes corresponding to available betting strategies.…
We introduce a "high probability" framework for repeated games with incomplete information. In our non-equilibrium setting, players aim to guarantee a certain payoff with high probability, rather than in expected value. We provide a high…
Probability forecasts are intended to account for the uncertainties inherent in forecasting. It is suggested that from an end-user's point of view probability is not necessarily sufficient to reflect uncertainties that are not simply the…
Coherent sets of almost desirable gambles and credal sets are known to be equivalent models. That is, there exists a bijection between the two collections of sets preserving the usual operations, e.g. conditioning. Such a correspondence is…
We study the problems of sequential nonparametric two-sample and independence testing. Sequential tests process data online and allow using observed data to decide whether to stop and reject the null hypothesis or to collect more data,…
Using the game-theoretic framework for probability, Vovk and Shafer. have shown that it is always possible, using randomization, to make sequential probability forecasts that pass any countable set of well-behaved statistical tests. This…
Suppose we are given two probability measures on the set of one-way infinite finite-alphabet sequences and consider the question when one of the measures predicts the other, that is, when conditional probabilities converge (in a certain…
We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define several notions of randomness associated with interval, rather than precise,…
We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…
Bayesian probability theory is one of the most successful frameworks to model reasoning under uncertainty. Its defining property is the interpretation of probabilities as degrees of belief in propositions about the state of the world…
In this paper, we study the conjunction of possibility measures when they are interpreted as coherent upper probabilities, that is, as upper bounds for some set of probability measures. We identify conditions under which the minimum of two…
The paper aim is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of…
We present a theoretical framework of probabilistic learning derived by Maximum Probability (MP) Theorem shown in the current paper. In this probabilistic framework, a model is defined as an event in the probability space, and a model or…
In this article, we introduce a formal definition of the concept of probability tree and conduct a detailed and comprehensive study of its fundamental structural properties. In particular, we define what we term an inductive probability…
A theory is universal contextual if its prediction cannot be reproduced by an ontological model satisfying both preparation and measurement noncontextuality assumptions. In this report, we first generalize the logical proofs of quantum…
We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem appears to be new but is closely related to results…