Related papers: Two ways game-theoretic probability can improve da…
In this paper, we propose a general method for testing composite hypotheses. Our idea is to use confidence limits to define stopping and decision rules. The requirements of operating characteristic function can be satisfied by adjusting the…
Traditional statistical theory assumes that the analysis to be performed on a given data set is selected independently of the data themselves. This assumption breaks downs when data are re-used across analyses and the analysis to be…
Probabilistic properties of tennis scoring systems are examined and compared with best-of-K systems. A model, where each player has his/her own probability of winning his/her service point and which remains invariant for the duration of the…
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…
In this paper, we present betting strategy of a football game using probability theory. We know all betting houses offer slightly unfair odds towards the player. Here we discuss a simple way to figure out which betting house is offering…
Kelly betting is a prescription for optimal resource allocation among a set of gambles which are typically repeated in an independent and identically distributed manner. In this setting, there is a large body of literature which includes…
Every interaction of a living organism with its environment involves the placement of a bet. Armed with partial knowledge about a stochastic world, the organism must decide its next step or near-term strategy, an act that implicitly or…
The main purpose of this study is to introduce a semi-classical model describing betting scenarios in which, at variance with conventional approaches, the payoff of the gambler is encoded into the internal degrees of freedom of a quantum…
The injunction to `analyze the way you randomize' is well-known to statisticians since Fisher advocated for randomization as the basis of inference. Yet even those convinced by the merits of randomization-based inference seldom follow this…
Probability forecasts of events are routinely used in climate predictions, in forecasting default probabilities on bank loans or in estimating the probability of a patient's positive response to treatment. Scoring rules have long been used…
This paper considers the use of observed and predicted match statistics as inputs to forecasts of the outcomes of football matches. It is shown that, were it possible to know the match statistics in advance, highly informative forecasts of…
Prediction markets are useful for estimating probabilities of claims whose truth will be revealed at some fixed time -- this includes questions about the values of real-world events (i.e. statistical uncertainty), and questions about the…
This paper develops a model-free sequential test for conditional independence. The proposed test allows researchers to analyze an incoming i.i.d. data stream with any arbitrary dependency structure, and safely conclude whether a feature is…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
This paper uses decision-theoretic principles to obtain new insights into the assessment and updating of probabilities. First, a new foundation of Bayesianism is given. It does not require infinite atomless uncertainties as did Savage s…
Shafer (2021) offers a betting perspective on statistical testing which may be useful for foundational debates, given that disputes over such testing continue to be intense. To be helpful for researchers, however, this perspective will need…
The notion of belief likelihood function of repeated trials is introduced, whenever the uncertainty for individual trials is encoded by a belief measure (a finite random set). This generalises the traditional likelihood function, and…
It is known that repeated gambling over the outcomes of independent and identically distributed (i.i.d.) random variables gives rise to alternate operational meaning of entropies in the classical case in terms of the doubling rates. We give…
Testing hypotheses is an issue of primary importance in the scientific research, as well as in many other human activities. Much clarification about it can be achieved if the process of learning from data is framed in a stochastic model of…
Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly…