Related papers: A game-theoretic version of Oakes' example for ran…
Statistical model checking (SMC) is a technique for analysis of probabilistic systems that may be (partially) unknown. We present an SMC algorithm for (unbounded) reachability yielding probably approximately correct (PAC) guarantees on the…
This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
Recently, it has been shown how sampling actions from the predictive distribution over the optimal action-sometimes called Thompson sampling-can be applied to solve sequential adaptive control problems, when the optimal policy is known for…
Calibration means that forecasts and average realized frequencies are close. We develop the concept of forecast hedging, which consists of choosing the forecasts so as to guarantee that the expected track record can only improve. This…
Foster and Hart proposed an operational measure of riskiness for discrete random variables. We show that their defining equation has no solution for many common continuous distributions including many uniform distributions, e.g. We show how…
Probabilistic classifiers output a probability distribution on target classes rather than just a class prediction. Besides providing a clear separation of prediction and decision making, the main advantage of probabilistic models is their…
We unify standard frameworks for approachability both in full or partial monitoring by defining a new abstract game, called the "purely informative game", where the outcome at each stage is the maximal information players can obtain,…
We study capital process behavior in the fair-coin game and biased-coin games in the framework of the game-theoretic probability of Shafer and Vovk (2001). We show that if Skeptic uses a Bayesian strategy with a beta prior, the capital…
Randomized benchmarking (RB) is a widely used strategy to assess the quality of available quantum gates in a computational context. RB involves applying known random sequences of gates to an initial state and using the statistics of a final…
This paper examines the relationship between Shafer's belief functions and convex sets of probability distributions. Kyburg's (1986) result showed that belief function models form a subset of the class of closed convex probability…
Continuous-time empirical dynamic discrete choice games offer notable computational advantages over discrete-time models. This paper addresses remaining computational and econometric challenges to further improve both model solution and…
The concept of biased Maker-Breaker games, introduced by Chv\'atal and Erd{\H o}s, is a central topic in the field of positional games, with deep connections to the theory of random structures. For any given hypergraph ${\cal H}$ the main…
We propose randomization tests of whether forecast 1 outperforms forecast 2 across a class of scoring functions. This hypothesis is of applied interest: While the prediction context often prescribes a certain class of scoring functions, it…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
Forecast of football outcomes in terms of Home Win, Draw and Away Win relies largely on ex ante probability elicitation of these events and ex post verification of them via computation of probability scoring rules (Brier, Ranked…
Discovery of an accurate causal Bayesian network structure from observational data can be useful in many areas of science. Often the discoveries are made under uncertainty, which can be expressed as probabilities. To guide the use of such…
Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational…
In this paper, we address the probabilistic error quantification of a general class of prediction methods. We consider a given prediction model and show how to obtain, through a sample-based approach, a probabilistic upper bound on the…
We introduce and study Swap Agnostic Learning. The problem can be phrased as a game between a predictor and an adversary: first, the predictor selects a hypothesis $h$; then, the adversary plays in response, and for each level set of the…