Related papers: Prequential probability: game-theoretic = measure …
We present a novel proof of de Finetti's Theorem characterizing permutation-invariant probability measures of infinite sequences of variables, so-called exchangeable measures. The proof is phrased in the language of Markov categories, which…
The probability `measure' for measurements at two consecutive moments of time is non-additive. These probabilities, on the other hand, may be determined by the limit of relative frequency of measured events, which are by nature additive. We…
This book introduces to the theory of probabilities from the beginning. Assuming that the reader possesses the normal mathematical level acquired at the end of the secondary school, we aim to equip him with a solid basis in probability…
The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…
The report suggests the concept of risk, outlining two mathematical structures necessary for risk genesis: the set of outcomes and, in a general case, partial order of preference on it. It is shown that this minimum partial order should…
Forecast reconciliation is an important research topic. Yet, there is currently neither formal framework nor practical method for the probabilistic reconciliation of count time series. In this paper we propose a definition of coherency and…
TThe problem is to identify a probability associated with a set of natural numbers, given an infinite data sequence of elements from the set. If the given sequence is drawn i.i.d. and the probability mass function involved (the target)…
The mathematics of classical probability theory was subsumed into classical measure theory by Kolmogorov in 1933. Quantum theory as nonclassical probability theory was incorporated into the beginnings of noncommutative measure theory by von…
Subjective probability is based on the intuitive idea that probability quantifies the degree of belief that an event will occur. A probability theory based on this idea represents the most general framework for handling uncertainty. A brief…
Causal inference in completely randomized treatment-control studies with binary outcomes is discussed from Fisherian, Neymanian and Bayesian perspectives, using the potential outcomes framework. A randomization-based justification of…
When prior information is lacking, the go-to strategy for probabilistic inference is to combine a "default prior" and the likelihood via Bayes's theorem. Objective Bayes, (generalized) fiducial inference, etc. fall under this umbrella. This…
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability…
We explore the interplay between random and deterministic phenomena using a representation of uncertainty based on the measure-theoretic concept of outer measure. The meaning of the analogues of different probabilistic concepts is…
Probabilistic forecasting relies on past observations to provide a probability distribution for a future outcome, which is often evaluated against the realization using a scoring rule. Here, we perform probabilistic forecasting with…
Kolmogorov's foundation of probability takes measure spaces, $\sigma$-algebras, and probability measures as basic objects. It is, however, widely recognized that this classical framework is inadequate for random phenomena involving quantum…
The presence of contextuality in quantum theory was first highlighted by Bell, Kochen and Specker, who discovered that for quantum systems of three or more dimensions, measurements cannot be viewed as revealing pre-existing properties of…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
The field of Game Theory provides a useful mechanism for modeling many decision-making scenarios. In participating in these scenarios individuals and groups adopt particular strategies, which generally perform with varying levels of…
We construct a probabilistic coherence measure for information sets which determines a partial coherence ordering. This measure is applied in constructing a criterion for expanding our beliefs in the face of new information. A number of…
One of quantum theory's salient features is its apparent indeterminism, i.e. measurement outcomes are typically probabilistic. We formally define and address whether this uncertainty is unavoidable or whether post-quantum theories can offer…