Related papers: Sets and Probability
In this paper we study different concepts of independence for convex sets of probabilities. There will be two basic ideas for independence. The first is irrelevance. Two variables are independent when a change on the knowledge about one…
This paper presents an advance in the direction of working with probabilities in a paracomplete setting using Logics of Formal Undeterminedness (LFUs). The undeterminedness is interpreted here as missing evidence. A theorem of total…
Two examples of the situation when the classical observables should be described by a noncommutative probability space are investigated. Possible experimental approach to find quantum-like correlations for classical disordered systems is…
We introduce the notion of evolution on sets and study several sets endowed with this structure and obtain some results about this new notion.
Soft set theory provides a direct framework for parameterized decision modeling by assigning to each attribute (parameter) a subset of a given universe, thereby representing uncertainty in a structured way [1, 2]. Over the past decades, the…
Multi-class classification methods that produce sets of probabilistic classifiers, such as ensemble learning methods, are able to model aleatoric and epistemic uncertainty. Aleatoric uncertainty is then typically quantified via the Bayes…
We seek random versions of some classical theorems on complex approximation by polynomials and rational functions, as well as investigate properties of random compact sets in connection to complex approximation.
We define a notion of randomness for individual and collections of formal languages based on automatic martingales acting on sequences of words from some underlying domain. An automatic martingale bets if the incoming word belongs to the…
A new class of probability distributions closely connected to generalized hyperbolic distributions is introduced. It is more adapted to study the distributions of sums of random number of random variables. The properties of these…
We prove a central limit theorem for a sequence of random variables whose means are ambiguous and vary in an unstructured way. Their joint distribution is described by a set of measures. The limit is (not the normal distribution and is)…
The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a…
We introduce a framework to describe probabilistic models in Bell experiments, and more generally in contextuality scenarios. Such a scenario is a hypergraph whose vertices represent elementary events and hyperedges correspond to…
The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.
A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…
For a stochastic process reset at random times, we discuss to what extent the probabilities of some orderings of observables associated with the intervals of time between resetting events are universal, i.e., independent of the choice of…
We define k-genericity and k-largeness for a subset of a group, and determine the value of k for which a k-large subset of G^n is already the whole of G^n , for various equationally defined subsets. We link this with the inner measure of…
Interpretation of the nonclassical total probability formula arising in some quantum experiments is provided based on stochastic models described by means of a sequence of random vectors changing in the measurement procedures.
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
This paper provides a thorough introduction to the causal set hypothesis aimed at students, and other interested persons, with some knowledge of general relativity and nonrelativistic quantum mechanics. I elucidate the arguments for why the…
We introduce the concept of numeraires of convex sets in the nonnegative orthant of the topological vector space of all random variables built over a probability space. A necessary and sufficient condition for an element of a convex set to…