Related papers: Non-Archimedean Probability
We construct in a rigorous mathematical way interacting quantum field theories on a p-adic spacetime. The main result is the construction of a measure on a function space which allows a rigorous definition of the partition function. The…
Many theorems about Kolmogorov complexity rely on existence of combinatorial objects with specific properties. Usually the probabilistic method gives such objects with better parameters than explicit constructions do. But the probabilistic…
Stochastic processes on topological vector spaces over non-Archimedean fields and with transition measures having values in non-Archimedean fields are defined and investigated. For this the non-Archimedean analog of the Kolmogorov theorem…
The paper studies the notion of supposition encoded in non-Archimedean conditional probability (and revealed in the acceptance of the so-called indicative conditionals). The notion of qualitative change of view that thus arises is…
We are living in the big data era, as current technologies and networks allow for the easy and routine collection of data sets in different disciplines. Bayesian Statistics offers a flexible modeling approach which is attractive for…
We establish an equivalence between two seemingly different theories: one is the traditional axiomatisation of incomplete preferences on horse lotteries based on the mixture independence axiom; the other is the theory of desirable gambles…
We show from a categorical point of view that probability measures on certain measurable or topological spaces arise canonically as the extension of probability distributions on countable sets. We do this by constructing probability monads…
We propose a new approach that combines multiple non-parametric likelihood-type components to build a data-driven approximation of the true likelihood function. Our approach is built on empirical likelihood, a non-parametric approximation…
This paper introduces a novel concept of interval probability measures that enables the representation of imprecise probabilities, or uncertainty, in a natural and coherent manner. Within an algebra of sets, we introduce a notion of weak…
In a prequential approach to algorithmic randomness, probabilities for the next outcome can be forecast `on the fly' without the need for fully specifying a probability measure on all possible sequences of outcomes, as is the case in the…
Classical probability theory is based on assumptions which are often violated in practice. Therefore quantum probability is a proposed alternative not only in quantum physics, but also in other sciences. However, so far it mostly criticizes…
Given some non-Archimedean field $\mathbb{K}$ and some $\mathbb{K}$-linear space $X$, the usual way to define a norm over $X$ involves the {\em ultrametric inequality} $\|x+y\|\leq\max\{\|x\|,\|y\|\}$. In this note we will try to analyse…
We solve two longstanding major problems in Free Probability. This is achieved by generalising the theory to one with values in arbitrary commutative algebras. We prove the existence of the multi-variable $S$-transform, and show that it is…
The Principle of Complementarity of Probabilities based on of noncommutative probability is introduced.
In this paper, we develop a general theory on the coverage probability of random intervals defined in terms of discrete random variables with continuous parameter spaces. The theory shows that the minimum coverage probabilities of random…
Quantum Mechanics is a good example of a successful theory. Most of atomic phenomena are described well by quantum mechanics and cases such as Lamb Shift that are not described by quantum mechanics, are described by quantum electrodynamics.…
Archetypal analysis serves as an exploratory tool that interprets a collection of observations as convex combinations of pure (extreme) patterns. When these patterns correspond to actual observations within the sample, they are termed…
We consider, and make precise, a certain extension of the Radon-Nikodym derivative operator, to functions which are additive, but not necessarily sigma-additive, on a subset of a given sigma-algebra. We give applications to probability…
We study Kakeya sets over local non-archimedean fields with a probabilistic point of view: we define a probability measure on the set of Kakeya sets as above and prove that, according to this measure, almost all non-archimedean Kakeya sets…
We define and study a probability monad on the category of complete metric spaces and short maps. It assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich-Wasserstein…