Related papers: On the connection between probability boxes and po…
The problem of combining p-values is an old and fundamental one, and the classic assumption of independence is often violated or unverifiable in many applications. There are many well-known rules that can combine a set of arbitrarily…
In this paper we propose a method to construct probability measures on the space of convex bodies with a given pushforward distribution. Concretely we show that there is a measure on the metric space of centrally symmetric convex bodies,…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
In this paper we present a surprisingly general extension of the main result of a paper that appeared in this journal: I. Montes et al., Sklar's theorem in an imprecise setting, Fuzzy Sets and Systems, 278 (2015), 48--66. The main tools we…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
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…
The p-values are often implicitly used as a measure of evidence for the hypotheses of the tests. This practice has been analyzed with different approaches. It is generally accepted for the one-sided hypothesis problem, but it is often…
We describe the interface between measure theoretic probability and causal inference by constructing causal models on probability spaces within the potential outcomes framework. We find that measure theory provides a precise and instructive…
We propose a scheme that can realize a class of positive-operator-valued measures (POVMs) by performing a sequence of projective measurements on the original system, in the sense that for an arbitrary input state the probability…
Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…
The general notion of a stochastic ordering is that one probability distribution is smaller than a second one if the second attaches more probability to higher values than the first. Motivated by recent work on barycentric maps on spaces of…
We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…
The equivalence of the characteristic function approach and the probabilistic approach to monotone and boolean convolutions is proven for non-compactly supported probability measures. A probabilistically motivated definition of the…
Motivated by recent developments on calculus in metric measure spaces $(X,\mathsf d,\mathfrak m)$, we prove a general duality principle between Fuglede's notion of $p$-modulus for families of finite Borel measures in $(X,\mathsf d)$ and…
A general notion of algebraic conditional plausibility measures is defined. Probability measures, ranking functions, possibility measures, and (under the appropriate definitions) sets of probability measures can all be viewed as defining…
A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…
We provide mathematicaly rigorous justification of using term "probability" in connection to the so called non-signalling theories,known also as Popescu's and Rohrlich's box worlds. No only do we prove correctness of these models (in the…
We axiomatically introduce risk-consistent conditional systemic risk measures defined on multidimensional risks. This class consists of those conditional systemic risk measures which can be decomposed into a state-wise conditional…
A sequence $x_1,\dots,x_n,\dots$ of discrete-valued observations is generated according to some unknown probabilistic law (measure) $\mu$. After observing each outcome, one is required to give conditional probabilities of the next…
Recently, it has been emphasized that the possibility theory framework allows us to distinguish between i) what is possible because it is not ruled out by the available knowledge, and ii) what is possible for sure. This distinction may be…