相关论文: Finitely additive beliefs and universal type space…
We introduce the $\Sigma_1$-definable universal finite sequence and prove that it exhibits the universal extension property amongst the countable models of set theory under end-extension. That is, (i) the sequence is $\Sigma_1$-definable…
Stemming from de Finetti's work on finitely additive coherent probabilities, the paradigm of coherence has been applied to many uncertainty calculi in order to remove structural restrictions on the domain of the assessment. Three possible…
We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome…
We define and study the independent natural extension of two local uncertainty models for the general case of infinite spaces, using the frameworks of sets of desirable gambles and conditional lower previsions. In contrast to Miranda and…
We study compressible types in the context of (local and global) NIP. By extending a result in machine learning theory (the existence of a bound on the recursive teaching dimension), we prove density of compressible types. Using this, we…
This article deals with plausible reasoning from incomplete knowledge about large-scale spatial properties. The availableinformation, consisting of a set of pointwise observations,is extrapolated to neighbour points. We make use of belief…
In statistical inference, confidence set procedures are typically evaluated based on their validity and width properties. Even when procedures achieve rate-optimal widths, confidence sets can still be excessively wide in practice due to…
The motivation for extending secret sharing schemes to cases when either the set of players is infinite or the domain from which the secret and/or the shares are drawn is infinite or both, is similar to the case when switching to abstract…
Confidence is a fundamental concept in statistics, but there is a tendency to misinterpret it as probability. In this paper, I argue that an intuitively and mathematically more appropriate interpretation of confidence is through…
Statistical models of natural stimuli provide an important tool for researchers in the fields of machine learning and computational neuroscience. A canonical way to quantitatively assess and compare the performance of statistical models is…
We show that if there exists a topologically expansive homeomorphism on a uniform space, then the space is always a regular space. Through examples we show that in general composition of topologically expansive homeomorphisms need not be…
Diversities have been recently introduced as a generalization of metrics for which a rich tight span theory could be stated. In this work we take up a number of questions about hyperconvexity, diversities and fixed points of nonexpansive…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Limit and Pseudotopological spaces are two generalizations of topological spaces which are defined by indicating what filters converge under some axioms. In this article, we introduce covering spaces and set forth some necessary conditions…
A metric space is indivisible if for any partition of it into finitely many pieces one piece contains an isometric copy of the whole space. Continuing our investigation of indivisible metric spaces, we show that a countable ultrametric…
In the author's PhD thesis (2019) universal envelopes were introduced as a tool for studying the continuously obtainable information on discontinuous functions. To any function $f \colon X \to Y$ between $\operatorname{qcb}_0$-spaces one…
We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…
A probabilistic secret sharing scheme is a joint probability distribution of the shares and the secret together with a collection of secret recovery functions. The study of schemes using arbitrary probability spaces and unbounded number of…
In this paper we study expansions of infinite dimensional Hilbert spaces with a unitary representation of a discrete countable group. When the group is finite, we prove the theory of the corresponding expansion, regardless if it is…
In concurrency theory, weak bisimilarity is often used to relate processes exhibiting the same observable behaviour. The probabilistic environment gives rise to several generalisations; we study the infinitary semantics, which abstracts…