Related papers: Plausibility measures on test spaces
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…
I propose a general quantum hypothesis testing theory that enables one to test hypotheses about any aspect of a physical system, including its dynamics, based on a series of observations. For example, the hypotheses can be about the…
In this work, we elaborate on a measure-theoretic approach to negative probabilities. We study a natural notion of contextuality measure and characterize its main properties. Then, we apply this measure to relevant examples of quantum…
Collapsibility deals with the conditions under which a conditional (on a covariate W) measure of association between two random variables X and Y equals the marginal measure of association, under the assumption of homogeneity over the…
Probabilistic concurrent systems are foundational models for modern mobile computing. In this paper, a unifying approach to probabilistic testing equivalences is proposed. With the help of a new distribution-based semantics for…
Measurement incompatibility describes two or more quantum measurements whose expected joint outcome on a given system cannot be defined. This purely non-classical phenomenon provides a necessary ingredient in many quantum information tasks…
Given a universe of discourse X-a domain of possible outcomes-an experiment may consist of selecting one of its elements, subject to the operation of chance, or of observing the elements, subject to imprecision. A priori uncertainty about…
Various semantics for studying the square of opposition and the hexagon of opposition have been proposed recently. We interpret sentences by imprecise (set-valued) probability assessments on a finite sequence of conditional events. We…
Preparation and measurement of physical systems are the operational building blocks of any physical experiment, and to describe them is the first purpose of any physical theory. It is remarkable that, in some situations, even when only…
Aumann's famous Agreeing to Disagree Theorem states that if a group of agents share a common prior, update their beliefs by Bayesian conditioning based on private information, and have common knowledge of their posterior beliefs regarding…
We consider highly inaccurate measurements made on classical stochastic and quantum systems. In the quantum case such a \e{weak} measurement preserves coherence between the system's alternatives. We demonstrate that in both cases the…
We present a comparative study between classical probability and quantum probability from the Bayesian viewpoint, where probability is construed as our rational degree of belief on whether a given statement is true. From this viewpoint,…
We consider the question of characterising the incompatibility of sets of high-dimensional quantum measurements. We introduce the concept of measurement incompatibility in subspaces. That is, starting from a set of measurements that is…
P-values are a mainstay in statistics but are often misinterpreted. We propose a new interpretation of p-value as a meaningful plausibility, where this is to be interpreted formally within the inferential model framework. We show that, for…
A long noted difficulty when assessing the reliability (or calibration) of forecasting systems is that reliability, in general, is a hypothesis not about a finite dimensional parameter but about an entire functional relationship. A…
In science, the most widespread statistical quantities are perhaps $p$-values. A typical advice is to reject the null hypothesis $H_0$ if the corresponding p-value is sufficiently small (usually smaller than 0.05). Many criticisms regarding…
This paper introduces a qualitative measure of ambiguity and analyses its relationship with other measures of uncertainty. Probability measures relative likelihoods, while ambiguity measures vagueness surrounding those judgments. Ambiguity…
According to a standard view, quantum mechanics (QM) is a contextual theory and quantum probability does not satisfy Kolmogorov's axioms. We show, by considering the macroscopic contexts associated with measurement procedures and the…
We prove a de Finetti theorem for exchangeable sequences of states on test spaces, where a test space is a generalization of the sample space of classical probability theory and the Hilbert space of quantum theory. The standard classical…
Contextuality is a central property in comparative analysis of classical, quantum, and supercorrelated systems. We examine and compare two well-motivated approaches to contextuality. One approach ("contextuality-by-default") is based on the…