Related papers: A new approach for imprecise probabilities

To answer questions of "causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is…

We define the empiric stochastic stability of an invariant measure in the finite-time scenario, the classical definition of stochastic stability. We prove that an invariant measure of a continuous system is empirically stochastically stable…

How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to…

We use the martingale-theoretic approach of game-theoretic probability to incorporate imprecision into the study of randomness. In particular, we define a notion of computable randomness associated with interval, rather than precise,…

Stochastic dominance has not been too employed in practice due to its important limitations. To increase its versatility, the concept has recently been adapted by introducing various indices that measure the degree to which one probability…

We explore precision in a measurement process incorporating pure probe states, unitary dynamics and complete measurements via a simple formalism. The concept of `information complement' is introduced. It undermines measurement precision and…

The Improbability Scale (IS) is proposed as a way of communicating to the general public the improbability (and by implication, the probability) of events predicted as the result of scientific research. Through the use of the Improbability…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…

When knowledge is obtained from a database, it is only possible to deduce confidence intervals for probability values. With confidence intervals replacing point values, the results in the set covering model include interval constraints for…

We revisit the definitions of error and disturbance recently used in error-disturbance inequalities derived by Ozawa and others by expressing them in the reduced system space. The interpretation of the definitions as mean-squared deviations…

The problem of comparing concepts of dependence in general rough sets with those in probability theory had been initiated by the present author in some of her recent papers. This problem relates to the identification of the limitations of…

Dempster-Shafer theory of imprecise probabilities has proved useful to incorporate both nonspecificity and conflict uncertainties in an inference mechanism. The traditional Bayesian approach cannot differentiate between the two, and is…

The concept of typicality refers to properties holding for the "overwhelming majority" of cases and is a fundamental idea of the qualitative approach to dynamical problems. We argue that measure-theoretical typicality would be the adequate…

We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.

We examine a new approach to modeling uncertainty based on plausibility measures, where a plausibility measure just associates with an event its plausibility, an element is some partially ordered set. This approach is easily seen to…

In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test…

For frequentist settings in which parameter randomness represents variability rather than uncertainty, the ideal measure of the support for one hypothesis over another is the difference in the posterior and prior log odds. For situations in…

This paper considers the problem of making statistical inferences about a parameter when a narrow interval centred at a given value of the parameter is considered special, which is interpreted as meaning that there is a substantial degree…

The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning.This paper introduces a new entropy measure, called the t-entropy, which exploits the concavity of the inverse-tan function. We analytically…