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This letter reports two moment extensions of the entropy of a distribution. By understanding the traditional entropy as the average of the original distribution up to a random variable transformation, the traditional moments equation become…
The ideas of aleatoric and epistemic uncertainty are widely used to reason about the probabilistic predictions of machine-learning models. We identify incoherence in existing discussions of these ideas and suggest this stems from the…
We propose a new perspective on Turbulence using Information Theory. We compute the entropy rate of a turbulent velocity signal and we particularly focus on its dependence on the scale. We first report how the entropy rate is able to…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
Uncertainty can be classified as either aleatoric (intrinsic randomness) or epistemic (imperfect knowledge of parameters). The majority of frameworks assessing infectious disease risk consider only epistemic uncertainty. We only ever…
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be compared. In this paper we argue that majorisation is a good candidate as a theory for uncertainty. We…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…
We analyze a distributed information network in which each node has access to the information contained in a limited set of nodes (its neighborhood) at a given time. A collective computation is carried out in which each node calculates a…
This paper examines the statistical properties of a distributional form that arises from pooled testing for the prevalence of a binary outcome. Our base distribution is a two-parameter distribution using a prevalence and excess intensity…
We present information value, a measure which quantifies the predictability of an utterance relative to a set of plausible alternatives. We introduce a method to obtain interpretable estimates of information value using neural text…
This paper begins with a description of methods for estimating image probability density functions that reflects the observation that such data is usually constrained to lie in restricted regions of the high-dimensional image space-not…
Distributed systems, such as biological and artificial neural networks, process information via complex interactions engaging multiple subsystems, resulting in high-order patterns with distinct properties across scales. Investigating how…
Diffusion models are loosely modelled based on non-equilibrium thermodynamics, where \textit{diffusion} refers to particles flowing from high-concentration regions towards low-concentration regions. In statistics, the meaning is quite…
The log-normal distribution is used to describe the positive data, that it has skewed distribution with small mean and large variance. This distribution has application in many sciences for example medicine, economics, biology and…
Information entropy is applied to the state of knowledge of reaction amplitudes in pseudoscalar meson photoproduction, and a scheme is developed that quantifies the information content of a measured set of polarization observables. It is…
Shannon based his information theory on the notion of probability measures as it we developed by Kolmogorov. In this paper we study some fundamental problems in information theory based on expectation measures. In the theory of expectation…
A great deal of inference in statistics is based on making the approximation that a statistic is normally distributed. The error in doing so is generally $O(n^{-1/2})$ and can be very considerable when the distribution is heavily biased or…
We propose a new model for forming beliefs and learning about unknown probabilities (such as the probability of picking a red marble from a bag with an unknown distribution of coloured marbles). The most widespread model for such situations…
Stimulated by the need of describing useful notions related to information measures, we introduce the `pdf-related distributions'. These are defined in terms of transformation of absolutely continuous random variables through their own…
Multiparticle production processes provide valuable information about the mechanism of the conversion of the initial energy of projectiles into a number of secondaries by measuring their multiplicity distributions and their distributions in…