Related papers: On Weighted Residual and Past Entropies
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
We consider a Bayesian problem of estimating of probability of success in a series of conditionally independent trials with binary outcomes. We study the asymptotic behaviour of differential entropy for posterior probability density…
The method of Maximum (relative) Entropy (ME) is used to translate the information contained in the known form of the likelihood into a prior distribution for Bayesian inference. The argument is guided by intuition gained from the…
In this paper, we introduce weighted fractional generalized cumulative past entropy of a nonnegative absolutely continuous random variable with bounded support. Various properties of the proposed weighted fractional measure are studied.…
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. This allows us to calculate the complexity of phenomena for which distributions are known. We…
We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find…
In the previous papers (Kui\'{c} et al. in Found Phys 42:319-339, 2012; Kui\'{c} in arXiv:1506.02622, 2015), it was demonstrated that applying the principle of maximum information entropy by maximizing the conditional information entropy,…
The transfer entropy is a well-established measure of information flow, which quantifies directed influence between two stochastic time series and has been shown to be useful in a variety fields of science. Here we introduce the transfer…
We present an entropy comparison result concerning weighted sums of independent and identically distributed random variables.
The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies…
Human dynamical social networks encode information and are highly adaptive. To characterize the information encoded in the fast dynamics of social interactions, here we introduce the entropy of dynamical social networks. By analysing a…
The time variation of entropy, as an alternative to the variance, is proposed as a measure of the diffusion rate. It is shown that for linear and time-translationally invariant systems having a large-time limit for the density, at large…
We show how the shared information between the past and future---the excess entropy---derives from the components of directional information stored in the present---the predictive and retrodictive causal states. A detailed proof allows us…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
Preserving biodiversity and ecosystem stability is a challenge that can be pursued through modern statistical mechanics modeling. Here we introduce a variational maximum entropy-based algorithm to evaluate the entropy in a minimal ecosystem…
Recently, authors have studied weighted version of Kerridge inaccuracy measure for truncated distributions. In the present communication we introduce the notion of weighted interval inaccuracy measure for two-sided truncated random…
The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
We propose utilizing entropy as a diagnostic tool to distinguish between constant and dynamical dark energy models. Entropy, a measure of the system's disorder or information content, captures the complexity and evolution of the universe.…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…