Related papers: A Bayesian Nonparametric Estimation to Entropy
The empirical distribution function assigns mass $1/n$ to each of the $n$ observations in a sample. As these are highly variable, estimation error may be reduced by replacing them with estimated observations that are asymptotically less…
Maximum likelihood estimators are proposed for the parameters and the densities in a semiparametric density ratio model in which the nonparametric baseline density is approximated by the Bernstein polynomial model. The EM algorithm is used…
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…
We provide a general method to analyze the asymptotic properties of a variety of estimators of continuous time diffusion processes when the data are not only discretely sampled in time but the time separating successive observations may…
When we use simulation to assess the performance of stochastic systems, the input models used to drive simulation experiments are often estimated from finite real-world data. There exist both input model and simulation estimation…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
Entropy is a measure of the randomness of a system. Estimating the entropy of a quantum state is a basic problem in quantum information. In this paper, we introduce a time-efficient quantum approach to estimating the von Neumann entropy…
Tsallis entropy is a generalized diversity index first derived in Patil and Taillie (1982) and then rediscovered in community ecology by Keylock (2005). Bayesian nonparametric estimation of Shannon entropy and Simpson's diversity under…
We study a parametric estimation problem related to moment condition models. As an alternative to the generalized empirical likelihood (GEL) and the generalized method of moments (GMM), a Bayesian approach to the problem can be adopted,…
Entropy is a measure of heterogeneity widely used in applied sciences, often when data are collected over space. Recently, a number of approaches has been proposed to include spatial information in entropy. The aim of entropy is to…
Entropy estimation plays a significant role in biology, economics, physics, communication engineering and other disciplines. It is increasingly used in software engineering, e.g. in software confidentiality, software testing, predictive…
This paper introduces a family of recursively defined estimators of the parameters of a diffusion process. We use ideas of stochastic algorithms for the construction of the estimators. Asymptotic consistency of these estimators and…
Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…
The Shannon entropy, and related quantities such as mutual information, can be used to quantify uncertainty and relevance. However, in practice, it can be difficult to compute these quantities for arbitrary probability distributions,…
This paper studies nonparametric empirical Bayes methods in a heterogeneous parameters framework that features unknown means and variances. We provide extended Tweedie's formulae that express the (infeasible) optimal estimators of…
We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved…
Mutual Information (MI) is a crucial measure for capturing dependencies between variables, but exact computation is challenging in high dimensions with intractable likelihoods, impacting accuracy and robustness. One idea is to use an…
There is no easy extension of Kaplan-Meier and Nelson-Aalen estimators to the bivariate case, and estimating bivariate survival distributions nonparametrically is associated with various non-trivial problems. The Dabrowska estimator will…
The likelihood function is central to both frequentist and Bayesian formulations of parametric statistical inference, and large-sample approximations to the sampling distributions of estimators and test statistics, and to posterior…
Baez, Fritz, and Leinster derived a method for characterizing Shannon entropy in classical systems. In this method, they considered a functor from a certain category to the monoid of non-negative real numbers with addition as a map from…