Related papers: New entropy estimates for the Oldroyd-B model, and…

In this paper, we study the optimal time decay rates for the higher order spatial derivatives of solutions to a diffusive Oldroyd-B model. As pointed out in the Section 1.2 of Huang-Wang-Wen-Zi (J. Differential Equations 306: 456-491,…

We develop a method, based on a Bochner-type identity, to obtain estimates on the exponential rate of decay of the relative entropy from equilibrium of Markov processes in discrete settings. When this method applies the relative entropy…

Inference for mechanistic models is challenging because of nonlinear interactions between model parameters and a lack of identifiability. Here we focus on a specific class of mechanistic models, which we term stable differential equations.…

The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably…

This paper establishes the global well-posedness of solutions to the Oldroyd-B model with purely horizontal viscosity and arbitrarily large initial data in two-dimensional settings, including the full space $\mathbb{R}^2$, the partially…

Computer simulations have been employed in recent years to evaluate the configurational entropy changes in model glass-forming liquids. We consider two methods, both of which involve the calculation of the `intra-basin' entropy as a means…

Statistical modeling often involves identifying an optimal estimate to some underlying probability distribution known to satisfy some given constraints. I show here that choosing as estimate the centroid, or center of mass, of the set…

The analyticity of the entropy and relative entropy rates of continuous-state hidden Markov models is studied here. Using the analytic continuation principle and the stability properties of the optimal filter, the analyticity of these rates…

In the article the $mm$-entropy (an entropy of a metric measure space) introduced by C. Shannon is evaluated for an $\alpha$-stable L\'evy process. For $\alpha<1$ the double-sided estimates of the same order are obtained for process…

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 analyzes identification issues of a behavorial New Keynesian model and estimates it using likelihood-based and limited-information methods with identification-robust confidence sets. The model presents some of the same…

For deterministic continuous time nonlinear control systems, epsilon-practical stabilization entropy and practical stabilization entropy are introduced. Here the rate of attraction is specified by a KL-function. Upper and lower bounds for…

The rate of entropy production provides a useful quantitative measure of a non-equilibrium system and estimating it directly from time-series data from experiments is highly desirable. Several approaches have been considered for stationary…

This study introduces a novel model that effectively captures asymmetric structures in multivariate contingency tables with ordinal categories. Leveraging the principle of maximum entropy, our approach employs f-divergence to provide a…

Estimating entropy production from real observation data can be difficult due to finite resolution in both space and time and finite measurement statistics. We characterize the statistical error introduced by finite sample size and compare…

The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…

A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…

Non-equilibrium stochastic dynamics of several active Brownian systems are modeled in terms of non-linear velocity dependent force. In general, this force may consist of both even and odd functions of velocity. We derive the expression for…

Estimation of permutation entropy (PE) using Bayesian statistical methods is presented for systems where the ordinal pattern sampling follows an independent, multinomial distribution. It is demonstrated that the PE posterior distribution is…

Accurately estimating uncertainties in neural network predictions is of great importance in building trusted DNNs-based models, and there is an increasing interest in providing accurate uncertainty estimation on many tasks, such as security…