Related papers: Maximum entropy methods as the bridge between macr…
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
The set of solutions inferred by the generic maximum entropy (MaxEnt) or maximum relative entropy (MaxREnt) principles of Jaynes - considered as a function of the moment constraints or their conjugate Lagrangian multipliers - is endowed…
There has been interest in finding a general variational principle for non-equilibrium statistical mechanics. We give evidence that Maximum Caliber (Max Cal) is such a principle. Max Cal, a variant of Maximum Entropy, predicts dynamical…
The microcanonical statistical mechanics of a set of self-gravitating particles is analyzed in mean-field approach. In order to deal with an upper bounded entropy functional, a softened gravitational potential is used. The softening is…
We present a series of closed-form maximum entropy upper bounds for the differential entropy of a continuous univariate random variable and study the properties of that series. We then show how to use those generic bounds for upper bounding…
We examine the fundamental aspects of statistical mechanics, dividing the problem into a discussion purely about probability, which we analyse from a Bayesian standpoint. We argue that the existence of a unique maximising probability…
We study the statistical properties of the entropic optimal (self) transport problem for smooth probability measures. We provide an accurate description of the limit distribution for entropic (self-)potentials and plans as the…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
We propose a framework for computing, optimizing and integrating with respect to a smooth marginal likelihood in statistical models that involve high-dimensional parameters/latent variables and continuous low-dimensional hyperparameters.…
We investigate the behavior of a two-state sandpile model subjected to a confining potential in one and two dimensions. From the microdynamical description of this simple model with its intrinsic exclusion mechanism, it is possible to…
Maximum-entropy ensembles are key primitives in statistical mechanics from which thermodynamic properties can be derived. Over the decades, several approaches have been put forward in order to justify from minimal assumptions the use of…
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic…
Given a bounded class of functions G and independent random variables X1, . . . , Xn, we provide an upper bound for the expectation of the supremum of the empirical process over elements of G having a small variance. Our bound applies in…
We present a maximum entropy approach to analyze the internal dynamics of a small system in contact with a large bath e.g. a solute-solvent system. For the small solute, the fluctuations around the mean values of observables are not…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
We investigate activities that have different periods of duration. We define the profit intensity as a measure of this economic category. The profit intensity in a repeated trading has a unique property of attaining its maximum at a fixed…
We develop the most probable wave functions for a single free quantum particle given its momentum and energy by imposing its quantum probability density to maximize Shannon information entropy. We show that there is a class of solutions in…
For the purpose of causal inference we employ a stochastic model of the data generating process, utilizing individual propensity probabilities for the treatment, and also individual and counterfactual prognosis probabilities for the…
Various lower bounds are established for the entropy of sums, products and their combinations. First, we derive a prime-field analogue of a version of the entropy power inequality established by Tao over torsion-free groups. Next, we prove…
This paper presents a conceptual model describing the medium and long-term co-evolution of natural and socio-economic subsystems of Earth. An economy is viewed as an out-of-equilibrium dissipative structure that can only be maintained with…