相关论文: Applications of the divergence theorem in Bayesian…

Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…

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…

The fluctuations of the work done by an external Gaussian random force on a harmonic oscillator that is also in contact with a thermal bath is studied. We have obtained the exact large deviation function as well as the complete asymptotic…

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…

Equilibrium statistical physics is considered from the point of view of statistical estimation theory. This involves the notions of statistical model, of estimators, and of exponential family. A useful property of the latter is the…

A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…

Starting from an axiomatic perspective, \emph{fluctuation geometry} is developed as a counterpart approach of inference geometry. This approach is inspired on the existence of a notable analogy between the general theorems of…

Bayesian inference is applied directly to the problem of unfolding. The outcome is a posterior probability density for the spectrum before smearing, defined in the multi-dimensional space of all possible spectra. Regularization consists in…

The significance of statistical physics concepts such as entropy extends far beyond classical thermodynamics. We interpret the similarity between partitions in statistical mechanics and partitions in Bayesian inference as an articulation of…

The theory of probability, based on very general rules referred to as the Cox-Polya-Jaynes Desiderata, can be used both as a theory of random mass phenomena and as a quantitative theory of plausible inference about the parameters of…

We describe the relation between the isothermal atomic compressibility and density fluctuations in mixtures of two-component fermions with population or mass imbalance. We derive a generalized version of the fluctuation-dissipation theorem…

We develop an iterative framework for Bayesian inference problems where the posterior distribution may involve computationally intensive models, intractable gradients, significant posterior concentration, and pronounced non-Gaussianity. Our…

Systems that evolve towards a state from which they cannot depart are common in nature. But the fluctuation-dissipation theorem, a fundamental result in statistical mechanics, is mainly restricted to systems near-stationarity. In processes…

Damping on an object generally depends on its conformation (shape size etc.). We consider the Langevin dynamics of a model system with a conformation dependent damping and generalize the fluctuation dissipation relation to fit in such a…

We present a continuation method that entails generating a sequence of transition probability density functions from the prior to the posterior in the context of Bayesian inference for parameter estimation problems. The characterization of…

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as Bayesian inference, estimators or hypothesis…

Suppose $X_1,\dots, X_n$ is a random sample from a bounded and decreasing density $f_0$ on $[0,\infty)$. We are interested in estimating such $f_0$, with special interest in $f_0(0)$. This problem is encountered in various statistical…

We analyze the microscopic evolution of a system undergoing a far-from-equilibrium thermodynamic process. Explicitly accounting for the degrees of freedom of participating heat reservoirs, we derive a hybrid result, similar in form to both…

In order to account for possible nonstatistical fluctuations in a hadronizing system (leading to the characteristic power-like behavior of the respective single particle spectra and to the broadening of the corresponding multiparticle…

Recently many results namely the Fluctuation theorems (FT), have been discovered for systems arbitrarily away from equilibrium. Many of these relations have been experimentally tested. The system under consideration is usually driven out of…