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The statistical mechanical basis of the fluctuation theory of mixtures is reviewed. An overview of the statistical mechanical relations between the microscopic properties of a system and its macroscopic properties is presented. The…
We describe a new method for evaluating Bayes factors. The key idea is to introduce a hypermodel in which the competing models are components of a mixture distribution. Inference for the mixing probabilities then yields estimates of the…
Estimation of the $\phi$-divergence between two unknown probability distributions using empirical data is a fundamental problem in information theory and statistical learning. We consider a multi-variate generalization of the data dependent…
We analyze here in details the probability to find a given number of particles in a finite volume inside a normal or superfluid finite system. This probability, also known as counting statistics, is obtained using projection operator…
An interesting opportunity to determine thermodynamic and transport properties in more detail is to identify generic statistical properties of initial density perturbations. Here we study event-by-event fluctuations in terms of correlation…
A general random effects model is proposed that allows for continuous as well as discrete distributions of the responses. Responses can be unrestricted continuous, bounded continuous, binary, ordered categorical or given in the form of…
This paper introduces a novel decomposition framework to explain heterogeneity in causal effects observed across different studies, considering both observational and randomized settings. We present a formal decomposition of between-study…
A study of eccentricity ($\varepsilon_{n}$) fluctuations and its possible impact on final state momentum anisotropy ($v_{n}$) for symmetric collisions are presented in the framework of Glauber model. Effect of fluctuations of nucleon's…
We apply random matrix theory to study the impact of measurement uncertainty on dynamic mode decomposition. Specifically, when the measurements follow a normal probability density function, we show how the moments of that density propagate…
The fluctuations in the particle size distribution for processes of fragmentation and aggregation are studied for stationary state regimes. The system is described in terms of a stochastic process over an adequate tree structure. The RMS…
Learning the structure of Bayesian networks from data provides insights into underlying processes and the causal relationships that generate the data, but its usefulness depends on the homogeneity of the data population, a condition often…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
There has been a surge in the interest of using machine learning techniques to assist in the scientific process of formulating knowledge to explain observational data. We demonstrate the use of Bayesian Hidden Physics Models to first…
An important problem in the analysis of experimental data showing fractal properties, is that such samples are composed by a set of points limited by an upper and a lower cut off. We study how finite size effect due to the discreteness of…
A mixture with varying concentrations is a modification of a finite mixture model in which the mixing probabilities (concentrations of mixture components) may be different for different observations. In the paper, we assume that the…
In the absence of direct accelerator data to constrain particle models, and given existing astrophysical uncertainties associated with the phase space distribution of WIMP dark matter in our galactic halo, extracting information on…
Volume or centrality fluctuations (CF) is one of the main uncertainties for interpreting the centrality dependence of many experimental observables. The CF is constrained by centrality selection based on particle multiplicity in a reference…
Ecological networks such as plant-pollinator systems and food webs vary in space and time. This variability includes fluctuations in global network properties such as total number and intensity of interactions but also in the local…
The exploration of the rich dynamics of electrons is a frontier in fundamental nano-physics. The dynamical behavior of electrons is dominated by random and chaotic thermal motion with ultrafast ($\approx$ ps) and nanoscale scatterings. This…
The experimentally measured multiplicity distributions exhibit, after closer inspection, peculiarly enhanced void probability and oscillatory behavior of the modified combinants. We show that both these features can be used as additional…