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In this paper, we give a method to construct "good" exponential families systematically by representation theory. More precisely, we consider a homogeneous space $G/H$ as a sample space and construct an exponential family invariant under…
We generalize parts of a special non-Euclidean calculus of pseudodifferential operators, which was invented by S. Zelditch for hyperbolic surfaces, to symmetric spaces $X=G/K$ of the noncompact type and their compact quotients…
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior…
According to Benford's Law, many data sets have a bias towards lower leading digits (about $30\%$ are $1$'s). The applications of Benford's Law vary: from detecting tax, voter and image fraud to determining the possibility of match-fixing…
The probability distribution function for an out of equilibrium system may sometimes be approximated by a physically motivated "trial" distribution. A particularly interesting case is when a driven system (e.g., active matter) is…
We propose a family of four-parameter distributions that contain the K-distribution as special case. The family is derived as a mixture distribution that uses the three-parameter reflected Gamma distribution as parental and the…
We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…
The sparse structure of the solution for an inverse problem can be modelled using different sparsity enforcing priors when the Bayesian approach is considered. Analytical expression for the unknowns of the model can be obtained by building…
We relate two types of phase space distributions associated to eigenfunctions $\phi_{ir_j}$ of the Laplacian on a compact hyperbolic surface $X_{\Gamma}$: (1) Wigner distributions $\int_{S^*\X} a dW_{ir_j}=< Op(a)\phi_{ir_j},…
The Pearson family of ergodic diffusions with a quadratic diffusion coefficient and a linear force are characterized by explicit dynamics of their integer moments and by explicit relaxation spectral properties towards their steady state.…
The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the…
Distributions exhibiting fat tails occur frequently in many different areas of science. A dynamical reason for fat tails can be a so-called superstatistics, where one has a superposition of local Gaussians whose variance fluctuates on a…
We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…
Bayesian posterior distributions are widely used for inference, but their dependence on a statistical model creates some challenges. In particular, there may be lots of nuisance parameters that require prior distributions and posterior…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We introduce the beta generalized exponential distribution that includes the beta exponential and generalized exponential distributions as special cases. We provide a comprehensive mathematical treatment of this distribution. We derive the…
We discuss the diffusion phenomenon in the parabolic and hyperbolic regimes. New effects related to the finite velocity of the diffusion process are predicted, that can partially explain the strange behavior associated to adsorption…
A simple and transparent example of a non-autonomous flow system, with hyperbolic strange attractor is suggested. The system is constructed on a basis of two coupled van der Pol oscillators, the characteristic frequencies differ twice, and…
We study Gabor frames in the case when the window function is of hyperbolic secant type, i.e., $g(x) = (e^{ax}+e^{-bx})^{-1}$, ${\rm Re}\,a, {\rm Re}\,b>0$. A criterion for half-irregular sampling is obtained: for a separated…
In this paper, we propose a new class of distributions by exponentiating the random variables associated with the probability density functions of composite distributions. We also derive some mathematical properties of this new class of…