Related papers: Geometry of escort distributions
We investigate the asymptotic behavior of Bayesian posterior distributions under independent and identically distributed ($i.i.d.$) misspecified models. More specifically, we study the concentration of the posterior distribution on…
The prediction of the variance-covariance matrix of the multivariate normal distribution is important in the multivariate analysis. We investigated Bayesian predictive distributions for Wishart distributions under the Kullback-Leibler…
Skewed generalizations of the normal distribution have been a topic of great interest in the statistics community due to their diverse applications across several domains. One of the most popular skew normal distributions, due to its…
We propose a simple phenomenological modification, a Gaussian screening, of the probability distribution function which was obtained by Beck to explain experimentally measured distribution from fully developed fluid turbulence, within the…
We consider the problem of estimating undirected triangle-free graphs of high dimensional distributions. Triangle-free graphs form a rich graph family which allows arbitrary loopy structures but 3-cliques. For inferential tractability, we…
In an attempt to characterize the distribution of forms and shapes of nodal domains in wave functions, we define a geometric parameter - the ratio $\rho$ between the area of a domain and its perimeter, measured in units of the wavelength…
We present a framework for describing the evolution of stochastic observables having a non-stationary distribution of values. The framework is applied to empirical volume-prices from assets traded at the New York stock exchange. Using…
We consider the Fisher-Snedecor diffusion; that is, the Kolmogorov-Pearson diffusion with the Fisher-Snedecor invariant distribution. In the nonstationary setting, we give explicit quantitative rates for the convergence rate of respective…
We study the statistical properties of Lanczos coefficients over an ensemble of random initial operators generating the Krylov space. We propose two statistical quantities that are important in characterizing the complexity: the average…
The Marshall-Olkin (MO) distribution has been considered a key model in reliability theory and in risk analysis, where it is used to model the lifetimes of dependent components or entities of a system and dependency is induced by "shocks"…
This paper proposes an alternative approach for constructing invariant Jeffreys prior distributions tailored for hierarchical or multilevel models. In particular, our proposal is based on a flexible decomposition of the Fisher information…
Macroscopic mechanical properties of polymers are determined by their microscopic molecular chain distribution. Due to randomness of these molecular chains, probability theory has been used to find their micro-states and energy…
Two geometrical structures have been extensively studied for a manifold of probability distributions. One is based on the Fisher information metric, which is invariant under reversible transformations of random variables, while the other is…
In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is…
Fisher information is a lower bound on the uncertainty in the statistical estimation of classical and quantum mechanical parameters. While some deterministic dynamical systems are not subject to random fluctuations, they do still have a…
The manifold of empirical mean values of statistical data ad infinitum has a geometric shape that depends on the probability measure that governs the generating model. Large deviation theory produces entropy functions that depend on both…
We propose point estimators for the three-parameter (location, scale, and the fractional parameter) variant distributions generated by a Wright function. We also provide uncertainty quantification procedures for the proposed point…
The distribution of the spacing, or the difference between consecutive order statistics, is known only for uniform and exponential random variates. We add here logistic and Gumbel variates, and present an estimator for distributions with a…
Regression analysis with probability measures as input predictors and output response has recently drawn great attention. However, it is challenging to handle multiple input probability measures due to the non-flat Riemannian geometry of…
Parametric portfolio policies may experience estimation risk. I develop a generalized Bayesian framework that updates priors, delivering a posterior distribution over characteristic tilts and out-of-sample returns that is the unique…