Related papers: Geometry of escort distributions
The paper considers gossip distributed estimation of a (static) distributed random field (a.k.a., large scale unknown parameter vector) observed by sparsely interconnected sensors, each of which only observes a small fraction of the field.…
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…
Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…
This note presents a novel Bayesian attitude estimator with the matrix Fisher distribution on the special orthogonal group, which can smoothly accommodate both unit and non-unit vector measurements. The posterior attitude distribution is…
A Wright function based framework is proposed to combine and extend several distribution families. The $\alpha$-stable distribution is generalized by adding the degree of freedom parameter. The PDF of this two-sided super distribution…
In this work, a subclass of the generalized Kerr-Schild class of spacetimes is specified, with respect to which the Ricci tensor (regardless of the position of indices) proves to be linear in the so-called profile function of the geometry.…
Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…
In this paper, we analyze the impact of compressed sensing with complex random matrices on Fisher information and the Cram\'{e}r-Rao Bound (CRB) for estimating unknown parameters in the mean value function of a complex multivariate normal…
In this paper, we attempt to provide mathematical models of Mendelian and Non-Mendelian inheritances of the bisexual population system having Fisher's {\textbf{1:1}} principle. In our model, we always assume that distributions of the same…
Elliptically symmetric distributions are a classic example of a semiparametric model where the location vector and the scatter matrix (or a parameterization of them) are the two finite-dimensional parameters of interest, while the density…
Amari's Information Geometry is a dually affine formalism for parametric probability models. The literature proposes various nonparametric functional versions. Our approach uses classical Weyl's axioms so that the affine velocity of a…
Wasserstein geometry and information geometry are two important structures introduced in a manifold of probability distributions. The former is defined by using the transportation cost between two distributions, so it reflects the metric…
Information geometry is the application of differential geometry in statistics, where the Fisher-Rao metric serves as the Riemannian metric on the statistical manifold, providing an intrinsic property for parameter sensitivity. In this…
The Fisher metric on a manifold of probability distributions is usually treated as a metric on the tangent bundle. In this paper, we focus on the metric on the cotangent bundle induced from the Fisher metric with calling it the Fisher…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
The shortcomings of the traditional univariate distributions in the past greatly encouraged mathematical statisticians to develop new generalizations of distributions. The New Generalized Fisk distribution, a unique distribution presented…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
We consider the asymptotic behavior of posterior distributions if the model is misspecified. Given a prior distribution and a random sample from a distribution $P_0$, which may not be in the support of the prior, we show that the posterior…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parameterized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…