Related papers: Geometry of escort distributions
We discuss generalized linear models for directional data where the conditional distribution of the response is a von Mises-Fisher distribution in arbitrary dimension or a Bingham distribution on the unit circle. To do this properly, we…
Data sets of multivariate normal distributions abound in many scientific areas like diffusion tensor imaging, structure tensor computer vision, radar signal processing, machine learning, just to name a few. In order to process those normal…
In this paper we introduce a new method to add a parameter to a family of distributions. The additional parameter is completely studied and a full description of its behaviour in the distribution is given. We obtain several mathematical…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
In this article the statistical properties of symmetrical random matrices whose elements are drawn from a q-parametrized non-extensive statistics power-law distribution are investigated. In the limit as q->1 the well known Gaussian…
Statistical models for multivariate data often include a semi-orthogonal matrix parameter. In many applications, there is reason to expect that the semi-orthogonal matrix parameter satisfies a structural assumption such as sparsity or…
A new unimodal distribution family indexed by the mode and three other parameters is derived from a mixture of a Gumbel distribution for the maximum and a Gumbel distribution for the minimum. Properties of the proposed distribution are…
Latent space geometry has shown itself to provide a rich and rigorous framework for interacting with the latent variables of deep generative models. The existing theory, however, relies on the decoder being a Gaussian distribution as its…
Bayesian nonparametric statistics is an area of considerable research interest. While recently there has been an extensive concentration in developing Bayesian nonparametric procedures for model checking, the use of the Dirichlet process,…
This paper proposes an original Riemmanian geometry for low-rank structured elliptical models, i.e., when samples are elliptically distributed with a covariance matrix that has a low-rank plus identity structure. The considered geometry is…
This paper deals with Cram\'er-Rao inequalities in the context of nonextensive statistics and in estimation theory. It gives characterizations of generalized q-Gaussian distributions, and introduces generalized versions of Fisher…
In many applications in biology, engineering and economics, identifying similarities and differences between distributions of data from complex processes requires comparing finite categorical samples of discrete counts. Statistical…
Here I present the analytic form of two common distance metrics, the symmetrised Kullback-Leibler Divergence and the Kolmogorov-Smirnov statistic, as well as an extension of the Kolmogorov-Smirnov statistic for comparing theoretical gamma…
We generalize the classical Fisher information metric on statistical models to $L^p$-metrics on various spaces of differential forms or group of diffeomorphisms. Using this new interpretation from information geometry, we derive several new…
The traditional class of elliptical distributions is extended to allow for asymmetries. A completely robust dispersion matrix estimator (the `spectral estimator') for the new class of `generalized elliptical distributions' is presented. It…
The orientation fluctuations of the director of a liquid crystal are measured, by a sensitive polarization interferometer, close to the Fr\'eedericksz transition, which is a second order transition driven by an electric field. We show that…
A statistic on a statistical model is sufficient if it has no information loss, namely, the Fisher metric of the induced model coincides with that of the original model due to Kullback and Ay-Jost-L\^e-Schwachh\"ofer. We introduce a…
This paper is focused on probabilistic estimation for the attitude dynamics of a rigid body on the special orthogonal group. We select the matrix Fisher distribution to represent the uncertainties of attitude estimates and measurements in a…
Directional data consists of unit vectors in q-dimensions that can be described in polar or Cartesian coordinates. Axial data can be viewed as a pair of directions pointed in opposite directions or as a projection matrix of rank 1.…
This paper investigates the theoretical Cramer-Rao bounds on estimation accuracy of longitudinal vehicle dynamics parameters. This analysis is motivated by the value of parameter estimation in various applications, including chassis model…