Results 11 to 20 of about 175,776 (260)

Local mixture models of exponential families [PDF]

, 2007
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view.
Anaya-Izquierdo, Karim, Marriott, Paul
core   +6 more sources

Deformed Algebras and Generalizations of Independence on Deformed Exponential Families

Entropy, 2015
A deformed exponential family is a generalization of exponential families. Since the useful classes of power law tailed distributions are described by the deformed exponential families, they are important objects in the theory of complex systems.
Hiroshi Matsuzoe, Tatsuaki Wada
doaj   +1 more source

Group Invariance of Information Geometry on q-Gaussian Distributions Induced by Beta-Divergence

Entropy, 2013
We demonstrate that the q-exponential family particularly admits natural geometrical structures among deformed exponential families. The property is the invariance of structures with respect to a general linear group, which transitively acts on the space
Shinto Eguchi, Atsumi Ohara
doaj   +1 more source

On the Fisher Metric of Conditional Probability Polytopes

Entropy, 2014
We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of ...
Guido Montúfar, Johannes Rauh, Nihat Ay
doaj   +1 more source

Nonparametric regression in exponential families [PDF]

, 2010
Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques including wavelet thresholding methods have been developed and shown to be highly adaptive.
Brown, Lawrence D., Cai, T. Tony, Zhou, Harrison H.   +2 more
core   +4 more sources

Using Geometry to Select One Dimensional Exponential Families That Are Monotone Likelihood Ratio in the Sample Space, Are Weakly Unimodal and Can Be Parametrized by a Measure of Central Tendency

Entropy, 2014
One dimensional exponential families on finite sample spaces are studied using the geometry of the simplex Δn°-1  and that of a transformation Vn-1 of its interior.
Paul Vos, Karim Anaya-Izquierdo
doaj   +1 more source

Characterization of the cubic exponential families by orthogonality of polynomials [PDF]

, 2004
This paper introduces a notion of 2-orthogonality for a sequence of polynomials to give extended versions of the Meixner and Feinsilver characterization results based on orthogonal polynomials.
Hassairi, Abdelhamid, Zarai, Mohammed
core   +3 more sources

Small area estimation with spatially varying natural exponential families [PDF]

Journal of Statistical Computation and Simulation, 2020
Two-stage hierarchical models have been widely used in small area estimation to produce indirect estimates of areal means. When the areas are treated exchangeably and the model parameters are assumed to be the same over all areas, we might lose the efficiency in the presence of spatial heterogeneity.
Shonosuke Sugasawa, Yuki Kawakubo, Kota Ogasawara   +2 more
openaire   +2 more sources

Bayesian approach to cubic natural exponential families [PDF]

Statistics & Probability Letters, 2013
For a natural exponential family (NEF), one can associate in a natural way two standard families of conjugate priors, one on the natural parameter and the other on the mean parameter. These families of conjugate priors have been used to establish some remarkable properties and characterization results of the quadratic NEF's.
Hamza, Marwa, Hassairi, Abdelhamid
openaire   +3 more sources

Geometric Theory of Heat from Souriau Lie Groups Thermodynamics and Koszul Hessian Geometry: Applications in Information Geometry for Exponential Families

Entropy, 2016
We introduce the symplectic structure of information geometry based on Souriau’s Lie group thermodynamics model, with a covariant definition of Gibbs equilibrium via invariances through co-adjoint action of a group on its moment space, defining physical ...
Frédéric Barbaresco
doaj   +1 more source