Titlebook: Geometric Modeling in Probability and Statistics; Ovidiu Calin,Constantin Udrişte Textbook 2014 Springer International Publishing Switzerl

THROB

勾引

Dual Laplacianshe definition and main properties of dual Laplacians and .-Laplacians. Their relationship with Hessians, curvature vector fields, and dual volume elements is emphasized..In this chapter (., ., ∇, ∇.) is a manifold . structured by a metric ., and endowed with a pair of dual connections ∇ and ∇..

新奇

Contrast Functions Geometrytatistical manifold or statistical model .. A contrast function, .(. | | .), for density functions ., is a smooth, non-negative function that vanishes for . = .. Eguchi [., ., .] has shown that a contrast function . induces a Riemannian metric by its second order derivatives, and a pair of dual conn

coagulate

Contrast Functions on Statistical Modelsative entropy, .-divergence, Hellinger distance, Chernoff information, Jefferey distance, Kagan divergence, and exponential contrast function. The relation with the skewness tensor and .-connection is made. The goal of this chapter is to produce hands-on examples for the theoretical concepts introdu

散步

Epithelium

watertight,

ANTIC

Evocative

Textbook 2014tions. This is a field that is increasingly attracting the interest of researchers from many different areas of science, including mathematics, statistics, geometry, computer science, signal processing, physics and neuroscience. It is the authors’ hope that the present book will be a valuable refere

Eviction

f topics.Use of hands-on software to clarify and understand .This book covers topics of Informational Geometry, a field which deals with the differential geometric study of the manifold probability density functions. This is a field that is increasingly attracting the interest of researchers from ma