A q-exponential statistical Banach manifold

Letµbe a given probability measure andMµ the set ofµ-equivalent strictly positive probability densities -- In this paper we construct a Banach manifold on Mµ, modeled on the space L∞(p · µ) where p is a reference density, for the non-parametric q-exponential statistical models (Tsallis’s deformed exponential), where 0 < q < 1 is any real number -- This family is characterized by the fact that when q → 1, then the non-parametric exponential models are obtained and the manifold constructed by Pistone and Sempi is recovered, up to continuous embeddings on the modeling space -- The coordinate mappings of the manifold are given in terms of Csiszár’s Φ-divergences; the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score function

• Autores: Quiceno Echavarría, Héctor Román; Loaiza Ossa, Gabriel Ignacio
• Fecha de publicación: 2013
• Institución: Universidad EAFIT
• Repositorio: Repositorio EAFIT
• Idioma: eng
• OAI Identifier: oai:repository.eafit.edu.co:10784/5245
• Acceso en línea: http://hdl.handle.net/10784/5245
• Palabra clave: TEORÍA DE LA INFORMACIÓN; ENTROPÍA (TEORÍA DE LA INFORMACIÓN); ESPACIOS DE BANACH; FÍSICA CUÁNTICA; ANÁLISIS MATEMÁTICO; GEOMETRÍA DIFERENCIAL; FUNCIONES ANALÍTICAS; Information theory; Entropy (information theory); Banach spaces; Quantum physical; Mathematical analysis; Geometry, differential; Analytic functions; Espacios de Orlicz
• License: Copyright © 2012 Elsevier Ltd. All rights reserved.