A q-exponential statistical Banach manifold

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Loaiza, G.¹  Quiceno, H. R.¹ 

[1] Univ EAFIT, Dept Ciencias Basicas, Medellin, Colombia

关键词: Differential geometry;    Differentiable mappings;    Information theory;   

DOI  :  10.1016/j.jmaa.2012.08.046

来源: Elsevier

【 摘 要 】

Let mu be a given probability measure and M-mu the set of mu-equivalent strictly positive probability densities. In this paper we construct a Banach manifold on 931, modeled on the space L-infinity(p . mu) 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 Csiszar's phi-divergences: the tangent vectors are identified with the one-dimensional q-exponential models and q-deformations of the score function. (c) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free