Geometry for q-exponential families
Geometry for q-exponential families
复制标题
DOI：
10.1142/9789814355476_0004
复制
发表时间：
2011-09
期刊：
影响因子：
--
通讯作者：
H. Matsuzoe;A. Ohara
中科院分区：
文献类型：
--
作者：
H. Matsuzoe;A. Ohara
本文研究了q指数族的几何问题。Q指数族是一组概率分布，它是标准指数族的自然推广。Q指数族具有信息几何结构和对偶平坦结构。为了描述这些关系，本文研究了统计流形的广义共形结构。作为q指数族几何的一个应用，还研究了统计推断的几何推广。
Geometry for q-exponential families is studied in this paper. A q-exponential family is a set of probability distributions, which is a natural generalization of the standard exponential family. A q-exponential family has information geometric structure and a dually flat structure. To describe these relations, generalized conformal structures for statistical manifolds are studied in this paper. As an application of geometry for q-exponential families, a geometric generalization of statistical inference is also studied.