指数统计流形性质和应用  

Information geometric structures of exponential family manifold and its applications

作　　者：张士诚[1,2] 孙华飞[2] 李春晖[2] 

机构地区：[1]徐州师范大学数学科学学院,江苏徐州221116 [2]北京理工大学理学院,北京100081

出　　处：《徐州师范大学学报（自然科学版）》2009年第4期34-37,共4页Journal of Xuzhou Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10871218);徐州师范大学自然科学基金资助项目(08XLB02)

摘　　要：利用信息几何的观点,考虑了指数族流形的α几何结构,并利用这些几何性质研究了热力学统计流形,在更少的限制条件下,得到的定理与一些文献的结论是相同的.最后,给出两个例子加以说明.From the view of information geometry,we consider the α-geometric structure of the exponential family manifolds and apply its characters to the thermodynamic manifold.Some results are obtained in the removal of some conditions used by others,which are consistent with some of those by several authors.Two examples are given for illustrating our conclusions.

关 键 词：指数族流形 统计流形 信息几何 

分 类 号：O186[理学—数学]