指数统计流形性质和应用

Information geometric structures of exponential family manifold and its applications

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.