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原文連結
論文資訊
- 類型：已發表論文
- 日期：2014-07-15
摘要
資訊 geometry provides a geometric approach to families of 統計 models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the criterion for passing from one model to another without loss of 資訊. This leads to the question how the geometric structures behave under such sufficient statistics. While this is well studied in the finite sample size case, in the infinite case, we encounter technical problems concerning the appropriate topologies. Here, we introduce notions of parametrized measure models and tensor fields on them that exhibit the right behavior under 統計 transformations. Within this framework, we can then handle the topological issues and show that the Fisher metric and the Amari-Chentsov
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