The Differential Geometric View of Statistics and Estimation

: Statistics and estimation theory is enriched with techniques derived from differential geometry. This establishes the increasing topic of information geometry. This allows new insights into these classical topics. Differential geometry offers a wide spectrum of applications within statistic inference and estimation theory. Especially, many topics of information theory can be interpreted in a geometric way, which offers new insights into this discipline. This is widely called information geometry. Therefore, parameterised probability densities determine manifold like structures, the so called statistic manifolds. The log-likelihood determines an embedding of this manifolds into affine spaces. The Fisher information delivers a metric for this static manifolds. Further one can define geodesics in this manifolds, which allows to measure the distance between different probability densities. Other topics are asymptotic of estimators, sufficiency of statistics, flatness, and divergence of d...

• Type: Journal
• Year: 2009
• Where: GI
• Authors: Felix Opitz
• Keywords: GI 2009, Information Geometry, Manifold, Probability Densities, Theoretical Computer Science