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Keywords:

  • dual geometries;
  • simplicial geometries;
  • information;
  • exponential families

Abstract

Geometry is a broad area that has applications to many areas of statistics. In this article the focus will be on the role of dual information geometries to statistical inference. A great deal of research has been done in the application of these dual geometries to higher order asymptotics and a brief review is given. Greater attention is given to providing insight into dual geometries as extensions of Euclidean geometry, and how, a further extension, called the dual simplicial geometry, can provide a general framework for computational algorithms. WIREs Comp Stat 2010 2 686–694 DOI: 10.1002/wics.128

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