Statistical Theory Through Differential Geometry
This thesis will take a look at the roots of modern-day information geometry and some applications into statistical modeling. In order to truly grasp this field, we will first provide a basic and relevant introduction to differential geometry. This includes the basic concepts of manifolds as well as...
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| Format: | Others |
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Scholarship @ Claremont
2019
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| Online Access: | https://scholarship.claremont.edu/cmc_theses/2181 https://scholarship.claremont.edu/cgi/viewcontent.cgi?article=3264&context=cmc_theses |
| Summary: | This thesis will take a look at the roots of modern-day information geometry and some applications into statistical modeling. In order to truly grasp this field, we will first provide a basic and relevant introduction to differential geometry. This includes the basic concepts of manifolds as well as key properties and theorems. We will then explore exponential families with applications of probability distributions. Finally, we select a few time series models and derive the underlying geometries of their manifolds. |
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