Large deviations approximation to normalizing constants in exponential models
- Exponential families are a class of probability distributions that contain many common distributions and thus have been a subject of considerable study by statisticians. A basic problem in statistics is the estimation of the normalizing constant of these models. In many cases, this constant is not available in closed form, and direct numerical computation is infeasible. This thesis studies techniques for numerically approximating the normalizing constant with application to maximum likelihood estimation through the use of some recent results from large deviations theory. Three examples are explored in this thesis: the Curie-Weiss model from statistical physics, exponential random graph models, and a model for relatedness in the California condor. Methods for approximately computing the normalizing constant are carried out in all three examples, and a new technique for performing maximum likelihood estimation is developed in the last example. This new technique appears to be a reasonable alternative to exisitng methods for maximum likelihood estimation in models with unknown normalizing constants.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Chern, Bobbie Glen
|Stanford University, Department of Electrical Engineering.
|Statement of responsibility
|Bobbie Glen Chern.
|Submitted to the Department of Electrical Engineering.
|Thesis (Ph.D.)--Stanford University, 2016.
- © 2016 by Bobbie Glen Chern
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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