Large deviations approximation to normalizing constants in exponential models

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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 text
Form electronic; electronic resource; remote
Extent 1 online resource.
Publication date 2016
Issuance monographic
Language English


Associated with Chern, Bobbie Glen
Associated with Stanford University, Department of Electrical Engineering.
Primary advisor Diaconis, Persi
Thesis advisor Diaconis, Persi
Thesis advisor Chatterjee, Sourav
Thesis advisor Özgür, Ayfer
Thesis advisor Weissman, Tsachy
Advisor Chatterjee, Sourav
Advisor Özgür, Ayfer
Advisor Weissman, Tsachy


Genre Theses

Bibliographic information

Statement of responsibility Bobbie Glen Chern.
Note Submitted to the Department of Electrical Engineering.
Thesis Thesis (Ph.D.)--Stanford University, 2016.
Location electronic resource

Access conditions

© 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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