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dc.contributor.advisor Wolpert, Robert L en_US
dc.contributor.advisor Mukherjee, Sayan en_US
dc.contributor.author Lunagomez, Simon en_US
dc.date.accessioned 2009-08-27T18:39:55Z
dc.date.available 2009-08-27T18:39:55Z
dc.date.issued 2009 en_US
dc.identifier.uri http://hdl.handle.net/10161/1354
dc.description Dissertation en_US
dc.description.abstract We formulate a novel approach to infer conditional independence models or Markov structure of a multivariate distribution. Specifically, our objective is to place informative prior distributions over graphs (decomposable and unrestricted) and sample efficiently from the induced posterior distribution. We also explore the idea of factorizing according to complete sets of a graph; which implies working with a hypergraph that cannot be retrieved from the graph alone. The key idea we develop in this paper is a parametrization of hypergraphs using the geometry of points in $R^m$. This induces informative priors on graphs from specified priors on finite sets of points. Constructing hypergraphs from finite point sets has been well studied in the fields of computational topology and random geometric graphs. We develop the framework underlying this idea and illustrate its efficacy using simulations. en_US
dc.format.extent 1796450 bytes
dc.format.mimetype application/pdf
dc.language.iso en_US
dc.subject Statistics en_US
dc.subject Bayesian methods en_US
dc.subject Computational topology en_US
dc.subject Graphical models en_US
dc.subject Random geometric graphs en_US
dc.title A Geometric Approach for Inference on Graphical Models en_US
dc.type Dissertation en_US
dc.department Statistical Science en_US

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