Inference for Preferential Attachment Models and Related Topics
Date
2014-05
Authors
Saxton, Daniel
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Abstract
Preferential attachment models arise in several areas of mathematics and scientific applications such as in the analysis of social, financial, and gene regulatory networks. However, inferential questions related to such models are challenging and have so far not been addressed. In this dissertation, we provide a framework using branching processes within which to investigate these issues. In particular, we develop theory that may be employed to extract information about the strength of preferential attachment from graph data, as well as information about degree asymptotics. We also study an extension of the model incorporating random effects which helps to introduce added heterogeneity into the process which is not represented in existing models. Questions concerning cascades on trees are also studied.
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Statistics