Statistical Inference on Stochastic Graphs
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Date
2011-07-08T20:01:18Z
Authors
Hosseinkashi, Yasaman
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
This thesis considers modelling and applications of random graph processes.
A brief review on contemporary random graph models and a general Birth-Death
model with relevant maximum likelihood inference procedure are provided in chapter
one. The main result in this thesis is the construction of an epidemic model by
embedding a competing hazard model within a stochastic graph process (chapter
2). This model includes both individual characteristics and the population connectivity
pattern in analyzing the infection propagation. The dynamic outdegrees and
indegrees, estimated by the model, provide insight into important epidemiological
concepts such as the reproductive number. A dynamic reproductive number based
on the disease graph process is developed and applied in several simulated and actual
epidemic outbreaks. In addition, graph-based statistical measures are proposed
to quantify the effect of individual characteristics on the disease propagation. The
epidemic model is applied to two real outbreaks: the 2001 foot-and-mouth epidemic
in the United Kingdom (chapter 3) and the 1861 measles outbreak in Hagelloch,
Germany (chapter 4). Both applications provide valuable insight into the behaviour
of infectious disease propagation with di erent connectivity patterns and human
interventions.