Statistical Inference on Stochastic Graphs

Statistics

Hosseinkashi, Yasaman

University of Waterloo

关键词: Statistics;   

Others  :  https://uwspace.uwaterloo.ca/bitstream/10012/6029/1/Hosseinkashi_Yasaman.pdf

瑞士|英语

来源: UWSPACE Waterloo Institutional Repository

【 摘 要 】

This thesis considers modelling and applications of random graph processes.A brief review on contemporary random graph models and a general Birth-Deathmodel with relevant maximum likelihood inference procedure are provided in chapterone. The main result in this thesis is the construction of an epidemic model byembedding a competing hazard model within a stochastic graph process (chapter2). This model includes both individual characteristics and the population connectivitypattern in analyzing the infection propagation. The dynamic outdegrees andindegrees, estimated by the model, provide insight into important epidemiologicalconcepts such as the reproductive number. A dynamic reproductive number basedon the disease graph process is developed and applied in several simulated and actualepidemic outbreaks. In addition, graph-based statistical measures are proposedto quantify the effect of individual characteristics on the disease propagation. Theepidemic model is applied to two real outbreaks: the 2001 foot-and-mouth epidemicin the United Kingdom (chapter 3) and the 1861 measles outbreak in Hagelloch,Germany (chapter 4). Both applications provide valuable insight into the behaviourof infectious disease propagation with di erent connectivity patterns and humaninterventions.