Estimating Network Features and Associated Measures of Uncertainty and Their Incorporation in Network Generation and Analysis
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CitationGoyal, Ravi. 2012. Estimating Network Features and Associated Measures of Uncertainty and Their Incorporation in Network Generation and Analysis. Doctoral dissertation, Harvard University.
AbstractThe efficacy of interventions to control HIV spread depends upon many features of the communities where they are implemented, including not only prevalence, incidence, and per contact risk of transmission, but also properties of the sexual or transmission network. For this reason, HIV epidemic models have to take into account network properties including degree distribution and mixing patterns. The use of sampled data to estimate properties of a network is a common practice; however, current network generation methods do not account for the uncertainty in the estimates due to sampling. In chapter 1, we present a framework for constructing collections of networks using sampled data collected from ego-centric surveys. The constructed networks not only target estimates for density, degree distributions and mixing frequencies, but also incorporate the uncertainty due to sampling. Our method is applied to the National Longitudinal Study of Adolescent Health and considers two sampling procedures. We demonstrate how a collection of constructed networks using the proposed methods are useful in investigating variation in unobserved network topology, and therefore also insightful for studying processes that operate on networks. In chapter 2, we focus on the degree to which impact of concurrency on HIV incidence in a community may be overshadowed by differences in unobserved, but local, network properties. Our results demonstrate that even after controlling for cumulative ego-centric properties, i.e. degree distribution and concurrency, other network properties, which include degree mixing and clustering, can be very inﬂuential on the size of the potential epidemic. In chapter 3, we demonstrate the need to incorporate information about degree mixing patterns in such modeling. We present a procedure to construct collections of bipartite networks, given point estimates for degree distribution, that either makes use of information on the degree mixing matrix or assumes that no such information is available. These methods permit a demonstration of the differences between these two network collections, even when degree sequence is ﬁxed. Methods are also developed to estimate degree mixing patterns, given a point estimate for the degree distribution.
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