ISBN 978-3-8439-1668-4

978-3-8439-1668-4, Reihe Statistik

Juliane Manitz
Statistical Inference for Propagation Processes on Complex Networks

201 Seiten, Dissertation Georg-August-Universität Göttingen (2014), Softcover, A5

Zusammenfassung / Abstract

Scientists of various research fields have discovered the advantages of network-centric analysis, which captures complex systems by networks and allows for their representation as a collection of nodes connected by links. Currently available network-theoretic methods mainly focus on the descriptive analysis of network topology. In this thesis, different approaches to obtain inferences about propagation processes on complex networks are proposed. The methods are motivated by real-world problems ranging from food-borne disease dispersal to propagation of train delays and the regularization of genetic effects. Firstly, dynamic metapopulation modeling is used for the development of a general food-borne disease model, which integrates the local disease dynamics with the spatial dispersal of contaminated food. This provides the opportunity to simulate efficiently a variety of realistic epidemics. Secondly, an explorative approach for fast and efficient origin detection of propagation processes is proposed. Based on a network-based redefinition of geodesic distance, complex spreading patterns can be mapped onto simple, regular wave propagation patterns if the process origin is chosen as the reference node. This approach is successfully applied to the 2011 EHEC/HUS outbreak in Germany. The results suggest that our method could become a useful supplement to ordinary time-consuming outbreak investigations. Moreover, this approach is generalized to the problem of source train delay identification in railway systems. Extensive simulation studies mimicking various propagation mechanisms, indicate good performance and promise the general applicability of the source detection approach to propagation processes in a wide range of other applications. To demonstrate a probabilistic analysis of processes on complex networks, a kernel regression is utilized. A novel kernel based on network-interactions for the logistic kernel machine test is suggested. This kernel allows seamless integration of biological knowledge and pathway information into the analysis of data from genome-wide association studies. Applications to case-control studies for lung cancer and rheumatoid arthritis demonstrate the ease of implementation and the efficiency of the proposed method. Altogether, the results from the proposed approaches demonstrate that network-theoretic analysis of propagation processes can substantially contribute to solve diverse problems in various research fields.