Ludkin, Matthew Robert and Neal, Peter and Eckley, Idris (2017) The autoregressive stochastic block model with changes in structure. PhD thesis, Lancaster University.
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Abstract
Network science has been a growing subject for the last three decades, with sta- tistical analysis of networks seing an explosion since the advent of online social networks. An important model within network analysis is the stochastic block model, which aims to partition the set of nodes of a network into groups which behave in a similar way. This thesis proposes Bayesian inference methods for problems related to the stochastic block model for network data. The presented research is formed of three parts. Firstly, two Markov chain Monte Carlo samplers are proposed to sample from the posterior distribution of the number of blocks, block memberships and edge-state parameters in the stochastic block model. These allow for non-binary and non-conjugate edge models, something not considered in the literature. Secondly, a dynamic extension to the stochastic block model is presented which includes autoregressive terms. This novel approach to dynamic network models allows the present state of an edge to influence future states, and is therefore named the autoregresssive stochastic block model. Furthermore, an algorithm to perform inference on changes in block membership is given. This problem has gained some attention in the literature, but not with autoregressive features to the edge-state distribution as presented in this thesis. Thirdly, an online procedure to detect changes in block membership in the au- toregresssive stochastic block model is presented. This allows networks to be monitored through time, drastically reducing the data storage requirements. On top of this, the network parameters can be estimated together with the block memberships. Finally, conclusions are drawn from the above contributions in the context of the network analysis literature and future directions for research are identified.