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.