  When analysing multiple time series that may be subject to changepoints, it
is sometimes possible to specify a priori, by means of a graph, which pairs of
time series are likely to be impacted by simultaneous changepoints. This
article proposes an informative prior for changepoints which encodes the
information contained in the graph, inducing a changepoint model for multiple
time series that borrows strength across clusters of connected time series to
detect weak signals for synchronous changepoints. The graphical model for
changepoints is further extended to allow dependence between nearby but not
necessarily synchronous changepoints across neighbouring time series in the
graph. A novel reversible jump Markov chain Monte Carlo (MCMC) algorithm making
use of auxiliary variables is proposed to sample from the graphical changepoint
model. The merit of the proposed approach is demonstrated through a changepoint
analysis of computer network authentication logs from Los Alamos National
Laboratory (LANL), demonstrating an improvement at detecting weak signals for
network intrusions across users linked by network connectivity, whilst limiting
the number of false alerts.
