  When analysing multiple time series that may be subject to changepoints, it
is sometimes possible to specify a priori, by means of a graph G, which pairs
of time series are likely to be impacted by simultaneous changepoints. This
article proposes a novel Bayesian changepoint model for multiple time series
that borrows strength across clusters of connected time series in G to detect
weak signals for synchronous changepoints. The graphical changepoint model is
further extended to allow dependence between nearby but not necessarily
synchronous changepoints across neighbour time series in G. A novel reversible
jump MCMC algorithm making use of auxiliary variables is proposed to sample
from the graphical changepoint model. The merit of the proposed model is
demonstrated via a changepoint analysis of real network authentication data
from Los Alamos National Laboratory (LANL), with some success at detecting weak
signals for network intrusions across users that are linked by network
connectivity, whilst limiting the number of false alerts.
