  Spatial correlation in areal unit count data is typically modelled by a set
of random effects that are assigned a conditional autoregressive (CAR) prior
distribution. The spatial correlation structure implied by this model depends
on a binary neighbourhood matrix, where two random effects are assumed to be
partially autocorrelated if their areal units share a common border, and are
conditionally independent otherwise. This paper proposes a novel graph-based
optimisation algorithm for estimating the neighbourhood matrix from the data,
by viewing the areal units as the vertices of the graph and the neighbour
relations as the set of edges. The superiority of our methodology compared to
using the border sharing rule is comprehensively evidenced by simulation,
before the method is applied to a new respiratory disease surveillance study in
the Greater Glasgow and Clyde Health board in Scotland between 2011 and 2017.
