  It has become routine in neuroscience studies to measure brain networks for
different individuals using neuroimaging. These networks are typically
expressed as adjacency matrices, with each cell containing a summary of
connectivity between a pair of brain regions. There is an emerging statistical
literature describing methods for the analysis of such multi-network data in
which nodes are common across networks but the edges vary. However, there has
been essentially no consideration of the important problem of outlier
detection. In particular, for certain subjects, the neuroimaging data are so
poor quality that the network cannot be reliably reconstructed. For such
subjects, the resulting adjacency matrix may be mostly zero or exhibit a
bizarre pattern not consistent with a functioning brain. These outlying
networks may serve as influential points, contaminating subsequent statistical
analyses. We propose a simple Outlier DetectIon for Networks (ODIN) method
relying on an influence measure under a hierarchical generalized linear model
for the adjacency matrices. An efficient computational algorithm is described,
and ODIN is illustrated through simulations and an application to data from the
UK Biobank. ODIN was successful in identifying moderate to extreme outliers.
Removing such outliers can significantly change inferences in downstream
applications.
