To incorporate overdispersion and spatial correlation in detecting clusters from the spatial Poisson point process, the authors proposed the null model that includes spatial correlation, which is referred as the spatial generalized linear mixed model (SGLMM), or generalized spatial linear model (GSLM). They show theoretically this over-dispersion and spatial correlation leads to the increase of false positives, which is verified through a simulation study as well. Their simulation study also illustrates that their modified scan statistic substantially reduces the false alarm.
Due to the complexity of the models and theories, the authors rely on simulation study heavily. Nonetheless, the figures that illustrates the posterior distributions of the scan statistic are difficult to read (due to the low resolution scanned images). Please, keep this in your mind while you are reading it.
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