The AstroStat Slog » over-dispersion http://hea-www.harvard.edu/AstroStat/slog Weaving together Astronomy+Statistics+Computer Science+Engineering+Intrumentation, far beyond the growing borders Fri, 09 Sep 2011 17:05:33 +0000 en-US hourly 1 http://wordpress.org/?v=3.4 [ArXiv] Spatial Correlation in the Scan Statistic http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spatial-correlation-in-the-scan-statistic/ http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spatial-correlation-in-the-scan-statistic/#comments Wed, 12 Dec 2007 05:50:13 +0000 hlee http://hea-www.harvard.edu/AstroStat/slog/2007/arxiv-spatial-correlation-in-the-scan-statistic/ Accounting for Spatial Correlation in the Scan Statistic by Loh &Zhu [stat.AP:0712.1458] provides a picture that helps us to understand excessive false alarms in source detection when the image data set is based on the Poisson point process. Without any experience in source detection analysis, empirically I cannot state the detection statistics nor the p-values of detection methods. However, with acknowledging the over-dispersed Poisson count data and the unknown spatial correlation prior to detecting analysis, we could guess that the false discovery of sources occurs more often than what we expect.

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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