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A comparison of likelihood-based spatiotemporal monitoring methods under non-homogenous population size. (English) Zbl 1314.62191

Summary: This article discusses the spatio-temporal surveillance problem of detecting rate changes of Poisson data considering non-homogenous population sample size. By applying Monte Carlo simulations, we investigate the performance of several likelihood-based approaches under various scenarios depending on four factors: (1) population trend, (2) change magnitude, (3) change coverage, and (4) change time. Our article evaluates the performance of spatio-temporal surveillance methods based on the average run length at different change times. The simulation results show that no method is uniformly better than others in all scenarios. The difference between the generalized likelihood ratio (GLR) approach and the weighted likelihood ratio (WLR) approach depends mainly on population size, not change coverage, change magnitude, or change time. We find that changes associated with a small population in time periods and/or spatial regions favor the WLR approach, but those associated with a large population favor the GLR under any trends of population changes.

MSC:

62L99 Sequential statistical methods
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