Abstract
Cluster detection is an important problem in many researches. In the case of disease cluster detection, the popular scan statistics of Kulldorff et al is easy to understand and fast to execute, but there are still some drawbacks. It often leads to many false alarms in highly correlation data. Also it cannot detect small clusters even if their infection rates are very high. The spatial hierarchical models proposed by Gangnon and Clayton recently provide information about cluster and spatial/spatial-temporal background. But they do not take into account the possible correlation among the noises. Besides, it has to set the maximum number of clusters which affect the results. In this thesis, we propose spatial and spatial-temporal correlation models and develop the two-stage estimation method which does not need to set the number of clusters in advance. The proposed models are helpful for importation and forecasting purposes. Simulation studies show that they have low false alarm rate and high detection rate. Our empirical studies are announced disease cases in epidemiology. The upstate New York leukemia data is used for our spatial correlation model. The model provides spatial correlation which makes possible the imputation of missing observation. It can find small clusters which is not possible using scan statistics. The forecast deviance is large when case number rises which hints it potential as a monitoring tool. For the spatial-temporal correlation model, the mumps and dengue fever in Taiwan, which have different routes of infection, are used. For the mumps data, the spatial and temporal correlations are not clear, and the clusters take place in the north of Taiwan and Ping Tung frequently. Dengue fever clusters usually occur in Tainan, Kaohsiung and Taipei, and the spatial and temporal correlations of dengue fever are significant. The clusters which occur in southern Taiwan last quite long, often starting in summer and vanishing in winter. The clusters in northern Taiwan are usually not sustained. Dengue fever infects fast, so the department of health has to pay close attention as long as one case takes place. Similarly the prediction deviances, for both diseases, are large when the number of cases increases, indicating its potential usage as a monitoring tool.