This thesis develops a latent modeling framework and likelihood based inference tool to detect multiple temporal or spatial clusters.Cluster detection is important to researchers from various fields. Practical applications include: biological studies of DNA sequencing, environmental researches, epidemiological studies and surveillance for biological terrorism. The traditional scan statistics procedures have technical difficulties to detect multiple clusters of varying sizes. Some Bayesian

more »

... ches have to limitthe potential clusters in cell divisions. A recently proposed stepwise regression method tends to be inefficient in some cases. We utilize some probability distributions to model the latent clusters and mimic the sample data generation process. With model selection techniques, we can obtain an optimal number of total potential clusters. Based on a Monte-Carlo EM algorithm and likelihood based inference, we are able to estimate the associated model parameters, detect significant clusters and identify their locations and sizes. Compared with other procedures, this new approach is intuitive and simple. It is also more efficient and flexible for further extensions.