Grant: Discovery Grants Program - Individual

This research is aiming at two different directions: one is to develop models, computation, inferences and diagnostics for count data time series, and the other one is to develop algorithms and grouping methodology for generalized cluster analysis. Count data time series arise from dynamic phenomena or systems in environmental science, climatology, hydrology, internet administration, cancer research, insurance industry, etc., where non-negative integer-valued observations are obtained at different time points. The serial dependence and marginal characteristics are of interests. We have developed a series of models to describe various scenarios of serial dependence as well as margins. With these models developed, the computation becomes the number one concern in inferences and applications. Currently, we are developing numerical algorithms for model fitting, testing and diagnostic. In addition, we attempt to develop non-stationary models allowing time-varying features, which will further lead to a new modelling approach in GLM and longitudinal studies to permit series dependence other than the latent approach. Cluster analysis partitions objects into different groups according to a similarity feature. Applications arise in many disciplines such as field zoning in environmetric studies, species classification in biology, etc. Classic cluster analysis uses the centroid to characterize the similarity, where one observation corresponds to one object. Generalized cluster analysis extends to other similarity characteristics, and permits a data set for each object. Using probabilistic clustering (namely finite mixture model), we are developing a data-driven algorithm for model fitting and bias reduction for estimates. Besides, we are proposing the techniques of model linking and model clustering for the situation where each object has a data set associated with many covariates.