Flexible Dependence Models for Multivariate Data

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The last three decades have witnessed fascinating scientific discoveries, from the expansion of our universe to the completion of human genome. These could only be imagined in the realms of science fiction just a century ago. Modern technology plays a pivotal role in these achievements by enabling scientists to collect hard-to-reach data and in massive amounts. However, converting the information in data to meaningful knowledge is always what we are indebted to proper statistical analysis, directed by scientists' expertise.****This research program focuses on extracting and characterizing dependence information concealed in multivariate data.To extract dependence, we use a machinery called copula that separates marginal characteristics of variables from their joint behaviour, and to characterize dependence we propose nonparametric strategies that are flexible enough to capture (1) dynamic conditional dependencies, and (2) complex interrelations among a large number of variables. Our methodological contributions will greatly extend the capabilities and flexibility of copula-based dependence models in applications.**The proposed methods can be used to shed light into, for instance, studies of skeletal anatomy by revealing bone and muscle interactions, twin or family studies by detecting the shared characteristics that affect co-twin or familial dependence, or water quality monitoring in hydrological systems by specifying dependencies between the level of different hazards. In particular, this research will offer elaborate analyses of conditional and joint dependencies of water-quality measurements to the Manitoba Great Lakes Project of the University of Manitoba.**************************