Models, methods and inference for non-standard correlated data

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The advent of sophisticated tools of measurement has given rise to new modes of data collection resulting in non-standard correlated data, oftentimes involving disparate responses, frequently with a mixture of discrete and continuous responses, or of longitudinal and survival outcomes, and possibly from multiple sources or different study designs. The resulting complex structure typically requires non-standard statistical approaches that usually entail computationally intensive methodologies. These are particularly common in many applications in engineering, finance, and in medicine and health. Conventional tools that generally rely on the assumption that the data, or some suitable transformations of them, follow a Gaussian distribution, do not directly apply in these contexts.The research proposed here concerns the development of joint models and methodologies for application in non-standard correlated data settings. It pays specific focus on situations involving complex dependence structures arising from data comprising possibly high-dimensional non-standard correlated responses. Particular emphasis is given on development and computational implementation of new methodologies for use by practitioners in engineering and the medical/health sciences. The proposed research is anticipated to yield improved, flexible, and powerful techniques for data analysis in the age of big data.