Dependence Models for Complex and Massive Data

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Scientific and technological advancements over the last few decades have brought a significant growth in the amount and complexity of data. This invited many challenges and opportunities for statistical research, both as an interdisciplinary and fundamental discipline. In many applications, understanding the dependence mechanisms in the collected data is crucial to bring insights into the nature of the underlying biological or physical process. However, statistical analyses of massive amounts of data are often limited to univariate features, lacking an understanding of multivariate dependencies among outcomes of interest. On the other hand, in small- to medium-scale studies, manually tailored multivariate models may not always sufficiently account for the various sources of complexity in the data. This research program bridges these two aspects by contributing novel multivariate modeling strategies to account for statistical dependence. The first theme of the research program addresses data complexities arising from study design and data collection process in small- to medium-scale studies, with a particular focus on incomplete data settings. These include (i) censored survival data in clinical studies, (ii) mismeasured data in physical and biomedical applications, (iii) latent variables arising in survey data, and (iv) missing or unequally spaced data in neuroimaging and longitudinal studies. These aspects will be tackled in this research using a wide range of copula-based dependence models such as conditional copulas, vine copulas and factor copulas. The second theme of this research program addresses some of the statistical challenges in analyzing high-throughput data from large-scale multi-center research consortia. Specifically, we contribute multivariate modeling strategies and novel meta-analysis methods to shed light into cross-phenotype dependencies in multi-center experiments involving model organisms. Statistical tools developed under this research program will help evaluate and ensure reproducibility in scientific experiments. Moreover, this research program will provide several opportunities to train students on methodological, applied and computational aspects, and to involve them in cutting-edge biomedical, clinical and genetic research.