Bayesian modelling of complex dependence structures
Emanuele Aliverti · Padua@research (University of Padova) · 2019
Complex dependence structures characterising modern data are routinely encountered in a large variety of research fields. Medicine, biology, psychology and social sciences are enriched by intricate architectures such as networks, tensors and more generally high-dimensional dependent data. Rich dependence structures stimulate challenging research questions and open wide methodological avenues in different areas of statistical research, providing an exciting atmosphere to develop innovative tools. A primary interest in statistical modelling of complex data is on adequately extracting information to conduct meaningful inference, providing reliable results in terms of uncertainty quantification and generalisability into future samples. These aims require ad-hoc statistical methodologies to appropriately characterize the dependence structures defining complex data as such, further improving the understanding of the mechanisms underlying the observed configurations. The focus of the thesis is on Bayesian modelling of complex dependence structures via latent variable constructs. This strategy characterises the dependence structure in an unobservable latent space, specifying the observed quantities as conditionally independent given a set of latent attributes, facilitating tractable posterior inference and an eloquent interpretation. The thesis is organized into three main parts, illustrating case studies from different fields of application and focused on studying modern challenges in neuroscience, psychology and criminal justice. Bayesian modelling of the complex data arising in these domains via latent features effectively provides valuable insights on different aspects of such structures, addressing the questions of interest and contributing to the scientific understanding.