Statistical Inference for Bayesian Semi-Structured Regression Models

Statistical modeling has been one of the most ubiquitously applied and practically relevant achievements of statistical science over the last centuries. While recent advancements partially reflect the surge in complex data structures and types such as hierarchically structured observations or functional data measurements, the increasing availability of large non-tabular data sets—including text and images—over the last years necessitates the development of new methods adapted to these circumstances. Today’s challenges of statistical modeling involve millions of data points with differently structured data sources, data-driven hypotheses, and an unprecedented complexity of data-generating processes that statistical models need to mimic. The present proposal builds on the use of semi-structured models to model such data sets. It aims to develop principled, flexible, and scalable approaches to statistical inference for all model components.