Three Essays in Applied Statistics and Methodology

Abstract

In the increasingly complex data landscape of the modern world, the growing diversity of data has opened up exciting new avenues of research. This thesis presents three forays into areas representing different challenges in the realms of time series, text, and image data across an array of applications. • Chapter 1 proposes a Bayesian algorithm for learning about the memory distribution of a superposition of autoregressions. The parameterization of this model structure is delicate and experiments suggest a solution which can be deployed in practice. The methods are illustrated by an analysis of U.S. inflation data. • Chapter 2 examines the integration of text and traditional covariates into a heteroge- nous dataset within the Concise Comparative Summaries framework. We address key methodological challenges, including optimization strategies, penalization, handling missing data, and reconciling scaling differences. We further compare our integrated approach with text-only and covariate-only analyses, and illustrate its effectiveness through a comprehensive analysis of a heterogeneous medical dataset focused on fre- quent users of intensive care units. • Chapter 3 leverages machine learning methodology on a dataset of over 200,000 pottery fragment images from the Sanxingdui Bronze culture to achieve precise chronologi- cal classification and uncover an anomalous excavation site. This work highlights the untapped potential of applying modern data-driven methods to traditional archaeologi- cal practices in demonstrating the value of previously overlooked pottery fragments in archaeological research.