Statistics Ph.D. Dissertation Defense - Beatrice Cantoni

This 2025 Dissertation Defense will be held on Monday, November 3 from 11:30 a.m. to 1:30 p.m. with Beatrice Cantoni. This event will be hybrid. If you are able to attend in person, it will be held in WEL 5.285. If you need the Zoom link,  please email stat.admin@austin.utexas.edu.

Title: Bayesian State Space Models for Inference in Presence of Data Complexities

Advisors: Dr. Corwin Zigler and Dr. Peter Mueller 

Abstract: In this dissertation, we study inference methods and design approaches for Bayesian state space models aimed at solving issues arising in selected data settings. Such models represent intuitive yet powerful tools for longitudinal data, but present limitations under various aspects, the design of effective borrowing of information structures, computational complexity, and missing data being just a few. At first, we focus on the goal of borrowing information through clustering when dealing with  binary longitudinal observations. Such data can, at an individual and independent level, intuitively be framed using state space models. Challenges arise when aiming at constructing a hierarchical joint model. We describe the issue of the observed time series being unaligned in time, and how a model and inference strategy can be built in response to this challenge. In the second project we present, we propose a framework to rigorously map common missing data assumptions to the context of state space models. In particular, we offer a rigorous consideration of assumptions about missing data mechanisms in the common paradigm of discrete, meaningful, underlying states, with implications on model design practices to guarantee effective parameters inference. With this regard, we present a methodology to make inference with physical activity (PA) data coming from wearable devices worn in free living conditions, based on a nonhomogeneous hidden Markov model (NHMM). Finally, we consider building a strategy capable of performing borrowing of information when using PA data. In particular, we build on the previously unveiled challenges to more broadly consider computational and hierarchical modeling issues arising with state space models for large and imbalanced data. We explore building alternative algorithms aimed at improving mixing through wider kernel step sizes and that rely on information learned from other individuals.