Statistics Ph.D. Dissertation Defense - Michael Schwob

This 2025 Dissertation Defense will be held on Wednesday, April 2 from 1:00 p.m. to 3:00 p.m. with Michael Schwob. This event will be hybrid. If you are able to attend in person, it will be held in WEL 5.204. If you need the Zoom link, please email stat.admin@austin.utexas.edu.

Title: Bayesian Hierarchical Models for Dependent Ecological Data

Advisor: Dr. Mevin Hooten

Abstract: Ecological data are inherently dependent due to spatial and temporal autocorrelation, species interactions, seasonality, and environmental gradients. In this dissertation, I developed statistical methods that account for various forms of dependence that arise in ecological data. I first proposed a dynamic population model for the analysis of abundance data, which often experience a high degree of temporal autocorrelation. The model was fit to mosquito abundance data collected across North America. An additional source of dependence came in the form of temporal preferential sampling (TPS), where data collection was informed by the observed abundance. I accounted for temporal autocorrelation and TPS in a Bayesian hierarchical model (BHM), which was specified mechanistically such that the observed abundance was related to the Gompertz growth function. Due to the mechanistic specification, inference was made for abundance and phenological quantities of interest. Then, I developed a BHM to infer the relationship between population genetic data and the environment. Such data arise in the field of landscape genomics, where there is interest in the functional connectivity and migration patterns of populations. Population genetic data are highly dependent, and I accounted for spatial and temporal autocorrelation via composite likelihoods. The BHM contains a dyadic regression, which is linked to an advection-diffusion differential equation to infer how Bronze Age humans migrated throughout Europe. Finally, I developed a BHM for the analysis of spatial compositional data, which often arise in community ecology, organismal composition studies, and ecosystem forecasting. The model accounts for spatial autocorrelation and the compositional nature of the data. In particular, I transformed the compositional data to directional data and modeled it using a novel hyperspheric distribution. This is the first spatial hyperspheric approach to contain fixed and latent spatial random effects, while accounting for the compositional constraints inherent to the data. I applied the model to bioacoustic signal classifications obtained from a machine learning classifier.