Mechanistic models for spatial and spatio-temporal data.

Open Access
- Author:
- Wikle, Nathan
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 15, 2021
- Committee Members:
- Tyler Wagner, Outside Unit & Field Member
David Hunter, Major Field Member
Ephraim Hanks, Chair & Dissertation Advisor
Murali Haran, Major Field Member
Ephraim Mont Hanks, Program Head/Chair - Keywords:
- spatial statistics
spatio-temporal statistics
mechanistic models
COVID-19
air pollution
ant trophallaxis - Abstract:
- Many processes in ecology, epidemiology, and environmental science are dynamic. While statistical and machine learning methods exist for accurate near-time prediction of such systems, interpretable scientific inference of the key dynamics driving such processes is often limited. Instead, models that incorporate known physical and biological mechanisms offer a promising path towards interpretable statistical inference of dynamical systems. In this dissertation, I develop new statistical methodology for the analysis of dynamic processes from spatial and space-time data. My contributions include: (1) a time inhomogeneous, continuous-time Markov chain model of longitudinal contact networks, with transition rates modeled as a function of time-varying covariates. This model is used to analyze ant trophallaxis (i.e., feeding) interactions in a colony of 73 ants, observed second-by-second for four hours; (2) a mechanistic model of the effect of sulfur dioxide emissions from coal-fired power plants on average sulfate concentrations in the central United States. A multivariate Ornstein-Uhlenbeck (OU) process is used to approximate the dynamics of the underlying space-time chemical transport process, and its distributional properties are leveraged to specify novel probability models for spatial data that are viewed as either a snapshot or a time-averaged observation of the OU process; and (3) a time-inhomogeneous negative binomial process model of the coronavirus disease 2019 (COVID-19) epidemic in Rhode Island, where the negative binomial process intensity is modeled as a mechanistic, compartmental model of COVID-19 transmission and clinical progression. This formulation provides a compelling joint likelihood model for the analysis of heterogeneous, dependent data streams from emerging epidemics.