Advances in Spatial Statistics and Inference Methods for Markov Population Models
Open Access
- Author:
- Walder, Adam
- Graduate Program:
- Statistics (PHD)
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 14, 2021
- Committee Members:
- Matthew Ferrari, Outside Unit & Field Member
Ephraim Hanks, Chair & Dissertation Advisor
Aleksandra Slavkovic, Major Field Member
Murali Haran, Major Field Member
Ephraim Mont Hanks, Program Head/Chair - Keywords:
- Spatial Generalized Mixed Models
Bayesian Privacy
Markov Population Models
Laplace Approximations
Laplace Moving Average Models - Abstract:
- Spatial generalized linear mixed models (SGLMMs) commonly rely on Gaussian random fields (GRFs) to capture spatially correlated error. We investigate the results of replacing Gaussian processes with Laplace moving averages (LMAs) in SGLMMs. We demonstrate that LMAs offer improved predictive power when the data exhibits localized spikes in the response. SGLMMs with LMAs are shown to maintain analogous parameter inference and similar computing to Gaussian SGLMMs. We propose a novel discrete space LMA model for irregular lattices and construct conjugate samplers for LMAs with georeferenced and areal support. We provide a Bayesian analysis of SGLMMs with LMAs and GRFs over multiple data support and response types We develop methods for privatizing spatial location data, such as spatial locations of individual disease cases. We propose two novel Bayesian methods for generating synthetic location data based on log-Gaussian Cox processes (LGCPs). We show that conditional predictive ordinate (CPO) estimates can easily be obtained for point process data. We construct a novel risk metric that utilizes CPO estimates to evaluate individual disclosure risks. We adapt the propensity mean square error (pMSE) data utility metric for LGCPs. We demonstrate that our synthesis methods offer an improved risk vs. utility balance in comparison to radial synthesis with a case study of Dr. John Snow’s cholera outbreak data. We demonstrate how to perform inference on Markov population processes with Laplace approximations. We derive a sparse covariance structure for the linear noise approximation (LNA) which offers a joint Gaussian likelihood for Markov population models based solely on the solution to a set of deterministic equations. We show that Laplace approximations allow inference with LNAs to be parallelized and require no stochastic infill. We also demonstrate that our method offers comparable accuracy to MCMC on a simulated Susceptible-Infected-Susceptible data set. We use Laplace approximations to fit a stochastic susceptible-exposed-infected-recovered system to the Princess Diamond COVID-19 cruise ship data set.