Bayesian spatiotemporal models have been successfully applied to various fields of science, such as ecology and epidemiology. The complicated nature of spatiotemporal patterns can be well represented through priors such as Gaussian processes. This dissertation is focused on two applications of Bayesian spatiotemporal models: a) anomaly detection for spatiotemporal data with missingness and b) zero-inflated spatiotemporal count data analysis. Missingness in spatiotemporal data prohibits anomaly detection algorithms from learning characteristic rules and patterns due to the lack of most data. This project is motivated by a challenge provided by the National Science Foundation (NSF) and the National Geospatial-Intelligence Agency (NGA). The proposed model uses traffic patterns at nearby hours of the same day and the same time on different days of the week to recover the complete data. We compare the proposed model with the baseline and other models on the given dataset. It is also tested on a new dataset by the challenge organizer. In the zero-inflated spatiotemporal data analysis, a set of latent variables from Pólya-Gamma distributions are introduced to the Bayesian zero-inflated negative binomial model. The parameters of interest have conjugate priors conditional on the latent variables, which facilitates efficient posterior Markov chain Monte Carlo sampling. Varying spatial and temporal random effects are accommodated through Gaussian processes. To overcome the computation bottleneck that Gaussian processes may suffer when the sample size is large, a nearest-neighbor Gaussian process approach is implemented by constructing a sparse covariance matrix. The proposed Bayesian zero-inflated nearest-neighbor Gaussian processes model has been applied to simulated and COVID-19 data.
If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at STARS@ucf.edu
Doctor of Philosophy (Ph.D.)
College of Sciences
Statistics & Data Science
Big Data Analytics
Length of Campus-only Access
Doctoral Dissertation (Campus-only Access)
He, Qing, "Bayesian Spatiotemporal Modeling with Gaussian Processes" (2022). Electronic Theses and Dissertations, 2020-. 1383.
Restricted to the UCF community until December 2023; it will then be open access.