Methods and applications for space-time data

Spatial and spatio-temporal data are presented in a variety of forms and require a unique set of techniques to analyze. The goal of such analyses is often to estimate the spatial and/or temporal dependency structures of the underlying random field. This estimation in turn can then be used to make inference about the underlying random process. Recurring challenges with spatial data include a lack of multiple realizations of the process, e.g. a lack of replicates and the estimation of dependency structures given this difficulty. In this work, I contributed to solving this problem based on both geostatistical and areal data using likelihood and Bayesian methods respectively. A nonstationary spatio-temporal model is proposed which applies the concept of the dimension expansion method in Bornn et al. (2012). The estimation of this model is investigated and simulations are conducted for both separable and nonseparable space-time covariance models. The model is also illustrated with wind speed and streamflow datasets. Both simulation and data analyses show that modeling nonstationarity in both space and time can improve the predictive performance over stationary covariance models or models that are nonstationary in space but stationary in time. In demand of predicting new HIV diagnosis rates based on publicly available HIV data that is abundant in space but has few points in time, a class of spatially varying autoregressive (SVAR) models compounded with conditional autoregressive (CAR) spatial correlation structures is proposed. The copula approach coupled with a flexible CAR formulation are employed to model the dependency between adjacent counties. These models allow for spatial and temporal correlation as well as space-time interactions and are naturally suitable for predicting spatio-temporal disease data that feature such a data structure. The models also allow us to estimate the spatially varying evolution pattern of the disease. We apply the proposed models to HIV data over Florida, California and New England states and compare them to a range of linear mixed models that have been recently popular for modeling spatio-temporal disease data. The results show that for such data our proposed models outperform the others in terms of prediction.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Statistics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2017

Author dc:creator

• Shand, Lyndsay Elizabeth

Contributors dc:contributor

• Li, Bo
• Douglas, Jeff
• Guerrier, Stéphane
• O'Hara Ruiz, Marilyn

• Spatio-temporal data
• Nonstationary models
• Areal data
• Conditional autoregressive (CAR) model
• Copula models

Statement dc:rights

• Copyright 2017 Lyndsay Shand

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/97696

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/97696