Methods and applications for space-time data

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

Shand, Lyndsay Elizabeth

关键词: Spatio-temporal data;    Nonstationary models;    Areal data;    Conditional autoregressive (CAR) model;    Copula models;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/97696/SHAND-DISSERTATION-2017.pdf?sequence=1&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

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 randomfield. 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.