Bayesian Spatio-Temporal Modeling for Forecasting, Trend Assessment and Spatial Trend Filtering

This work develops Bayesian spatio-temporal modeling techniques specifically aimed at studying several aspects of our motivating applications, to include vector-borne disease incidence and air pollution levels. A key attribute of the proposed techniques are that they are scalable to extremely large data sets which consist of spatio-temporally oriented observations. The scalability of our modeling strategies is accomplished in two primary ways. First, through the introduction of carefully constructed latent random variables we are able to develop Markov chain Monte Carlo (MCMC) sampling algorithms that consist primarily of Gibbs steps. This leads to the fast and easy updating of the model parameters from common distributions. Second, for the spatio-temporal aspects of the models, a novel sampling strategy for Gaussian Markov random fields (GRMFs) that can be easily implemented (in parallel) within MCMC sampling algorithms is used. The performance of the proposed modeling strategies are demonstrated through extensive numerical studies and are further used to analyze vector-borne disease data measured on canines throughout the conterminous United States and PM 2.5 levels measured at weather stations throughout the Eastern United States. In particular, we begin by developing a Poisson regression model that can be used to forecast the incidence of vector-borne disease throughout a large geographic area. The proposed model accounts for spatio-temporal dependence through a vector autoregression and is fit through a Metropolis-Hastings based Markov chain Monte Carlo (MCMC) sampling algorithm. The model is used to forecast the prevalence of Lyme disease (Chapter 2) and Anaplasmosis (Chapter 3) in canines throughout the United States. As a part of these studies we also evaluate the significance of various climatic and socio-economic drivers of disease. We then present (Chapter 4) the development of the \u27chromatic sampler\u27 for GMRFs. The chromatic sampler is an MCMC sampling technique that exploits the Markov property of GMRFs to sample large groups of parameters in parallel. A greedy algorithm for finding such groups of parameters is presented. The methodology is found to be superior, in terms of computational effort, to both full block and single-site updating. For assessing spatio-temporal trends, we develop (Chapter 5) a binomial regression model with spatially varying coefficients. This model uses Gaussian predictive processes to estimate spatially varying coefficients and a conditional autoregressive structure embedded in a vector autoregression to account for spatio-temporal dependence in the data. The methodology is capable of estimating both widespread regional and small scale local trends. A data augmentation strategy is used to develop a Gibbs based MCMC sampling routine. The approach is made computationally feasible through adopting the chromatic sampler for GMRFs to sample the spatio-temporal random effects. The model is applied to a dataset consisting of 16 million test results for antibodies to Borrelia burgdoferi and used to identify several areas of the United States experiencing increasing Lyme disease risk. For nonparametric functional estimation, we develop (Chapter 6) a Bayesian multidimensional trend filter (BMTF). The BMTF is a flexible nonparameteric estimator that extends traditional one dimensional trend filtering methods to multiple dimensions. The methodology is computationally scalable to a large support space and the expense of fitting the model is nearly independent of the number of observations. The methodology involves discretizing the support space and estimating a multidimensional step function over the discretized support. Two adaptive methods of discretization which allows the data to determine the resolution of the resulting function is presented. The BMTF is then used (Chapter 7) to allow for spatially varying coefficients within a quantile regression model. A data augmentation strategy is introduced which facilitates the development of a Gibbs based MCMC sampling routine. This methodology is developed to study various meteorological drivers of high levels of PM 2.5, a particularly hazardous form of air pollution consisting of particles less than 2.5 micrometers in diameter

Estimating Movement from Mobile Telephony Data

Mobile enabled devices are ubiquitous in modern society. The information gathered by their normal service operations has become one of the primary data sources used in the understanding of human mobility, social connection and information transfer. This thesis investigates techniques that can extract useful information from anonymised call detail records (CDR). CDR consist of mobile subscriber data related to people in connection with the network operators, the nature of their communication activity (voice, SMS, data, etc.), duration of the activity and starting time of the activity and servicing cell identification numbers of both the sender and the receiver when available. The main contributions of the research are a methodology for distance measurements which enables the identification of mobile subscriber travel paths and a methodology for population density estimation based on significant mobile subscriber regions of interest. In addition, insights are given into how a mobile network operator may use geographically located subscriber data to create new revenue streams and improved network performance. A range of novel algorithms and techniques underpin the development of these methodologies. These include, among others, techniques for CDR feature extraction, data visualisation and CDR data cleansing. The primary data source used in this body of work was the CDR of Meteor, a mobile network operator in the Republic of Ireland. The Meteor network under investigation has just over 1 million customers, which represents approximately a quarter of the country’s 4.6 million inhabitants, and operates using both 2G and 3G cellular telephony technologies. Results show that the steady state vector analysis of modified Markov chain mobility models can return population density estimates comparable to population estimates obtained through a census. Evaluated using a test dataset, results of travel path identification showed that developed distance measurements achieved greater accuracy when classifying the routes CDR journey trajectories took compared to traditional trajectory distance measurements. Results from subscriber segmentation indicate that subscribers who have perceived similar relationships to geographical features can be grouped based on weighted steady state mobility vectors. Overall, this thesis proposes novel algorithms and techniques for the estimation of movement from mobile telephony data addressing practical issues related to sampling, privacy and spatial uncertainty