Climate change presents a clear threat to the future of global food security. Changes in the patterns of temperature and precipitation have the potential to greatly decrease agri- cultural production. Developing successful adaptation strategies is dependent on under- standing both the potential changes in yield of a given crop, as well as the likelihood those changes occurring. This requires an understanding of the uncertainty in the geographic patterns of future climate change, as well as the response of a crop to those changes. In this dissertation I explore a framework for generating rapid estimates of the risk of climate change to agricultural yields. Using data from multiple climate models I use a regression based pattern scaling ap- proach in conjunction with a multi-resolution Gaussian spatial process model to emulate the output of a multi-model ensemble of global climate models. The approach is flexible across climate scenarios, allowing it to be easily used in conjunction with other impact models. Using this model I am able to rapidly emulate thousands of runs of a climate model on a laptop computer. The resulting synthetic distributions retain the spatial variability of the initial emulated models and provide a tool for generating probabilistic forecasts of regional climate change. Next I use a generalized additive model approach to estimate the stable manifold yield response surface of a set of irrigated and rained crops in China. This approach highlights the nonlinear relationship between changes in temperature and precipitation and yield. Results suggest that irrigation alone cannot prevent losses from climate change. Predictions of future temperature and precipitation show a trend towards temperatures above the critical threshold for many crops, indicating the potential for large losses. In the final chapter I combine the previously described methods to assess the impact of climate change on the spatial patterns of crop yield change in China. Result indicate overall losses to crop yield in the majority of cropped regions for both irrigated and non irrigated crops. These results represent a new methodology for rapidly assessing the risk of climate change to crop yield, and provide a new tool for prioritizing adaptation measures.

The application of spatial methods to epidemic estimation and prediction problems is a vibrant and active area of research. In many cases, however, well thought out and laboratory supported models for epidemic patterns may be easy to specify but extremely difficult to fit efficiently. While this problem exists in many scientific disciplines, epidemic modeling is particularly prone to this challenge due to the rate at which the problem scope grows as a function of the size of the spatial and temporal domains involved. An additional barrier to widespread use of spatiotemporal epidemic models is the lack of user friendly software packages capable of fitting them. In particular, compartmental epidemic models are easy to understand, but in most cases difficult to fit. This class of epidemic models describes a set of states, or compartments, which captures the disease progression in a population. This dissertation attempts to expand the problem scope to which spatio-temporal compartmental epidemic models are applicable both computationally and practically. In particular, a general family of spatially heterogeneous SEIRS models is developed alongside a software library with the dual goals of high computational performance and ease of use in fitting models in this class. We emphasize the task of model specification, and develop a framework describing the components of epidemic behavior. In addition, we establish methods to estimate and interpret reproductive numbers, which are of fundamental importance to the study of infectious disease. Finally, we demonstrate the application of these techniques both under simulation, and in the context of a diverse set of real diseases, including Ebola Virus Disease, Smallpox, Methicillin-resistant Staphylococcus aureus, and Influenza.

<p>This thesis explores how to sparsely represent distributions of points for geometric statistical problems. A <italic>coreset<italic> C is a small summary of a point set P such that if a certain statistic is computed on P and C, then the difference in the results is guaranteed to be bounded by a parameter &epsilon;. Two examples of coresets are &epsilon;-samples and &epsilon;-kernels. An &epsilon;-sample can estimate the density of a point set in any range from a geometric family of ranges (e.g., disks, axis-aligned rectangles). An &epsilon;-kernel approximates the width of a point set in all directions. Both coresets have size that depends only on &epsilon;, the error parameter, not the size of the original data set. We demonstrate several improvements to these coresets and how they are useful for geometric statistical problems.</p><p>We reduce the size of &epsilon;-samples for density queries in axis-aligned rectangles to nearly a square root of the size when the queries are with respect to more general families of shapes, such as disks. We also show how to construct &epsilon;-samples of probability distributions. </p><p>We show how to maintain &ldquo;stable&rdquo; &epsilon;-kernels, that is if the point set P changes by a small amount, then the &epsilon;-kernel also changes by a small amount. This is useful in surveillance tracking problems and the stable properties leads to more efficient algorithms for maintaining &epsilon;-kernels. </p><p>We next study when the input point sets are uncertain and their uncertainty is modeled by probability distributions. Statistics on these point sets (e.g., radius of smallest enclosing ball) do not have exact answers, but rather distributions of answers. We describe data structures to represent approximations of these distributions and algorithms to compute them. We also show how to create distributions of &epsilon;-kernels and &epsilon;-samples for these uncertain data sets. </p><p>Finally, we examine a spatial anomaly detection problem: computing a spatial scan statistic. The input is a point set P and measurements on the point set. The spatial scan statistic finds the range (e.g., an axis-aligned bounding box) where the measurements inside the range are the most different from measurements outside of the range. We show how to compute this statistic efficiently while allowing for a bounded amount of approximation error. This result generalizes to several statistical models and types of input point sets.</p> / Dissertation

Criminal justice researchers and crime geographers have long recognized the importance of understanding where crimes happen as well as to whom and by whom. Although past research often focused on violent crimes, calls for research into non-lethal white-collar crimes emerged in the 1970s. Today, identity theft is among the fastest growing white-collar crimes in the United States, although official recognition of it as a criminal act is a relatively recent development. Remaining largely unmet, the need for white-collar crime research has greatly intensified considering the escalating identity theft problem. Furthermore, many studies conclude that identity theft will continue to rise due to increasing technology-driven offenses via the Internet and widespread use of digital consumer databases. Utilizing theoretical framework established in crime geography, GIS mapping and spatial statistics are employed to produce a spatial analysis of identity theft in the U.S. from 2002-2006. Distinct regional variations, such as high rates in the western and southwestern states, and low rates in New England and the central plains states, are identified for identity theft as reported by the FTC. Significant spatial patterns of identity theft victims alongside social demographic variables are also revealed in order to better understand the regional patterns that may indicate underlying social indicators contributing to identity theft. Potential social variables, such as race/ethnicity and urban-rural populations, are shown to have similar patterns that may be directly associated with U.S. identity theft victims. To date, no in-depth geographic studies exist on the geographic patterns of identity theft, although numerous existing studies attempt basic spatial pattern recognition and propose the need for better spatial interpretation. This thesis is the first empirical study on the geographies of identity theft. It fills in a void in the literature by revealing significant geographical patterns of identity theft in the digital age, attempts at understanding the social factors driving the patterns, and examines some of the social implications of identity theft.

In recent years, the application of resampling methods to dependent data, such as time series or spatial data, has been a growing field in the study of statistics. In this dissertation, we discuss two such applications. In spatial statistics, the reliability of Kriging prediction methods relies on the observations coming from an underlying Gaussian process. When the observed data set is not from a multivariate Gaussian distribution, but rather is a transformation of Gaussian data, Kriging methods can produce biased predictions. Bootstrap resampling methods present a potential bias correction. We propose a parametric bootstrap methodology for the calculation of either a multiplicative or additive bias correction factor when dealing with Trans-Gaussian data. Furthermore, we investigate the asymptotic properties of the new bootstrap based predictors. Finally, we present the results for both simulated and real world data. In time series analysis, the estimation of covariance parameters is often of utmost importance. Furthermore, the understanding of the distributional behavior of parameter estimates, particularly the variance, is useful but often difficult. Block bootstrap methods have been particularly useful in such analyses. We introduce a new procedure for the estimation of covariance parameters for replicated time series data.

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Neighbourhood stressors have an incubating effect for a variety of health-related disorders involving children. It is of interest is to determine if asthma prevalence is greater amongst school children at age 7-8 resident of chronic stress neighbourhoods in Winnipeg, after adjusting for family history of asthma and socioeconomic status. The urban component of children (1472 entire; 698 birth home) extracted from the Study of Asthma, Genes and the Environment (SAGE) Survey administered in 2002-2003 to a birth cohort from 1995 in Manitoba. Dichotomous parent report of child asthma from the SAGE Survey nested within birth cohort was geocoded by postal code, which allowed designation of neighbourhood in hierarchical linear modelling. Children living in census tracts assigned low SES scores by compositional stressors were found to have a decreased odds of parent report of asthma, while those inhabiting profiles with high contextual crime rates were at increased risk.

Matrix factorisation treats observations as linear combinations of basis vectors together with, possibly, additive noise. Notable techniques in this family are Principal Components Analysis and Independent Components Analysis. Applied to brain images, matrix factorisation provides insight into the spatial and temporal structure of data. We improve on current practice with methods that unify different stages of analysis simultaneously for all subjects in a dataset, including dimension estimation and reduction. This results in uncertainty information being carried coherently through the analysis. A computationally efficient approach to correlated multivariate normal distributions is set out. This enables spatial smoothing during the inference of basis vectors, to a level determined by the data. Applied to neuroimaging, this reduces the need for blurring of the data during preprocessing. Orthogonality constraints on the basis are relaxed, allowing for overlapping ‘networks’ of activity. We consider a nonparametric matrix factorisation model inferred using Markov Chain Monte Carlo (MCMC). This approach incorporates dimensionality estimation into the infer- ence process. Novel parallelisation strategies for MCMC on repeated graphs are provided to expedite inference. In simulations, modelling correlation structure is seen to improve source separation where latent basis vectors are not orthogonal. The Cambridge Centre for Ageing and Neuroscience (Cam-CAN) project obtained fMRI data while subjects watched a short film, on 30 of whose recordings we demonstrate the approach. To conduct inference on larger datasets, we provide a fixed dimension Structured Matrix Factorisation (SMF) model, inferred through Variational Bayes (VB). By modelling the components as a mixture, more general distributions can be expressed. The VB approach scaled to 600 subjects from Cam-CAN, enabling a comparison to, and validation of, the main findings of an earlier analysis; notably that subjects’ responses to movie watching became less synchronised with age. We discuss differences in results obtained under the MCMC and VB inferred models.

Tropical forests are extremely important ecosystems which play a substantial role in the global carbon budget and are increasingly dominated by anthropogenic disturbance through deforestation and forest degradation, contributing to emissions of greenhouse gases to the atmosphere. There is an urgent need for forest monitoring over extensive and inaccessible tropical forest which can be best accomplished using spaceborne satellite data. Currently, two key processes are extremely challenging to monitor: forest degradation and post-disturbance re-growth. The thesis work focuses on these key processes by considering change indicators derived from radar remote sensing signal that arise from changes in forest structure. The problem is tackled by exploiting spaceborne Synthetic Aperture Radar (SAR) and Interferometric SAR (InSAR) observations, which can provide forest structural information while simultaneously being able to collect data independently of cloud cover, haze and daylight conditions which is a great advantage over the tropics. The main principle of the work is that a connection can be established between the forest structure distribution in space and signal variation (spatial statistics) within backscatter and Digital Surface Models (DSMs) provided by SAR. In turn, forest structure spatial characteristics and changes are used to map forest condition (intact or degraded) or disturbance. The innovative approach focuses on looking for textural patterns (and their changes) in radar observations, then connecting these patterns to the forest state through supporting evidence from expert knowledge and auxiliary remote sensing observations (e.g. high resolution optical, aerial photography or LiDAR). These patterns are descriptors of the forest structural characteristics in a statistical sense, but are not estimates of physical properties, such as above-ground biomass or canopy height. The thesis tests and develops methods using novel remote sensing technology (e.g. single-pass spaceborne InSAR) and modern image statistical analysis methods (wavelet-based space-scale analysis). The work is developed on an experimental basis and articulated in three test cases, each addressing a particular observational setting, analytical method and thematic context. The first paper deals with textural backscatter patterns (C-band ENVISAT ASAR and L-band ALOS PALSAR) in semi-deciduous closed forest in Cameroon. Analysis concludes that intact forest and degraded forest (arising from selective logging) are significantly different based on canopy structural properties when measured by wavelet based space-scale analysis. In this case, C-band data are more effective than longer wavelength L-band data. Such a result could be explained by the lower wave penetration into the forest volume at shorter wavelength, with the mechanism driving the differences between the two forest states arising from upper canopy heterogeneity. In the second paper, wavelet based space-scale analysis is also used to provide information on upper canopy structure. A DSM derived from TanDEM-X acquired in 2014 was used to discriminate primary lowland Dipterocarp forest, secondary forest, mixed-scrub and grassland in the Sungai Wain Protection Forest (East Kalimantan, Indonesian Borneo) which was affected by the 1997/1998 El Niño Southern Oscillation (ENSO). The Jeffries- Matusita separability of wavelet spectral measures of InSAR DSMs between primary and secondary forest was in some cases comparable to results achieved by high resolution LiDAR data. The third test case introduces a temporal component, with change detection aimed at detecting forest structure changes provided by differencing TanDEM-X DSMs acquired at two dates separated by one year (2012-2013) in the Republic of Congo. The method enables cancelling out the component due to terrain elevation which is constant between the two dates, and therefore the signal related to the forest structure change is provided. Object-based change detection successfully mapped a gradient of forest volume loss (deforestation/forest degradation) and forest volume gain (post-disturbance re-growth). Results indicate that the combination of InSAR observations and wavelet based space-scale analysis is the most promising way to measure differences in forest structure arising from forest fires. Equally, the process of forest degradation due to shifting cultivation and post-disturbance re-growth can be best detected using multiple InSAR observations. From the experiments conducted, single-pass InSAR appears to be the most promising remote sensing technology to detect forest structure changes, as it provides three-dimensional information and with no temporal decorrelation. This type of information is not available in optical remote sensing and only partially available (through a 2D mapping) in SAR backscatter. It is advised that future research or operational endeavours aimed at mapping and monitoring forest degradation/regrowth should take advantage of the only currently available high resolution spaceborne single-pass InSAR mission (TanDEM-X). Moreover, the results contribute to increase knowledge related to the role of SAR and InSAR for monitoring degraded forest and tracking the process of forest degradation which is a priority but still highly challenging to detect. In the future the techniques developed in the thesis work could be used to some extent to support REDD+ initiatives.

The World Bank estimated that 1.4 billion people in the world were living in poverty in 2008. In the last several decades, many countries have succeeded in not only reducing the number and percent of people living in poverty, but also increasing overall economic strength. Yet, while some countries have succeeded, many others have not. This unequal growth has led to newer development theories that include the importance of geography and the physical environment. A leading researchers in this field, Jeffrey Sachs, argues that geography and physical ecology, along with some economic indicators are responsible for this difference in success. This research tests the theory that was suggested by Sachs. Spatial statistics techniques were used to analyze these theories with new methods and shed new light on the variables. Results showed that certain variables (coastal population, proximity to a major market) were not as significant in development, when regional differences were accounted for. However, other variables, particularly malaria and consumption, were very significant. In addition, testing variables regionally provided much better results than previously-used global models. Lastly, the results were used to analyze outliers. The outliers helped to discuss other important variables and pave the way for future research.