Analytical problems caused by over-fitting, confounding and non-independence in the data is a major challenge for variable selection. As more variables are tested against a certain data set, there is a greater risk that some will explain the data merely by chance, but will fail to explain new data. The main aim of this study is to employ a systematic and practicable variable selection process for the spatial analysis and mapping of historical malaria risk in Botswana using data collected from the MARA (Mapping Malaria Risk in Africa) project and environmental and climatic datasets from various sources. Details of how a spatial database is compiled for a statistical analysis to proceed is provided. The automation of the entire process is also explored. The final bayesian spatial model derived from the non-spatial variable selection procedure using Markov Chain Monte Carlo simulation was fitted to the data. Winter temperature had the greatest effect of malaria prevalence in Botswana. Summer rainfall, maximum temperature of the warmest month, annual range of temperature, altitude and distance to closest water source were also significantly associated with malaria prevalence in the final spatial model after accounting for spatial correlation. Using this spatial model malaria prevalence at unobserved locations was predicted, producing a smooth risk map covering Botswana. The automation of both compiling the spatial database and the variable selection procedure proved challenging and could only be achieved in parts of the process. The non-spatial selection procedure proved practical and was able to identify stable explanatory variables and provide an objective means for selecting one variable over another, however ultimately it was not entirely successful due to the fact that a unique set of spatial variables could not be selected.

One of the key concerns in spatial analysis and modelling is to study and analyse similarities or dissimilarities between places over geographical space. However, ”global“ spatial models may fail to identify spatial variations of relationships (spatial heterogeneity) by assuming spatial stationarity of relationships. In many real-life situations spatial variation in relationships possibly exists and the assumption of global stationarity might be highly unrealistic leading to ignorance of a large amount of spatial information. In contrast, local spatial models emphasise differences or dissimilarity over space and focus on identifying spatial variations in relationships. These models allow the parameters of models to vary locally and can provide more useful information on the processes generating the data in different parts of the study area. In this study, a framework for localising spatial interaction models, based on geographically weighted (GW) techniques, has been developed. This framework can help in detecting, visualising and analysing spatial heterogeneity in spatial interaction systems. In order to apply the GW concept to spatial interaction models, we investigate several approaches differing mainly in the way calibration points (flows) are defined and spatial separation (distance) between flows is calculated. As a result, a series of localised geographically weighted spatial interaction (GWSI) models are developed. Using custom-built algorithms and computer code, we apply the GWSI models to a journey-to-work dataset in Switzerland for validation and comparison with the related global models. The results of the model calibrations are visualised using a series of conventional and flow maps along with some matrix visualisations. The comparison of the results indicates that in most cases local GWSI models exhibit an improvement over the global models both in providing more useful local information and also in model performance and goodness-of-fit.

Species Distribution Modelling (SDM) plays a key role in a number of biological applications: assessment of temporal trends in distribution, environmental impact assessment and spatial conservation planning. From a statistical perspective, this thesis develops two methods for increasing the accuracy and reliability of maps of density surfaces and provides a solution to the problem of how to collate multiple density maps of the same region, obtained from differing sources. From a biological perspective, these statistical methods are used to analyse two marine mammal datasets to produce accurate maps for use in spatial conservation planning and temporal trend assessment. The first new method, Complex Region Spatial Smoother [CReSS; Scott-Hayward et al., 2013], improves smoothing in areas where the real distance an animal must travel (`as the animal swims') between two points may be greater than the straight line distance between them, a problem that occurs in complex domains with coastline or islands. CReSS uses estimates of the geodesic distance between points, model averaging and local radial smoothing. Simulation is used to compare its performance with other traditional and recently-developed smoothing techniques: Thin Plate Splines (TPS, Harder and Desmarais [1972]), Geodesic Low rank TPS (GLTPS; Wang and Ranalli [2007]) and the Soap lm smoother (SOAP; Wood et al. [2008]). GLTPS cannot be used in areas with islands and SOAP can be very hard to parametrise. CReSS outperforms all of the other methods on a range of simulations, based on their fit to the underlying function as measured by mean squared error, particularly for sparse data sets. Smoothing functions need to be flexible when they are used to model density surfaces that are highly heterogeneous, in order to avoid biases due to under- or over-fitting. This issue was addressed using an adaptation of a Spatially Adaptive Local Smoothing Algorithm (SALSA, Walker et al. [2010]) in combination with the CReSS method (CReSS-SALSA2D). Unlike traditional methods, such as Generalised Additive Modelling, the adaptive knot selection approach used in SALSA2D naturally accommodates local changes in the smoothness of the density surface that is being modelled. At the time of writing, there are no other methods available to deal with this issue in topographically complex regions. Simulation results show that CReSS-SALSA2D performs better than CReSS (based on MSE scores), except at very high noise levels where there is an issue with over-fitting. There is an increasing need for a facility to combine multiple density surface maps of individual species in order to make best use of meta-databases, to maintain existing maps, and to extend their geographical coverage. This thesis develops a framework and methods for combining species distribution maps as new information becomes available. The methods use Bayes Theorem to combine density surfaces, taking account of the levels of precision associated with the different sets of estimates, and kernel smoothing to alleviate artefacts that may be created where pairs of surfaces join. The methods were used as part of an algorithm (the Dynamic Cetacean Abundance Predictor) designed for BAE Systems to aid in risk mitigation for naval exercises. Two case studies show the capabilities of CReSS and CReSS-SALSA2D when applied to real ecological data. In the first case study, CReSS was used in a Generalised Estimating Equation framework to identify a candidate Marine Protected Area for the Southern Resident Killer Whale population to the south of San Juan Island, off the Pacific coast of the United States. In the second case study, changes in the spatial and temporal distribution of harbour porpoise and minke whale in north-western European waters over a period of 17 years (1994-2010) were modelled. CReSS and CReSS-SALSA2D performed well in a large, topographically complex study area. Based on simulation results, maps produced using these methods are more accurate than if a traditional GAM-based method is used. The resulting maps identified particularly high densities of both harbour porpoise and minke whale in an area off the west coast of Scotland in 2010, that might be a candidate for inclusion into the Scottish network of Nature Conservation Marine Protected Areas.

Fine-scale urban land cover information is important for a number of applications, including urban tree canopy mapping, green space analysis, and urban hydrologic modeling. Land cover information has traditionally been extracted from satellite or aerial images using automated image classification techniques, which classify pixels into different categories of land cover based on their spectral characteristics. However, in fine spatial resolution images (4 meters or better), the high degree of within-class spectral variability and between-class spectral similarity of many types of land cover leads to low classification accuracy when pixel-based, purely spectral classification techniques are used. Object-based classification methods, which involve segmenting an image into relatively homogeneous regions (i.e. image segments) prior to classification, have been shown to increase classification accuracy by incorporating the spectral (e.g. mean, standard deviation) and non-spectral (e.g. te xture, size, shape) information of image segments for classification. One difficulty with the object-based method, however, is that a segmentation parameter (or set of parameters), which determines the average size of segments (i.e. the segmentation scale), is difficult to choose. Some studies use one segmentation scale to segment and classify all types of land cover, while others use multiple scales due to the fact that different types of land cover typically vary in size. In this dissertation, two multi-scale object-based classification methods were developed and tested for classifying high resolution images of Deerfield Beach, FL and Houston, TX. These multi-scale methods achieved higher overall classification accuracies and Kappa coefficients than single-scale object-based classification methods. / Since the two dissertation methods used an automated algorithm (Random Forest) for image classification, they are also less subjective and easier to apply to other study areas than most existing multi-scale object-based methods that rely on expert knowledge (i.e. decision rules developed based on detailed visual inspection of image segments) for classifying each type of land cover. / by Brian A. Johnson. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web.

Reliable geographic intelligence is essential for urban areas; land-cover classification creates the data for urban spatial decision making. This research tested a methodology to create a land-cover map for the main campus of Florida Atlantic University in Boca Raton, Florida. The accuracy of nine separate land-cover classification results were tested; the one with the highest accuracy was chosen for the final map. Object-based image segmentation was applied to fused and LiDAR point cloud (elevation and intensity) data and aerial imagery. These were classified by Random Forest, k-Nearest Neighbor and Support Vector Machines classifiers. Shadow features were reclassified hierarchically in order to create a complete map. The Random Forest classifier used with the fused data set gave the highest overall accuracy at 82.3%, and a Kappa value at 0.77. When combined with the results from the shadow reclassification, the overall accuracy increased to 86.3% and the Kappa value improved to 0.82. / Includes bibliography. / Thesis (M.A.)--Florida Atlantic University, 2016. / FAU Electronic Theses and Dissertations Collection

Lin, Hualiang. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 140-177). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

The microbial communities found in soils are inherently heterogeneous and often exhibit spatial variations on a small scale. Becker et al. (2006) investigate this phenomenon and present statistical analyses to support their findings. In this project, alternative statistical methods and models are considered and employed in a re-analysis of the data from Becker. First, parametric nested random effects models are considered as an alternative to the nonparametric semivariogram models and kriging methods employed by Becker to analyze patterns of spatial variation. Second, multiple logistic regression models are employed to investigate factors influencing microbial community structure as an alternative to the simple logistic models used by Becker. Additionally, the microbial community profile data of Becker were unobservable at several points in the spatial grid. The Becker analysis assumes that the data are missing completely at random and as such have relatively little impact on inference. In this re-analysis, this assumption is investigated and it is shown that the pattern of missingness is correlated with both metabolic potential and spatial coordinates and thus provides useful information that was previously ignored by Becker. Multiple imputation methods are employed to incorporate the information present in the missing data pattern and results are compared with those of Becker.

Abstract not available

A copula is the representation of a multivariate distribution. Copulas are used to model multivariate data in many fields. Recent developments include copula models for spatial data and for discrete marginals. We will present a new methodological approach for modeling discrete spatial processes and for predicting the process at unobserved locations. We employ Bayesian methodology for both estimation and prediction. Comparisons between the new method and Generalized Additive Model (GAM) are done to test the performance of the prediction. Although there exists a large variety of copula functions, only a few are practically manageable and in certain problems one would like to choose the Gaussian copula to model the dependence. Furthermore, most copulas are exchangeable, thus implying symmetric dependence. However, none of them is flexible enough to catch the tailed (upper tailed or lower tailed) distribution as well as elliptical distributions. An elliptical copula is the copula corresponding to an elliptical distribution by Sklar's theorem, so it can be used appropriately and effectively only to fit elliptical distributions. While in reality, data may be better described by a "fat-tailed" or "tailed" copula than by an elliptical copula. This dissertation proposes a novel pseudo-copula (the modified Gaussian pseudo-copula) based on the Gaussian copula to model dependencies in multivariate data. Our modified Gaussian pseudo-copula differs from the standard Gaussian copula in that it can model the tail dependence. The modified Gaussian pseudo-copula captures properties from both elliptical copulas and Archimedean copulas. The modified Gaussian pseudo-copula and its properties are described. We focus on issues related to the dependence of extreme values. We give our pseudo-copula characteristics in the bivariate case, which can be extended to multivariate cases easily. The proposed pseudo-copula is assessed by estimating the measure of association from two real data sets, one from finance and one from insurance. A simulation study is done to test the goodness-of-fit of this new model. / Graduation date: 2012

Graphical models use Markov properties to establish associations among dependent variables. To estimate spatial correlation and other parameters in graphical models, the conditional independences and joint probability distribution of the graph need to be specified. We can rely on Gaussian multivariate models to derive the joint distribution when all the nodes of the graph are assumed to be normally distributed. However, when some of the nodes are discrete, the Gaussian model no longer affords an appropriate joint distribution function. We develop methods specifying the joint distribution of a chain graph with both discrete and continuous components, with spatial dependencies assumed among all variables on the graph. We propose a new group of chain graphs known as the generalized tree networks. Constructing the chain graph as a generalized tree network, we partition its joint distributions according to the maximal cliques. Copula models help us to model correlation among discrete variables in the cliques. We examine the method by analyzing datasets with simulated Gaussian and Bernoulli Markov random fields, as well as with a real dataset involving household income and election results. Estimates from the graphical models are compared with those from spatial random effects models and multivariate regression models. / Graduation date: 2013