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<p>This thesis consits of four papers dealing with distance based (non-Euclidean) tests for spatial clustering in inhomogeneous populations. </p><p>The density adjusted distance (DAD), which considers the underlying density, is defined in the first paper. The proposed distance can be used together with any of the old distance based methods developed for traditional homogeneous spatial patterns. </p><p>The test statistics in distance based tests can all be seen as a weighted sum of distance measures for distances between <i>n</i> cases with known co-ordinates. DAD based test statistics are developed and their performance is compared with the performance of previously suggested tests by simulation in the second paper. The tests are compared in different types of data set and for various kinds of clustering. It is shown that no test is the optimal choice for all alternative hypotheses and that the tests are unequally sensitive to the structure of the underlying data. Tests based on the DAD are often a good alternative. </p><p>Test statistics and graphical tools for the Empirical Distribution Function of DAD are developed and examined in the third paper. We show that the result of an EDF test combined with EDF plots provides more information about the possible nature of clustering in a sample than the result of a parametric test only. </p>

This thesis consits of four papers dealing with distance based (non-Euclidean) tests for spatial clustering in inhomogeneous populations. The density adjusted distance (DAD), which considers the underlying density, is defined in the first paper. The proposed distance can be used together with any of the old distance based methods developed for traditional homogeneous spatial patterns. The test statistics in distance based tests can all be seen as a weighted sum of distance measures for distances between n cases with known co-ordinates. DAD based test statistics are developed and their performance is compared with the performance of previously suggested tests by simulation in the second paper. The tests are compared in different types of data set and for various kinds of clustering. It is shown that no test is the optimal choice for all alternative hypotheses and that the tests are unequally sensitive to the structure of the underlying data. Tests based on the DAD are often a good alternative. Test statistics and graphical tools for the Empirical Distribution Function of DAD are developed and examined in the third paper. We show that the result of an EDF test combined with EDF plots provides more information about the possible nature of clustering in a sample than the result of a parametric test only.

<p>This dissertation focuses on solving some common problems associated with ecological field studies. In the core of the statistical methodology, lies spatial modeling that provides greater flexibility and improved predictive performance over existing algorithms. The applications involve prevalence datasets for hundreds of plants over a large area in the Cape Floristic Region (CFR) of South Africa.</p><p>In Chapter 2, we begin with modeling the categorical abundance data with a multi level spatial model using background information such as environmental and soil-type factors. The empirical pattern is formulated as a degraded version of the potential pattern, with the degradation effect accomplished in two stages. First, we adjust for land use transformation and then we adjust for measurement error, hence misclassification error, to yield the observed abundance classifications. With data on a regular grid over CFR, the analysis is done with a conditionally autoregressive prior on spatial random effects. With around ~ 37000 cells to work with, a novel paralleilization algorithm is developed for updating the spatial parameters to efficiently estimate potential and transformed abundance surfaces over the entire region.</p><p>In Chapter 3, we focus on a different but increasingly common type of prevalence data in the so called <italic>presence-only</italic> setting. We detail the limitations associated with a usual presence-absence analysis for this data and advocate modeling the data as a point pattern realization. The underlying intensity surface is modeled with a point-level spatial Gaussian process prior, after taking into account sampling bias and change in land-use pattern. The large size of the region enforces using an computational approximation with a bias-corrected predictive process. We compare our methodology against the the most commonly used maximum entropy method, to highlight the improvement in predictive performance.</p><p>In Chapter 4, we develop a novel hierarchical model for analyzing noisy point pattern datasets, that arise commonly in ecological surveys due to multiple sources of bias, as discussed in previous chapters. The effect of the noise leads to displacements of locations as well as potential loss of points inside a bounded domain. Depending on the assumption on existence of locations outside the boundary, a couple of different models -- <italic>island</italic> and <italic>subregion</italic>, are specified. The methodology assumes informative knowledge of the scale of measurement error, either pre-specified or learned from a training sample. Its performance is tested against different scales of measurement error related to the data collection techniques in CFR.</p><p>In Chapter 5, we suggest an alternative model for prevalence data, different from the one in Chapter 3, to avoid numerical approximation and subsequent computational complexities for a large region. A mixture model, similar to the one in Chapter 4 is used, with potential dependence among the weights and locations of components. The covariates as well as a spatial process are used to model the dependence. A novel birth-death algorithm for the number of components in the mixture is under construction.</p><p>Lastly, in Chapter 6, we proceed to joint modeling of multiple-species datasets. The challenge is to infer about inter-species competition with a large number of populations, possibly running into several hundreds. Our contribution involves applying hierarchical Dirichlet process to cluster the presence localities and subsequently developing measures of range overlap from posterior draws. This kind of simultaneous inference can potentially have implications for questions related to biodiversity and conservation studies. .</p> / Dissertation

Remediation of unexploded ordnance (UXO) and prioritization of excavation procedures for archaeological artifacts using electromagnetic (EM) induction are studied in this dissertation. Lowering of the false alarm rates that require excavation and artifact excavation prioritization can reduce the costs associated with unnecessary procedures. Data were taken over 5 areas at the San Jacinto Battleground near Houston, Texas, using an EM-63 metal detection instrument. The areas were selected using the archaeological concepts of cultural and natural formation processes applied to what is thought to be areas that were involved in the 1836 Battle of San Jacinto. Innovative use of a Statistical Point Pattern Analysis (PPA) is employed to identify clustering of EM anomalies. The K-function uses point {x,y} data to look for possible clusters in relation to other points in the data set. The clusters once identified using K-function will be further examined for classification and prioritization using the Weighted K-function. The Weighted K-function uses a third variable such as millivolt values or time decay to aid in segregation and prioritization of anomalies present. Once the anomalies of interest are identified, their locations are determined using the Gi-Statistics Technique. The Gi*-Statistic uses the individual Cartesian{x, y} points as origin locations to establish a range of distances to other cluster points in the data set. The segregation and location of anomalies supplied by this analysis will have several benefits. Prioritization of excavations will narrow down what areas should be excavated first. Anomalies of interest can be located to guide excavation procedures within the areas surveyed. Knowing what anomalies are of greater importance than others will help to lower false alarm rates for UXO remediation or for archaeological artifact selection. Knowing significant anomaly location will reduce the number of excavations which will subsequently save time and money. The procedures and analyses presented here are an interdisciplinary compilation of geophysics, archaeology and statistical analysis brought together for the first time to examine problems associated with UXO remediation as well as archaeological artifact selection at historic battlegrounds using electromagnetic data.

More than three quarters of the world’s economic activity is concentrated in cities. But what drives people and firms to agglomerate in urban areas? Clearly, some places may offer inherent benefits due to the location itself, such as a mild climate or the presence of natural harbours, but that does not tell the whole story. Rather urban areas also offer spaces for interaction among people and firms as well as the proximity to potential partners, customers, and competitors, which could have a significant impact on the appeal of a location for a firm. Using multiple novel methods based on a unique detailed geographical dataset, this dissertation explores how a location’s attractiveness is impacted by the presence of nearby firms in three studies. The first study explores the influence of the density of economic activity on wages at a given location and attempts to disentangle the separate mechanisms that could be at work. The second study is concerned with the locations of foreign-owned firms and more specifically whether foreign-owned firms are more influenced by agglomeration benefits than domestic firms. The final study switches from modelling the effects of location to modelling the location patterns themselves using economic theory-based spatial point processes. The results of these studies make significant contributions to empirical research both in economic geography and international business as a set of theoretical propositions are tested on a very detailed dataset using an advanced methodology. The results could also be of interest for practitioners as the importance of location decisions is further reinforced, as well as for policymakers as the analyses explore not only the benefits but also the detriments of agglomeration. Sergiy Protsiv is a researcher at the Center for Strategy and Competitiveness at the Stockholm School of Economics. He participated in several projects on clusters and regional development, most notably the European Cluster Observatory. / <p>Diss. Stockholm : Handelshögskolan, 2012</p>

La maladie de l’œdème est une maladie connue depuis de nombreuses années chez le porc. Les premiers cas recensés dans une population de suidés sauvages sont apparus en 2013 en Ardèche. Un nouveau foyer de cette maladie est ensuite apparu en 2016 dans les Pyrénées-Orientales à la frontière entre la France et l’Espagne. Comprendre les facteurs permettant son apparition ainsi que sa transmission est nécessaire afin d’anticiper de futures mortalités dues à cette maladie. Dans cette thèse, une analyse épidémiologique de cette maladie chez le sanglier a été réalisée. Des clusters de mortalités sont alors apparus et ont permis de mettre en évidence une possible source de contamination unique et récurrente dans le temps. La mise en place d’une nouvelle méthode pour étudier la détectabilité des cadavres de sanglier a souligné la difficulté de retrouver des cadavres de sanglier en forêt. La dernière analyse épidémiologique à partir d’un modèle de type « Spatial point pattern » a mis en avant de possibles facteurs de risque d’apparition et de transmission qui ont ensuite été analysés plus précisément. L’analyse des données issus des tableaux de chasse en Ardèche a été réalisée afin de détecter des variations de la densité et du ratio J/A des populations de sanglier suggérant un stress alimentaire chez le sanglier, un prodrome ou une conséquence de la maladie. Aucun stress alimentaire ne fut détecté lors de cette analyse. Des hypothèses ont pu être émises pour expliquer certaines variations observées : i) la conséquence directe de la maladie, ii) un phénomène environnemental particulier et iii) un évènement pathogénique. La piste de l’événement pathogénique a été approfondie avec la découverte du SDRP (syndrome dysgénésique et respiratoire du porc). Les interactions porcs-sangliers, nombreuses en Ardèche, ont été déterminées comme potentiellement responsables du passage de la bactérie entre le compartiment domestique et sauvage. Une étude génétique a également été effectuée pour investiguer le gène alpha-1-fucosyltransferase associé à la sensibilité du porc à la maladie. Tous les sangliers analysés étaient sensibles à la maladie. D’autres analyses complémentaires sont nécessaires afin de comprendre au mieux cette maladie ainsi que les différents facteurs de risque pour l’apparition mais également la transmission. / Edema disease has been a known disease in pigs for many years. The first cases recorded in a population of wild suids appeared in 2013 in Ardèche. A new outbreak of this disease then emerged in 2016 in the Pyrénées-Orientales on the border between France and Spain. Understanding the factors that enable its onset and transmission is necessary to anticipate future mortality from this disease. In this thesis, an epidemiological analysis of this disease in wild boar was carried out. Clusters of mortalities then emerged, highlighting a possible single and recurrent source of contamination over time. The introduction of a new method to study the detectability of wild boar corpses highlighted the difficulty of finding wild boar corpses in the forest. The latest epidemiological analysis using a Spatial point pattern model highlighted possible risk factors for onset and transmission, which were then analysed more precisely. Analysis of data from hunting tables in the Ardèche was carried out in order to detect variations in the density and J/A ratio of wild boar populations suggesting food stress in the wild boar, a prodrome or consequence of the disease. No dietary stress was detected during this analysis. Assumptions could be made to explain some observed variations: i) the direct consequence of the disease, ii) a particular environmental phenomenon and iii) a pathogenic event. The trail of the pathogenic event was deepened with the discovery of the PRRS (Pork Respiratory and Dygesic Syndrome). The pig-boar interactions, numerous in the Ardeche, were determined as potentially responsible for the passage of the bacteria between the domestic and wild compartment. A genetic study was also conducted to investigate the alpha-1-fucosyltransferase gene associated with the susceptibility of pigs to the disease. All the wild boars tested were susceptible to the disease.Further further analysis is needed in order to better understand this disease as well as the different risk factors for both onset and transmission.

Multiphoton laser scanning microscopy (MPLSM) is an advanced fluorescence imaging technology which can produce a less noisy microscope image and minimize the damage in living tissue. The MPLSM image in this research is the dehydroergosterol (DHE, a fluorescent sterol which closely mimics those of cholesterol in lipoproteins and membranes) on living cell's plasma membrane area. The objective is to use a statistical image analysis method to describe how cholesterol is distributed on a living cell's membrane. Statistical image analysis methods applied in this research include image segmentation/classification and spatial analysis. In image segmentation analysis, we design a supervised learning method by using smoothing technique with rank statistics. This approach is especially useful in a situation where we have only very limited information of classes we want to segment. We also apply unsupervised leaning methods on the image data. In image data spatial analysis, we explore the spatial correlation of segmented data by a Monte Carlo test. Our research shows that the distributions of DHE exhibit a spatially aggregated pattern. We fit two aggregated point pattern models, an area-interaction process model and a Poisson cluster process model, to the data. For the area interaction process model, we design algorithms for maximum pseudo-likelihood estimator and Monte Carlo maximum likelihood estimator under lattice data setting. For the Poisson Cluster process parameter estimation, the method for implicit statistical model parameter estimate is used. A group of simulation studies shows that the Monte Carlo maximum estimation method produces consistent parameter estimates. The goodness-of-fit tests show that we cannot reject both models. We propose to use the area interaction process model in further research.

Stochastic point processes and associated methodology provide a means for the statistical analysis and modeling of the spatial point pattern formed from forest tree stem locations. Stochastic Gibbs point processes were explored as models that could simulate short-range clustering arising from reproduction of trees by stump sprouting, and intermediate-range inhibition of trees that may result from competition for light and growing space. This study developed and compared three pairwise interaction processes with parametric models for 2nd-order potentials and three triplets processes with models for 2nd- and 3rd-order potentials applied to a mixed-species hardwood forest in the Southern Appalachian Mountains of western North Carolina. Although the 2nd-order potentials of both the pairwise interaction and triplets processes were allowed to be purely or partially attractive, the proposed Gibbs point process models were demonstrated to be locally stable. The proposed Gibbs point processes were simulated using Markov Chain Monte Carlo (MCMC) methods; in particular, a reversible-jump Metropolis-Hastings algorithm with birth, death, and shift proposals was utilized. Parameters for the models were estimated by a Bayesian inferential procedure that utilizes MCMC methods to draw samples from the Gibbs posterior density. Two Metropolis-Hastings algorithms that do this sampling were compared; one that estimated ratios of intractable normalizing constants of the Gibbs likelihood by importance sampling and another that introduced an auxiliary variable to cancel the normalizing constants with those in the auxiliary variable's proposal distribution. Results from this research indicated that attractive pairwise interaction models easily degenerate into excessively clustered patterns, whereas triplets processes with attractive 2nd-order and repulsive 3rd-order interactions are more robust against excessive clustering. Bayesian inference for the proposed triplets models was found to be very computationally expensive. Slow mixing of both algorithms used for the inference combined with the long iteration times limited the practicality of the Bayesian approach. However the results obtained here indicate that triplets processes can be used to draw inference for and simulate patterns of mixed-species Appalachian hardwood forests. / Ph. D.

With increasing levels of motor vehicle ownership, automobile crashes have become a serious public issue in the U.S. and around the world. Knowing when, where, and how traffic accidents happen is critical in order to ensure road safety and to plan for adequate road infrastructure. There is a rich body of literature pertaining to time-related fatal crashes, most of which focuses on non-spatial factors such as a driver’s visibility at night, drinking and drug use, and road conditions. These studies provide a theoretical basis for understanding the causes of crashes from a non-spatial perspective, and a number of traffic laws and policies consequently have been enacted to minimize the impacts of non-spatial factors. Over the past few years, advances in Geographic Information Systems (GIS) have greatly enhanced our ability to analyze traffic accidents from a spatial perspective. This study aims to fill a void in traffic safety studies by comparing and analyzing the differences in the spatial distribution of fatal crashes based on temporal factors, specifically in three periods: 1) day and night; 2) A.M. rush hours and P.M. rush hours; and 3) weekdays and weekends. With the Nashville Metropolitan Area as the study area, the research utilized a number of spatial point-pattern analysis (SPPA) methods, including planar KDE, planar global auto K function, network global cross K functions, and network local cross K functions. All fatal crashes in the Nashville area were found to be clustered and generally follow the patterns of average daily traffic flow. All time-based subtypes of fatal crashes also were found to be concentrated within the central urban area of Nashville, mostly along major roads, and especially near major road intersections and highway interchanges. No notable spatial differences were detected among the subtypes of fatal crashes when applying network global cross K function. However, with the help of the network local cross K function, some localized spatial differences were identified. Some specific locations of hotspots of nighttime and P.M. rush hour fatal crashes were found not to be at the same locations as those at of daytime and A.M. rush hour fatal crashes, respectively. The approach adopted in this study not only provides a new way to analyze spatial distribution of spatial point events such as fatal crashes, but it also can be applied readily to real-world applications. A good understanding of where these spatial differences are should help various agencies practice effective measures and policies in order to improve road conditions, reduce traffic accidents, and ensure road safety.