This research estimated the spatial-temporal patterns of tornadoes in the continental United States from 1950-2019 using the National Weather Service Storm Prediction Center’s Severe Weather GIS (SVRGIS) database. This study employed Space-Time Cube Analysis and Linear Kernel Density (Kernel Density Linear Process, (KDLP)) rather than the standard Kernel Density Estimation (KDE) approach; to evaluate whether tornado hotspot locations and intensities shift over time. The first phase of the study utilized KDLP to map changes in tornado hotspots and qualitatively assess decadal shifts in hotspot locations and intensities by occurrence and magnitude between decades using ArcGIS Pro and CrimeStat. Next an Emerging Hot Spot Analysis (EHSA) was employed to identify the changes in tornado occurrence and magnitude. ESHA results identified, by both occurrence and magnitude, significant intensifying hot spots in the Southeast region and diminishing hot spots in the Great Plains indicating an east-south-east shift.

No / This paper outlines the current challenges of driver behaviour modelling for real-world applications and presents the novel method to identify the pattern of usage to predict upcoming journeys in probability sense. The primary aim is to establish similarity between observed behaviour of drivers resulting in the ability to cluster them and deploy control strategies based on contextual intelligence and datadriven approach. The proposed approach uses the probability density function (PDF) driven by kernel density estimation (KDE) as a probabilistic approach to predict the type of the upcoming journey, expressed as duration and distance. Using the proposed method, the mathematical formulation and programming algorithm procedure have been indicated in detail, while the case study examples with the data visualisation are given for algorithm validation in simulation.

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There has been little research comprehensively documenting wildlife species in Harenna Forest within the Bale Mountains National Park of Ethiopia. This area is one of the few remaining afro-alpine biodiversity hotspots and is home to numerous endemic plants and animals and offers socio-economic benefits to the neighboring communities. Human population pressure, weak land protection policies, and uncertain land tenure rights have led to increases in farmland for subsistence and coffee farming, livestock grazing, and reduction of afro-alpine, shrubland and grassland habitats. Given these challenges, I used 48 camera trap stations to produce an inventory of wildlife species and to determine factors influencing occupancy (i.e., habitat use), detection, and temporal activity and overlap. I recorded 26 terrestrial and arboreal mammalian species and I had sufficient data to model occupancy for 13 species and temporal activity for 14 species. Occupancy and detection were generally higher for herbivores and omnivores (occupancy: 0.28-0.97; detection: 0.1-0.54) than carnivores (occupancy: 0.31-0.80; detection: 0.04-0.18). I found more evidence of positive anthropogenic impacts on herbivore and omnivore occupancy than negative, while detection was influenced by habitat or landscape features, rather than by humans. Carnivore occupancy was largely unaffected by anthropogenic or habitat variables, but detection was strongly, and mostly positively, influenced by anthropogenic impacts. Temporal activity analyses revealed that, for herbivores and omnivores, only tree hyraxes (Dendrohyrax arboreus) and crested porcupines (Hystrix cristata) were nocturnal, Menelik bushbucks (Tragelaphus scriptus meneliki) were crepuscular, and the remaining species ranged from diurnal to cathemeral. Neither similar body size nor similar diet affected overlap between species pairs. However, overlap with human temporal activity was low for Menelik bushbucks (Δ=0.45) and common duikers (Sylvicapra grimmia) appeared to become less active at stations with high human use. For carnivores, leopards (Panthera pardus) and honey badgers (Mellivora capensis) were crepuscular, and the remaining species were nocturnal. I found evidence that carnivores overlapped less when they were more similar in body size to other carnivores (average Δ=0.67-0.71) compared to species more dissimilar in body size (average Δ=0.75), although there was variation across species. In general, carnivores overlapped much less with humans (average Δ=0.20) than did herbivores (average Δ=0.52) and omnivores (average Δ=0.43). Spotted hyenas (Crocuta crocuta), in particular, appeared to alter activity to reduce overlap with humans. This study provides baseline information on presence, distribution, and activity of large- and medium-sized terrestrial and arboreal mammals in an understudied biodiversity hotspot. My findings are concerning for biodiversity conservation as rare and endangered species (e.g., mountain nyalas (Tragelaphus buxtoni), Ethiopian wolves (Canis simensis)) were rarely or never photographed, and larger carnivores (e.g., lions (Panthera leo), leopards, jackals), generally had low capture rates. The species with higher capture rates, occupancy, and activity tended to be those that can tolerate or take advantage of human activity and disturbance. Species sensitive to human disturbance eventually may be lost unless measures can be put in place to reduce human impacts. This baseline knowledge is important for future studies examining trends in mammalian wildlife populations, such as site extinction and colonization, or changes in overlap with humans, in a landscape that is continuing to experience human-caused, landscape change. / Master of Science / Harenna forest, which is located in Bale Mountains National Park, Ethiopia is an important habitat to both wildlife and people. However, it faces a number of challenges as a result of population growth leading to increased coffee farming and livestock grazing resulting in reduced habitat for wildlife species. I used 48 cameras located across the forest to record presence of terrestrial mammals and document their distribution and daily activity across the landscape. I also used data such as vegetation indices, elevation, and distances to human-disturbed areas to determine what influenced wildlife species. Cameras recorded 26 species of mammals. I had enough data to determine distribution for 13 species and daily activity for 14 species. I found that presence across the landscape and activity of herbivores and omnivores was generally higher than that of carnivores. Additionally, I found that human activity or disturbance often had a positive influence on herbivore and omnivore distribution, but my ability to detect species in camera traps was primarily influenced by habitat or landscape features. Carnivore distribution on the landscape was not influenced much by humans or habitat, but their detectability was often positively influenced by presence of humans. In addition to daily activity, I also analyzed overlap in activity between species pairs and between species and humans, to determine whether wildlife changed their temporal activity to overlap less with similar sized competitors or in response to high human use. For herbivores and omnivores, I found that tree hyraxes and crested porcupines were active at night, Menelik's bushbucks were active at sunrise and sunset, and cape bushbucks, common duiker, olive baboon, bushpig, and giant forest hogs were active either during the day or throughout the day and night. I found little evidence that the herbivores or omnivores avoided each other temporally and only the Menelik bushbuck and duiker appeared to avoid humans. For carnivores, I found that leopards and honey badgers were active early morning and evening, and the common genet, African civet, white-tailed mongoose, and spotted hyenas were all active at night only. Carnivores generally overlapped less with humans than herbivores and omnivores. I found some evidence that carnivores more similar in body size had lower temporal overlap with each other and that spotted hyaenas appeared to avoid activity during times of day when humans were active. My study not only provides baseline information on terrestrial and arboreal mammals present in Harenna forest, Ethiopia, but is also necessary for understanding how wildlife species use the landscape and particularly how presence of humans influences wild animal behavior. My findings are concerning for biodiversity conservation because I had few to no photographs, respectively, of the endangered mountain nyala and Ethiopian wolf. In fact, most of the species with a wide distribution on the landscape, or with high activity, were common or smaller species that are tolerant of, or could take advantage of, human disturbance. Without concerted effort to curtail the current landscape change caused by humans, the area is likely to lose species less tolerant of humans, and biodiversity will ultimately decline.

Data streams are ordered sets of values that are fast, continuous, mutable, and potentially unbounded. Examples of data streams include the pervasive time series which span domains such as finance, medicine, and transportation. Mining data streams require approaches that are efficient, adaptive, and scalable. For several stream mining tasks, knowledge of the data's probability density function (PDF) is essential to deriving usable results. Providing an accurate model for the PDF benefits a variety of stream mining applications and its successful development can have far-reaching impact to the general discipline of stream analysis. Therefore, this research focuses on the construction of efficient and effective approaches for estimating the PDF of data streams. In this work, kernel density estimators (KDEs) are developed that satisfy the stringent computational stipulations of data streams, model unknown and dynamic distributions, and enhance the estimation quality of complex structures. Contributions of this work include: (1) theoretical development of the local region based KDE; (2) construction of a local region based estimation algorithm; (3) design of a generalized local region approach that can be applied to any global bandwidth KDE to enhance estimation accuracy; and (4) application extension of the local region based KDE to multi-scale outlier detection. Theoretical development includes the formulation of the local region concept to effectively approximate the computationally intensive adaptive KDE. This work also analyzes key theoretical properties of the local region based approach which include (amongst others) its expected performance, an alternative local region construction criterion, and its robustness under evolving distributions. Algorithmic design includes the development of a specific estimation technique that reduces the time/space complexities of the adaptive KDE. In order to accelerate mining tasks such as outlier detection, an integrated set of optimizations are proposed for estimating multiple density queries. Additionally, the local region concept is extended to an efficient algorithmic framework which can be applied to any global bandwidth KDEs. The combined solution can significantly improve estimation accuracy while retaining overall linear time/space costs. As an application extension, an outlier detection framework is designed which can effectively detect outliers within multiple data scale representations. / Ph. D.

This thesis is in two parts. The first part considers a theoretical relationship between the natural variability of a stochastic model and its response to a small change in forcing. Over a large enough scale, both the real climate and a climate model are characterised as stochastic dynamical systems. The dynamics of the systems are encoded in the probabilities that the systems move from one state into another. When the systems’ states are discretised and listed, then transition matrices of all these transition probabilities may be formed. The responses of the systems to a small change in forcing are expanded in terms of the eigenfunctions and eigenvalues of the Fokker-Planck equations governing the systems’ transition densities, which may be estimated from the eigenvalues and eigenvectors of the transition matrices. Smoothing the data with a Gaussian kernel improves the estimate of the eigenfunctions, but not the eigenvalues. The significance of differences in two systems’ eigenvalues and eigenfunctions is considered. Three time series from HadCM3 are compared with corresponding series from ERA-40 and the eigenvalues derived from the three pairs of series differ significantly. The second part analyses a model of the coupled climate-economic system, which suggests that the pace of economic growth needs to be reduced and the resilience to climate change needs to be increased in order to avoid a collapse of the human economy. The model condenses the climate-economic system into just three variables: a measure of human wealth, the associated accumulation of greenhouse gases, and the consequent level of global warming. Global warming is assumed to dictate the pace of economic growth. Depending on the sensitivity of economic growth to global warming, the model climate-economy system either reaches an equilibrium or oscillates in century-scale booms and busts.

Les méthodes d'agrégation en apprentissage statistique combinent plusieurs prédicteurs intermédiaires construits à partir du même jeu de données dans le but d'obtenir un prédicteur plus stable avec une meilleure performance. Celles-ci ont été amplement étudiées et ont données lieu à plusieurs travaux, théoriques et empiriques dans plusieurs contextes, supervisés et non supervisés. Dans ce travail nous nous intéressons dans un premier temps à l'apport de ces méthodes au problème de l'estimation de la densité. Nous proposons plusieurs estimateurs simples obtenus comme combinaisons linéaires d'histogrammes. La principale différence entre ceux-ci est quant à la nature de l'aléatoire introduite à chaque étape de l'agrégation. Nous comparons ces techniques à d'autres approches similaires et aux estimateurs classiques sur un choix varié de modèles, et nous démontrons les propriétés asymptotiques pour un de ces algorithmes (Random Averaged Shifted Histogram). Une seconde partie est consacrée aux extensions du Boosting pour le cas multiclasse. Nous proposons un nouvel algorithme (Adaboost.BG) qui fournit un classifieur final en se basant sur un calcul d'erreur qui prend en compte la marge individuelle de chaque modèle introduit dans l'agrégation. Nous comparons cette méthode à d'autres algorithmes sur plusieurs jeu de données artificiels classiques. / Ensemble methods in statistical learning combine several base learners built from the same data set in order to obtain a more stable predictor with better performance. Such methods have been extensively studied in the supervised context for regression and classification. In this work we consider the extension of these approaches to density estimation. We suggest several new algorithms in the same spirit as bagging and boosting. We show the efficiency of combined density estimators by extensive simulations. We give also the theoretical results for one of our algorithms (Random Averaged Shifted Histogram) by mean of asymptotical convergence under milmd conditions. A second part is devoted to the extensions of the Boosting algorithms for the multiclass case. We propose a new algorithm (Adaboost.BG) accounting for the margin of the base classifiers and show its efficiency by simulations and comparing it to the most used methods in this context on several datasets from the machine learning benchmark. Partial theoretical results are given for our algorithm, such as the exponential decrease of the learning set misclassification error to zero.

Given two samples from two populations, one could ask how similar the populations are, that is, how close their probability distributions are. For absolutely continuous distributions, one way to measure the proximity of such populations is to use a measure of distance (metric) between the probability density functions (which are unknown given that only samples are observed). In this work, we work with the integrated squared distance as metric. To measure the uncertainty of the squared integrated distance, we first model the uncertainty of each of the probability density functions using a nonparametric Bayesian method. The method consists of estimating the probability density function f (or its logarithm) using Fourier series {f0;f1; :::;fI}. Assigning a prior distribution to f is then equivalent to assigning a prior distribution to the coefficients of this series. We used the prior suggested by Scricciolo (2006) (sieve prior), which not only places a prior on such coefficients, but also on I itself, so that in reality we work with a Bayesian mixture of finite dimensional models. To obtain posterior samples of such mixture, we marginalize out the discrete model index parameter I and use a statistical software called Stan. We conclude that the Bayesian Fourier series method has good performance when compared to kernel density estimation, although both methods often have problems in the estimation of the probability density function near the boundaries. Lastly, we showed how the methodology of Fourier series can be used to access the uncertainty regarding the similarity of two samples. In particular, we applied this method to dataset of patients with Alzheimer. / Dadas duas amostras de duas populações, pode-se questionar o quão parecidas as duas populações são, ou seja, o quão próximas estão suas distribuições de probabilidade. Para distribuições absolutamente contínuas, uma maneira de mensurar a proximidade dessas populações é utilizando uma medida de distância (métrica) entre as funções densidade de probabilidade (as quais são desconhecidas, em virtude de observarmos apenas as amostras). Nesta dissertação, utilizamos a distância quadrática integrada como métrica. Para mensurar a incerteza da distância quadrática integrada, primeiramente modelamos a incerteza sobre cada uma das funções densidade de probabilidade através de uma método bayesiano não paramétrico. O método consiste em estimar a função de densidade de probabilidade f (ou seu logaritmo) usando séries de Fourier {f0;f1; :::;fI}. Atribuir uma distribuição a priori para f é então equivalente a atribuir uma distribuição a priori aos coeficientes dessa serie. Utilizamos a priori sugerida em Scricciolo (2006) (priori de sieve), a qual não coloca uma priori somente nesses coeficientes, mas também no próprio I, de modo que, na realidade, trabalhamos com uma mistura bayesiana de modelos de dimensão finita. Para obter amostras a posteriori dessas misturas, marginalizamos o parâmetro (discreto) de indexação de modelos, I, e usamos um software estatístico chamado Stan. Concluímos que o método bayesiano de séries de Fourier tem boa performance quando comparado ao de estimativa de densidade kernel, apesar de ambos os métodos frequentemente apresentarem problemas na estimação da função de densidade de probabilidade perto das fronteiras. Por fim, mostramos como a metodologia de series de Fourier pode ser utilizada para mensurar a incerteza a cerca da similaridade de duas amostras. Em particular, aplicamos este método a um conjunto de dados de pacientes com doença de Alzheimer.