Nous étudions le comportement asymptotique de statistiques ou fonctionnelles liées à des processus à longue mémoire saisonnière. Nous nous concentrons sur les lignes de Donsker et sur le processus empirique. Les suites considérées sont de la forme $G(X_n)$ où $(X_n)$ est un processus gaussien ou linéaire. Nous montrons que les résultats que Taqqu et Dobrushin ont obtenus pour des processus à longue mémoire dont la covariance est à variation régulière à l'infini peuvent être en défaut en présence d'effets saisonniers. Les différences portent aussi bien sur le coefficient de normalisation que sur la nature du processus limite. Notamment nous montrons que la limite du processus empirique bi-indexé, bien que restant dégénérée, n'est plus déterminée par le degré de Hermite de la fonction de répartition des données. En particulier, lorsque ce degré est égal à 1, la limite n'est plus nécessairement gaussienne. Par exemple on peut obtenir une combinaison de processus de Rosenblatt indépendants. Ces résultats sont appliqués à quelques problèmes statistiques comme le comportement asymptotique des U-statistiques, l'estimation de la densité et la détection de rupture.

We consider time-of-arrival based robust geolocation in harsh line-of-sight/non-line-of-sight environments. Herein, we assume the probability density function (PDF) of the measurement error to be completely unknown and develop an iterative algorithm for robust position estimation. The iterative algorithm alternates between a PDF estimation step, which approximates the exact measurement error PDF (albeit unknown) under the current parameter estimate via adaptive kernel density estimation, and a parameter estimation step, which resolves a position estimate from the approximate log-likelihood function via a quasi-Newton method. Unless the convergence condition is satisfied, the resolved position estimate is then used to refine the PDF estimation in the next iteration. We also present the best achievable geolocation accuracy in terms of the Cramér-Rao lower bound. Various simulations have been conducted in both real-world and simulated scenarios. When the number of received range measurements is large, the new proposed position estimator attains the performance of the maximum likelihood estimator (MLE). When the number of range measurements is small, it deviates from the MLE, but still outperforms several salient robust estimators in terms of geolocation accuracy, which comes at the cost of higher computational complexity.

Lightning-caused forest fires are one of the major natural disturbances in Ontario managed boreal forests. Survival of these forests with fires for centuries shows that such disturbances are integral to the boreal ecosystem and its ecological functioning. Characterizing the fire regimes defined by fire ignition frequency, fire sizes and their spatial distribution patterns etc. thus can help to improve our understanding of the boreal forest dynamics and provide guidance for management practices attempting to maintain biodiversity and achieve sustainability. In this thesis the lightning-caused fire ignitions data for four ecoregions in Ontario managed boreal forests (3E, 3W, 3S and 4S) for 1960–2009 were analyzed using pattern analysis and density estimation to determine the spatial nature of fire ignitions. These fire ignition spatial patterns were further used (as weighted ignition scenario) to simulate forest fire regimes in the study area. Fire regimes were also simulated using spatially unweighted ignitions (unweighted ignition scenario). Non-spatial (total number of fires, total burn area, number of fires by size classes, annual burn fraction) and spatial (spatial burn probability) indicators of the simulated fire regimes under both ignition scenarios were compared to test the null hypothesis that modeled forest fire regime is not affected by the spatial patterns of input fire ignitions. All data analysis were performed for individual ecoregions. Spatial pattern of ignitions were analyzed using the nearest neighbour index and Ripley’s K-function. Ignition densities were estimated using the adaptive kernel density estimation method and the fire regimes were simulated using BFOLDS (Boreal Forests Landscape Dynamics Simulator). Results showed that lightning-caused fire ignitions are clustered in all ecoregions. Fire ignition density also varied spatially within ecoregions. Overall fire ignition density was highest in the northwestern ecoregion (4S) and lowest in the eastern ecoregion (3E), which corresponds to the combined gradient of effective humidity and temperature in Ontario. For each ecoregion, comparison of non-spatial simulated fire regime indicators showed statistically non-significant differences between unweighted and weighted ignitions. The spatial burn probability however captured clear spatial differences between unweighted and weighted ignitions. Spatial differences in spatial burn probability between both ignition scenarios were more prominent in ecoregions of high fire occurrence. Results of the weighted ignition scenario closely followed the spatial patterns of the estimated fire ignition density in the study area. Based on these results this thesis rejects the null hypothesis and emphasizes that ignition patterns must be considered in simulating fire regime in Ontario boreal forests.

No description available.

In both developed and emerging-economies, major cities continue to experience increasing traffic congestion. To address this issue, complex Traffic Management Systems (TMS) are employed in recent years to help manage traffic. These systems fuse traffic-surveillance-related information from a variety of sensors deployed across traffic networks. A TMS requires real-time information to make effective control decisions and to deliver trustworthy information to users, such as travel time, congestion level, etc. There are three fundamental inputs required by TMS, namely, traffic volume, vehicular speed, and traffic density. Using conventional traffic loop detectors one can directly measure flow and velocity. However, traffic density is more difficult to measure. The situation becomes more difficult for multi-lane motorways due to drivers lane-change behaviour. This research investigates statistical modelling and analysis of traffic flow. It contributes to the literature of transportation and traffic management and research in several aspects. First, it takes into account lane-changes in traffic modelling through incorporating a Markov chain model to describe the drivers lane-change behaviour. Secondly, the lane change probabilities between two adjacent lanes are not assumed to be fixed but rather they depend on the current traffic condition. A discrete choice model is used to capture drivers lane choice behaviour. The drivers choice probabilities are modelled by several traffic-condition related attributes such as vehicle time headway, traffic density and speed. This results in a highly nonlinear state equation for traffic density. To address the issue of high nonlinearity of the state space model, the EKF and UKF is used to estimate the traffic density recursively. In addition, a new transformation approach has been proposed to transform the observation equation from a nonlinear form to a linear one so that the potential approximation in the EKF & UKF can be avoided. Numerical studies have been conducted to investigate the performance of the developed method. The proposed method outperformed the existing methods for traffic density estimation in simulation studies. Furthermore, it is shown that the computational cost for updating the estimate of traffic densities for a multi-lane motorway is kept at a minimum so that online applications are feasible in practice. Consequently the traffic densities can be monitored and the relevant information can be fed into the traffic management system of interest.

This thesis develops flexible and principled nonparametric learning algorithms to explore, understand, and predict high dimensional and complex datasets. Such data appear frequently in modern scientific domains and lead to numerous important applications. For example, exploring high dimensional functional magnetic resonance imaging data helps us to better understand brain functionalities; inferring large-scale gene regulatory network is crucial for new drug design and development; detecting anomalies in high dimensional transaction databases is vital for corporate and government security. Our main results include a rigorous theoretical framework and efficient nonparametric learning algorithms that exploit hidden structures to overcome the curse of dimensionality when analyzing massive high dimensional datasets. These algorithms have strong theoretical guarantees and provide high dimensional nonparametric recipes for many important learning tasks, ranging from unsupervised exploratory data analysis to supervised predictive modeling. In this thesis, we address three aspects: 1 Understanding the statistical theories of high dimensional nonparametric inference, including risk, estimation, and model selection consistency; 2 Designing new methods for different data-analysis tasks, including regression, classification, density estimation, graphical model learning, multi-task learning, spatial-temporal adaptive learning; 3 Demonstrating the usefulness of these methods in scientific applications, including functional genomics, cognitive neuroscience, and meteorology. In the last part of this thesis, we also present the future vision of high dimensional and large-scale nonparametric inference.

No description available.

A primary focus of wildlife research is to understand how habitat conditions and human activities impact the health of wild animals. External factors, both natural and anthropogenic that impact the ability of an animal to acquire food and build energy reserves have important implications for reproductive success, avoidance of predators, and the ability to withstand disease, and periods of food scarcity. In the analyses presented here, I quantify the impacts of habitat quality and anthropogenic disturbance on indicators of health for individuals in a threatened grizzly bear population in Alberta, Canada. The first analysis relates spatial patterns of hair cortisol concentrations, a promising indicator of long-term stress in mammals, measured from 304 grizzly bears to a variety of continuous environmental variables representative of habitat quality (e.g., crown closure, landcover, and vegetation productivity), topographic conditions (e.g., elevation and terrain ruggedness), and anthropogenic disturbances (e.g., roads, forest harvest blocks, and oil and gas well-sites). Hair cortisol concentration point data were integrated with continuous variables by creating a stress surface for male and female bears using kernel density estimation validated through bootstrapping. The relationships between hair cortisol concentrations for males and females and environmental variables were quantified using random forests, and landscape scale stress levels for both genders was predicted based on observed relationships. Low female stress levels were found to correspond with regions with high levels of anthropogenic disturbance and activity. High female stress levels were associated primarily with high-elevation parks and protected areas. Conversely, low male stress levels were found to correspond with parks and protected areas and spatially limited moderate to high stress levels were found in regions with greater anthropogenic disturbance. Of particular concern for conservation is the observed relationship between low female stress and sink habitats which have high mortality rates and high energetic costs. Extending the first analysis, the second portion of this research examined the impacts of scale-specific habitat selection and relationships between biology, habitat quality, and anthropogenic disturbance on body condition in 85 grizzly bears represented using a body condition index. Habitat quality and anthropogenic variables were represented at multiple scales using isopleths of a utilization distribution calculated using kernel density estimation for each bear. Several hypotheses regarding the influence of biology, habitat quality, and anthropogenic disturbance on body condition quantified using linear mixed-effects models were evaluated at each habitat selection scale using the small sample Aikake Information Criterion. Biological factors were influential at all scales as males had higher body condition than females, and body condition increased with age for both genders. At the scale of most concentrated habitat selection, the biology and habitat quality hypothesis had the greatest support and had a positive effect on body condition. A component of biology, the influence of long-term stress, which had a negative impact on body condition, was most pronounced within the biology and habitat quality hypothesis at this scale. As the scale of habitat selection was represented more broadly, support for the biology and anthropogenic disturbance hypothesis increased. Anthropogenic variables of particular importance were distance decay to roads, density of secondary linear features, and density of forest harvest areas which had a negative relationship with body condition. Management efforts aimed to promote landscape conditions beneficial to grizzly bear health should focus on promoting habitat quality in core habitat and limiting anthropogenic disturbance within larger grizzly bear home ranges. / Graduate / 0768 / 0463 / 0478 / mathieub@uvic.ca

Lightning-caused forest fires are one of the major natural disturbances in Ontario managed boreal forests. Survival of these forests with fires for centuries shows that such disturbances are integral to the boreal ecosystem and its ecological functioning. Characterizing the fire regimes defined by fire ignition frequency, fire sizes and their spatial distribution patterns etc. thus can help to improve our understanding of the boreal forest dynamics and provide guidance for management practices attempting to maintain biodiversity and achieve sustainability. In this thesis the lightning-caused fire ignitions data for four ecoregions in Ontario managed boreal forests (3E, 3W, 3S and 4S) for 1960–2009 were analyzed using pattern analysis and density estimation to determine the spatial nature of fire ignitions. These fire ignition spatial patterns were further used (as weighted ignition scenario) to simulate forest fire regimes in the study area. Fire regimes were also simulated using spatially unweighted ignitions (unweighted ignition scenario). Non-spatial (total number of fires, total burn area, number of fires by size classes, annual burn fraction) and spatial (spatial burn probability) indicators of the simulated fire regimes under both ignition scenarios were compared to test the null hypothesis that modeled forest fire regime is not affected by the spatial patterns of input fire ignitions. All data analysis were performed for individual ecoregions. Spatial pattern of ignitions were analyzed using the nearest neighbour index and Ripley’s K-function. Ignition densities were estimated using the adaptive kernel density estimation method and the fire regimes were simulated using BFOLDS (Boreal Forests Landscape Dynamics Simulator). Results showed that lightning-caused fire ignitions are clustered in all ecoregions. Fire ignition density also varied spatially within ecoregions. Overall fire ignition density was highest in the northwestern ecoregion (4S) and lowest in the eastern ecoregion (3E), which corresponds to the combined gradient of effective humidity and temperature in Ontario. For each ecoregion, comparison of non-spatial simulated fire regime indicators showed statistically non-significant differences between unweighted and weighted ignitions. The spatial burn probability however captured clear spatial differences between unweighted and weighted ignitions. Spatial differences in spatial burn probability between both ignition scenarios were more prominent in ecoregions of high fire occurrence. Results of the weighted ignition scenario closely followed the spatial patterns of the estimated fire ignition density in the study area. Based on these results this thesis rejects the null hypothesis and emphasizes that ignition patterns must be considered in simulating fire regime in Ontario boreal forests.

This thesis is divided into two parts. In the first part we describe a new Monte Carlo algorithm for the consistent and unbiased estimation of multidimensional integrals and the efficient sampling from multidimensional densities. The algorithm is inspired by the classical splitting method and can be applied to general static simulation models. We provide examples from rare-event probability estimation, counting, optimization, and sampling, demonstrating that the proposed method can outperform existing Markov chain sampling methods in terms of convergence speed and accuracy. In the second part we present a new adaptive kernel density estimator based on linear diffusion processes. The proposed estimator builds on existing ideas for adaptive smoothing by incorporating information from a pilot density estimate. In addition, we propose a new plug-in bandwidth selection method that is free from the arbitrary normal reference rules used by existing methods. We present simulation examples in which the proposed approach outperforms existing methods in terms of accuracy and reliability.