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.

No description available.

With the advent of the internet and advances in computing power, the collection of very large high-dimensional datasets has become feasible { understanding and modelling high-dimensional data has thus become a crucial activity, especially in the field of pattern recognition. Since non-parametric density estimators are data-driven and do not require or impose a pre-defined probability density function on data, they are very powerful tools for probabilistic data modelling and analysis. Conventional non-parametric density estimation methods, however, originated from the field of statistics and were not originally intended to perform density estimation in high-dimensional features spaces { as is often encountered in real-world pattern recognition tasks. Therefore we address the fundamental problem of non-parametric density estimation in high-dimensional feature spaces in this study. Recent advances in maximum-likelihood (ML) kernel density estimation have shown that kernel density estimators hold much promise for estimating nonparametric probability density functions in high-dimensional feature spaces. We therefore derive two new iterative kernel bandwidth estimators from the maximum-likelihood (ML) leave one-out objective function and also introduce a new non-iterative kernel bandwidth estimator (based on the theoretical bounds of the ML bandwidths) for the purpose of bandwidth initialisation. We name the iterative kernel bandwidth estimators the minimum leave-one-out entropy (MLE) and global MLE estimators, and name the non-iterative kernel bandwidth estimator the MLE rule-of-thumb estimator. We compare the performance of the MLE rule-of-thumb estimator and conventional kernel density estimators on artificial data with data properties that are varied in a controlled fashion and on a number of representative real-world pattern recognition tasks, to gain a better understanding of the behaviour of these estimators in high-dimensional spaces and to determine whether these estimators are suitable for initialising the bandwidths of iterative ML bandwidth estimators in high dimensions. We find that there are several regularities in the relative performance of conventional kernel density estimators across different tasks and dimensionalities and that the Silverman rule-of-thumb bandwidth estimator performs reliably across most tasks and dimensionalities of the pattern recognition datasets considered, even in high-dimensional feature spaces. Based on this empirical evidence and the intuitive theoretical motivation that the Silverman estimator optimises the asymptotic mean integrated squared error (assuming a Gaussian reference distribution), we select this estimator to initialise the bandwidths of the iterative ML kernel bandwidth estimators compared in our simulation studies. We then perform a comparative simulation study of the newly introduced iterative MLE estimators and other state-of-the-art iterative ML estimators on a number of artificial and real-world high-dimensional pattern recognition tasks. We illustrate with artificial data (guided by theoretical motivations) under what conditions certain estimators should be preferred and we empirically confirm on real-world data that no estimator performs optimally on all tasks and that the optimal estimator depends on the properties of the underlying density function being estimated. We also observe an interesting case of the bias-variance trade-off where ML estimators with fewer parameters than the MLE estimator perform exceptionally well on a wide variety of tasks; however, for the cases where these estimators do not perform well, the MLE estimator generally performs well. The newly introduced MLE kernel bandwidth estimators prove to be a useful contribution to the field of pattern recognition, since they perform optimally on a number of real-world pattern recognition tasks investigated and provide researchers and practitioners with two alternative estimators to employ for the task of kernel density estimation. / PhD (Information Technology), North-West University, Vaal Triangle Campus, 2014

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

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.

The aim of this study is to develop novel forecasting methodologies. The applications of our proposed models lie in two different areas: macroeconomics and energy. Though we consider two very different applications, the common underlying theme of this thesis is to develop novel methodologies that are not only accurate, but are also parsimonious. For macroeconomic time series, we focus on generating forecasts for the US Gross National Product (GNP). The contribution of our study on macroeconomic forecasting lies in proposing a novel nonlinear and nonparametric method, called weighted random analogue prediction (WRAP) method. The out-of-sample forecasting ability of WRAP is evaluated by employing a range of different performance scores, which measure its accuracy in generating both point and density forecasts. We show that WRAP outperforms some of the most commonly used models for forecasting the GNP time series. For energy, we focus on two different applications: (1) Generating accurate short-term forecasts for the total electricity demand (load) for Great Britain. (2) Modelling Irish electricity smart meter data (consumption) for both residential consumers and small and medium-sized enterprises (SMEs), using methods based on kernel density (KD) and conditional kernel density (CKD) estimation. To model load, we propose methods based on a commonly used statistical dimension reduction technique, called singular value decomposition (SVD). Specifically, we propose two novel methods, namely, discount weighted (DW) intraday and DW intraweek SVD-based exponential smoothing methods. We show that the proposed methods are competitive with some of the most commonly used models for load forecasting, and also lead to a substantial reduction in the dimension of the model. The load time series exhibits a prominent intraday, intraweek and intrayear seasonality. However, most existing studies accommodate the ‘double seasonality’ while modelling short-term load, focussing only on the intraday and intraweek seasonal effects. The methods considered in this study accommodate the ‘triple seasonality’ in load, by capturing not only intraday and intraweek seasonal cycles, but also intrayear seasonality. For modelling load, we also propose a novel rule-based approach, with emphasis on special days. The load observed on special days, e.g. public holidays, is substantially lower compared to load observed on normal working days. Special day effects have often been ignored during the modelling process, which leads to large forecast errors on special days, and also on normal working days that lie in the vicinity of special days. The contribution of this study lies in adapting some of the most commonly used seasonal methods to model load for both normal and special days in a coherent and unified framework, using a rule-based approach. We show that the post-sample error across special days for the rule-based methods are less than half, compared to their original counterparts that ignore special day effects. For modelling electricity smart meter data, we investigate a range of different methods based on KD and CKD estimation. Over the coming decade, electricity smart meters are scheduled to replace the conventional electronic meters, in both US and Europe. Future estimates of consumption can help the consumer identify and reduce excess consumption, while such estimates can help the supplier devise innovative tariff strategies. To the best of our knowledge, there are no existing studies which focus on generating density forecasts of electricity consumption from smart meter data. In this study, we evaluate the density, quantile and point forecast accuracy of different methods across one thousand consumption time series, recorded from both residential consumers and SMEs. We show that the KD and CKD methods accommodate the seasonality in consumption, and correctly distinguish weekdays from weekends. For each application, our comprehensive empirical comparison of the existing and proposed methods was undertaken using multiple performance scores. The results show strong potential for the models proposed in this thesis.

A destruição de florestas tropicais é intensa e pode levar à extinção de espécies sensíveis à fragmentação. Na Mata Atlântica, mamíferos com importantes funções no equilíbrio do ecossistema, como Panthera onca (onça-pintada), já estão ausentes em grande parte do bioma. Logo, é de extrema urgência compreender os processos que influenciam na permanência dessas espécies em uma área, para evitar futuras extinções locais. Assim, o objetivo geral deste estudo foi analisar as influências das características ambientais sobre a riqueza e ocorrência de mamíferos terrestres de médio e grande porte e as relações espaço-temporais entre o predador de topo, mesopredadores e presas em uma área de Mata Atlântica contíngua ao Parque Estadual da Serra do Mar com recente histórico de perturbação (Parque das Neblinas, Bertioga, SP). A coleta de dados foi realizada por armadilhamento fotográfico, durante 90 dias em 2013 e 2014, em 27 pontos amostrais, distantes 1 km entre si. As características ambientais avaliadas foram altitude, densidade de drenagem, precipitação média, temperatura média, número de palmitos (Euterpe edulis) e presença de trilhas naturais. Para analisar as influências do ambiente sobre a riqueza e ocorrência de espécies (com mais de três registros por ano) foram utilizados Modelos Lineares Generalizados. Para as demais análises, as espécies foram agrupadas em predador, mesopredadores, presas de grande, médio e pequeno porte. O período e sobreposição de atividade destes grupos foram estimados por meio da densidade de Kernel. A abundância foi estimada para mesopredadores e presas, através de modelos N-mixture. Para analisar a probabilidade de ocupação e detecção do predador de topo foram usados modelos de ocupação single-season. Foram amostrados 18 mamíferos terrestres de médio e grande porte, dos quais nove estão ameaçados de extinção ((Cabassous unicinctus (tatu-de-rabo-mole), Cuniculus paca (paca), Leopardus guttulus (gato-do-mato-pequeno), Leopardus pardalis (jaguatirica), Leopardus wiedii (gato-maracajá), Pecari tajacu (cateto), Puma concolor (onça-parda), Puma yagouaroundi (gato-mourisco) e Tapirus terrestris (anta)). A riqueza de espécies foi positivamente influenciada pelo maior volume de chuvas e a ocorrência da maioria das espécies (C. unicinctus, Dasypus novemcinctus (tatu-galinha), P. concolor, Sylvilagus brasiliensis (tapiti) e T. terrestris) foi influenciada pela densidade de drenagem em 2013. Em 2014, a riqueza não foi explicada por nenhuma característica e apenas quatro espécies sofreram influência de alguma característica ambiental. O predador de topo registrado foi catemeral, os mesopredadores e presas de grande porte mostraram-se mais noturnos e presas de médio e pequeno porte foram mais diurnas. Presas menores apresentaram a maior sobreposição total com o predador (Δ1=0,72). A influência sobre a probabilidade de ocupação da área pelo predador variou entre os anos, tendo sido pela abundância de presas de grande e pequeno porte, em 2013, e pela abundância de presas de médio porte, em 2014. A detecção foi influenciada apenas em 2014, de forma negativa pelas ocasiões. A partir destes resultados foi possível identificar as características ambientais que devem ser mantidas na área, como a disponibilidade de recursos hídricos e abundância de presas, a fim de conservar das espécies resilientes. / The destruction of tropical forests is alarming and may lead to the extinction of species susceptible to fragmentation. In the Atlantic Forest, mammals with important functions in the ecosystem balance, such as Panthera onca (jaguar), are already absent in part of the biome. Therefore, it is urgent to understand the processes that influence the permanence of these species in an area, in order to prevent future local extinctions. Thus, this study aimed to analyze the influence of environmental characteristics on the richness and occurrence of terrestrial mammals of medium and large size; as well as the spatio-temporal relationship between the top predator, mesopredator and preys, in the Atlantic foreste area continuos continuous with Serra do Mar State Park, with recent degradation history (Neblinas Park, Bertioga, State of São Paulo). Sample data was collected by camera trapping for 90 days in 2013 and 2014, 27 sampling points 1km distant from each other. The environmental characteristics were altitude, drainage density, average rainfall, average temperature, number of palm hearts (Euterpe edulis) and the presence of nature trails. Generalized Linear Models were used to analyze the environmental influences on the richness and occurrence of species (with more than 3 records per year). For the other analyses, species were grouped into predator, mesopredators, preys of large, medium and small size. The period and overlap activity of these groups were estimated by the Kernel density. Abundance was estimated for mesopredators and prey through N-mixture models. Single-season occupancy models were used to analyze the probability of occupancy and detection of top predators. A total of 18 terrestrial mammals of medium and large size were sampled, with nine of them being threatened with extinction: Cabassous unicinctus (naked-tailed armadillo), Cuniculus paca (paca), Leopardus guttulus (oncilla), Leopardus pardalis (ocelot), Leopardus wiedii (margay), Pecari tajacu (collared peccary), Puma concolor (cougar), Puma yagouaroundi (jaguarundi) and Tapirus terrestris (tapir). In the 2013, the species richness was positively influenced by the largest volume of precipitation and the species occurrence (C. unicinctus, Dasypus novemcinctus (tatu-galinha), P. concolor, Sylvilagus brasiliensis (tapiti) e T. terrestris) was interfered by the drainage density. In 2014, richness was not explained by any of the environmental characteristics mentioned and only four species have suffered influence of them. The top predator recorded was catemeral, the mesopredator and large prey were mainly nocturnal and prey of medium and small size were mainly daylight. Smaller prey had the highest total overlap with the predator (Δ1=0.72). The influence on the probability of occupancy of the area by the predator varied between the years: in 2013 it was the abundance of large and small preys, and in 2014, the influence was the abundance of medium preys. The detection was negatively influenced by the occasion only in 2014. Our findings showed the environmental characteristics that should be maintained in the area, such as water resources and abundance of prey, for conservation of Atlantic Forest and its fauna community.

Deux parties principales composent cette thèse. La première d'entre elles est consacrée à la valvométrie, c'est-à-dire ici l'étude de la distance entre les deux parties de la coquille d'une huître au cours du temps. La valvométrie est utilisée afin de déterminer si de tels animaux sont en bonne santé, pour éventuellement tirer des conclusions sur la qualité de leur environnement. Nous considérons qu'un processus de renouvellement à quatre états sous-tend le comportement des huîtres étudiées. Afin de retrouver ce processus caché dans le signal valvométrique, nous supposons qu'une densité de probabilité reliée à ce signal est bimodale. Nous comparons donc plusieurs estimateurs qui prennent en compte ce type d'hypothèse, dont des estimateurs à noyau.Dans un second temps, nous comparons plusieurs méthodes de régression, dans le but d'analyser des données transcriptomiques. Pour comprendre quelles variables explicatives influent sur l'expression de gènes, nous avons réalisé des tests multiples grâce au modèle linéaire FAMT. La méthode SIR peut être envisagée pour trouver des relations non-linéaires. Toutefois, elle est principalement employée lorsque la variable à expliquer est univariée. Une version multivariée de cette approche a donc été développée. Le coût d'acquisition des données transcriptomiques pouvant être élevé, la taille n des échantillons correspondants est souvent faible. C'est pourquoi, nous avons également étudié la méthode SIR lorsque n est inférieur au nombre de variables explicatives p. / There are two main parts in this thesis. The first one concerns valvometry, which is here the study of the distance between both parts of the shell of an oyster, over time. The health status of oysters can be characterized using valvometry in order to obtain insights about the quality of their environment. We consider that a renewal process with four states underlies the behaviour of the studied oysters. Such a hidden process can be retrieved from a valvometric signal by assuming that some probability density function linked with this signal, is bimodal. We then compare several estimators which take this assumption into account, including kernel density estimators.In another chapter, we compare several regression approaches, aiming at analysing transcriptomic data. To understand which explanatory variables have an effect on gene expressions, we apply a multiple testing procedure on these data, through the linear model FAMT. The SIR method may find nonlinear relations in such a context. It is however more commonly used when the response variable is univariate. A multivariate version of SIR was then developed. Procedures to measure gene expressions can be expensive. The sample size n of the corresponding datasets is then often small. That is why we also studied SIR when n is less than the number of explanatory variables p.

The largest Florida manatee (Trichechus manatus latirostris) aggregation at a natural warm-water refuge occurs in Kings Bay, Crystal River, FL. Over the last 32 years, the U.S. Fish and Wildlife Service and the State of Florida have created a network of manatee protection areas within Kings Bay including a year-round refuge designation and seven Federal manatee sanctuaries during the winter manatee season (November 15 – March 31). Aerial survey data collected between 1983 and 2012 was used to examine the seasonal change in manatee distribution within Kings Bay in order to assess the effectiveness of current sanctuary sizes and locations. Regression analysis indicated a significant change in manatee abundance among the winter seasons (p < 0.05). The average winter manatee counts increased by 4.81 animals per year over the 30 year period. In contrast, no significant changes in average or peak manatee abundance was detected among the summer seasons (p = 0.71 and p = 0.45 respectively). The average manatee counts increased by only 0.109 animals per year over the summer periods. Spatially explicit models using Geographic Information System (GIS) analysis revealed a strong correlation between high manatee density and artesian springs during the winter seasons. Highest abundances were identified at three locations: King’s Spring, Three Sisters Springs, and Magnolia Springs. These three locations coincide well with pre-existing sanctuary designations, but additional coverage is needed to support the overflow of manatees outside of sanctuary boundaries. Manatees continued to use Kings Bay in the summer seasons but in lower numbers and densities. Because density patterns were not uniform across summer periods, a heavier reliance on boat speed regulation is recommended to provide adequate protection to the endangered Florida manatee. Within a habitat type, the Magnolia Springs, South Banana Island, and Three Sisters Springs sanctuaries exhibited a significant influence on manatee density, suggesting differences in quality among sanctuaries. Years coinciding with extreme cold weather events also had a significant influence on manatee density. Using GIS to investigate seasonal shifts in manatees can be very informative regarding many issues including habitat selection and may improve the design and management of protected areas.

In this master's thesis I presented a new statistical method KDE+ (Kernel Density Estimation plus) that allows detecting clusters of points on the linear data. I created a self-standing application that enables anybody to try the method and apply it on their own data. One possible usage of the method and application is for the detection of critical roads sections with a high concentration of traffic accidents. Development of the application includes analysis of KDE+ statistical method, design of appropriate program structures and the implementation. Optimization were carried out to achieve higher performance after creating the prototype. At the end the software was validated by analysing vehicle collision data from the police database of the Czech Republic.