This thesis focuses on (1) the statistical methodologies for the estimation of spatial data with outliers and (2) classification accuracy of disease diagnosis. Chapter I, Robust Estimation for Spatial Markov Random Field Models: Markov Random Field (MRF) models are useful in analyzing spatial lattice data collected from semiconductor device fabrication and printed circuit board manufacturing processes or agricultural field trials. When outliers are present in the data, classical parameter estimation techniques (e.g., least squares) can be inefficient and potentially mislead the analyst. This chapter extends the MRF model to accommodate outliers and proposes robust parameter estimation methods such as the robust M- and RA-estimates. Asymptotic distributions of the estimates with differentiable and non-differentiable robustifying function are derived. Extensive simulation studies explore robustness properties of the proposed methods in situations with various amounts of outliers in different patterns. Also provided are studies of analysis of grid data with and without the edge information. Three data sets taken from the literature illustrate advantages of the methods. Chapter II, Extending the Skill Test for Disease Diagnosis: For diagnostic tests, we present an extension to the skill plot introduced by Mozer and Briggs (2003). The method is motivated by diagnostic measures for osteoporosis in a study. By restricting the area under the ROC curve (AUC) according to the skill statistic, we have an improved diagnostic test for practical applications by considering the misclassification costs. We also construct relationships, using the Koziol-Green model and mean-shift model, between the diseased group and the healthy group for improving the skill statistic. Asymptotic properties of the skill statistic are provided. Simulation studies compare the theoretical results and the estimates under various disease rates and misclassification costs. We apply the proposed method in classification of osteoporosis data.

O presente estudo agrega os dados geoespaciais livres, cedidos pela prefeitura de São Paulo, IBGE, CNAE, RAIS, entre outros e particulares, cedidos pela empresa Maplink, com os recursos dos Sistemas de Informações Geográficas - SIG, para planejamento de Transportes. A megacidade de São Paulo com mais de dez milhões de habitantes tem milhares de estabelecimentos comerciais para atender a demanda dessa população, que precisa ser abastecidos. Os veículos de carga que abastecem, além de afetarem o trânsito e mobilidade urbana, emitem poluentes. O objetivo é hierarquizar as áreas da megacidade de São Paulo (Brasil) com características potenciais para alta concentração de poluentes decorrentes da circulação dos veículos de carga para abastecer os estabelecimentos comerciais. A metodologia correlaciona espacialmente os dois conjuntos de dados (localização de estabelecimentos comerciais e a circulação de veículos de transporte de cargas) utilizando ferramentas de análises espaciais, baseada em Kernel Density Estimator - KDE, a análise de multicritério, como a Analytic Hierarchy Process - AHP para avaliar como estes duas variáveis estão relacionadas, e também a lógica Fuzzy para calcular esses dados. Os resultados obtidos demonstra que as avenidas e rodovias do município de São Paulo possuem alta concentração de poluentes, sendo utilizadas como rotas para os veículos de carga que tanto fazem do município sua origem e/ou destino, as regiões que possuem alta concentração de poluentes atmosféricos são: Cerqueira César, Parque Dom Pedro II e Ibirapuera, com destaque também na Marginal Tietê e Marginal Pinheiros, além da zona leste (Itaquera e Itaim Paulista). / This study adds free geospatial data, granted by the city of São Paulo, IBGE, CNAE, RAIS, among others and individuals assigned by Maplink company with the capabilities of Geographic Information Systems - GIS for Transportation planning. The megacity of São Paulo with more than ten million inhabitants has thousands of shops to meet the needs of this population, which must be supplied. The cargo vehicles that supply, as well as affect the traffic and urban mobility, emit pollutants. The goal is to prioritize areas of the megacity of São Paulo (Brazil) with potential characteristics for high concentration of pollutants resulting from the movement of cargo vehicles to supply shops. The methodology spatially correlate the two sets of data (location of commercial establishments and the movement of cargo transport vehicles) using tools of spatial analysis based on Kernel Density Estimator - KDE, the multi-criteria analysis, as the Analytic Hierarchy Process - AHP to evaluate how these two variables are related, and also fuzzy logic to calculate this data. The results show that the avenues and highways of São Paulo have a high concentration of pollutants, being used as routes for freight vehicles that both make the city their origin and / or destination, the regions with high concentration of air pollutants they are: Cerqueira Cesar, Parque Dom Pedro II and Ibirapuera, highlighting also the Marginal Tiete and Pinheiros, besides the east side (Itaquera and Itaim Paulista).

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The main aim of this thesis was to investigate the occurrence of dolphins in Pacific waters adjacent to the Panama Canal in the context of biological, temporal and spatial factors. Acoustic data were collected at 101 sites at a range of distances and depths from the shipping region. Data were collected between March 2010 and April 2011 in a diurnal cycle over a total of 114 recording days. Received sound levels were split into 1/3 Octave bandwidths to study variation in sound pressure levels and then converted to spectrum density levels to show the sound components of the background noise in this region. Generalised Linear Models were used to relate dolphin whistle detections to temporal, spatial, environmental and acoustic variables. The major sources of background noise were biological noise from soniferous fish and snapping shrimp and anthropogenic noise from vessels characterised by mid to high frequencies produced by artisanal fishing boats. There was monthly and diurnal variation with some locations characterised by loud sounds in the mid to high frequencies at night. Whistle characteristics analysis revealed that the frequencies and range of the whistles were different to those previously reported under similar conditions. Whistles varied diurnally and in the presence of fish chorus and fishing boats. The study highlights a strong correlation between fish choruses and whistle detection. Temporal and spatial models showed that whistle detections varied monthly and in relation to fish noise and small vessel engine noise. Dolphins were distributed throughout most of the study area; however, whistle detections varied with distance from the coast. The results provide new knowledge about background noise composition in this region and provide the first information on the ecology of dolphin whistles in relation to this background noise, especially to fish chorus.

Management and conservation of populations of animals requires information on where they are, why they are there, and where else they could be. These objectives are typically approached by collecting data on the animals’ use of space, relating these to prevailing environmental conditions and employing these relations to predict usage at other geographical regions. Technical advances in wildlife telemetry have accomplished manifold increases in the amount and quality of available data, creating the need for a statistical framework that can use them to make population-level inferences for habitat preference and space-use. This has been slow-in-coming because wildlife telemetry data are, by definition, spatio-temporally autocorrelated, unbalanced, presence-only observations of behaviorally complex animals, responding to a multitude of cross-correlated environmental variables. I review the evolution of techniques for the analysis of space-use and habitat preference, from simple hypothesis tests to modern modeling techniques and outline the essential features of a framework that emerges naturally from these foundations. Within this framework, I discuss eight challenges, inherent in the spatial analysis of telemetry data and, for each, I propose solutions that can work in tandem. Specifically, I propose a logistic, mixed-effects approach that uses generalized additive transformations of the environmental covariates and is fitted to a response data-set comprising the telemetry and simulated observations, under a case-control design. I apply this framework to non-trivial case-studies using data from satellite-tagged grey seals (Halichoerus grypus) foraging off the east and west coast of Scotland, and northern gannets (Morus Bassanus) from Bass Rock. I find that sea bottom depth and sediment type explain little of the variation in gannet usage, but grey seals from different regions strongly prefer coarse sediment types, the ideal burrowing habitat of sandeels, their preferred prey. The results also suggest that prey aggregation within the water column might be as important as horizontal heterogeneity. More importantly, I conclude that, despite the complex behavior of the study species, flexible empirical models can capture the environmental relationships that shape population distributions.