Contributions to the theory of maximum entropy estimation for ill-posed models

As técnicas estatísticas são fundamentais em ciência e a análise de regressão linear é, quiçá, uma das metodologias mais usadas. É bem conhecido da literatura que, sob determinadas condições, a regressão linear é uma ferramenta estatística poderosíssima. Infelizmente, na prática, algumas dessas condições raramente são satisfeitas e os modelos de regressão tornam-se mal-postos, inviabilizando, assim, a aplicação dos tradicionais métodos de estimação. Este trabalho apresenta algumas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, em particular na estimação de modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. A investigação é desenvolvida em três vertentes, nomeadamente na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, na estimação do parâmetro ridge em regressão ridge e, por último, em novos desenvolvimentos na estimação com máxima entropia. Na estimação de eficiência técnica com fronteiras de produção condicionadas a estados contingentes, o trabalho desenvolvido evidencia um melhor desempenho dos estimadores de máxima entropia em relação ao estimador de máxima verosimilhança. Este bom desempenho é notório em modelos com poucas observações por estado e em modelos com um grande número de estados, os quais são comummente afetados por colinearidade. Espera-se que a utilização de estimadores de máxima entropia contribua para o tão desejado aumento de trabalho empírico com estas fronteiras de produção. Em regressão ridge o maior desafio é a estimação do parâmetro ridge. Embora existam inúmeros procedimentos disponíveis na literatura, a verdade é que não existe nenhum que supere todos os outros. Neste trabalho é proposto um novo estimador do parâmetro ridge, que combina a análise do traço ridge e a estimação com máxima entropia. Os resultados obtidos nos estudos de simulação sugerem que este novo estimador é um dos melhores procedimentos existentes na literatura para a estimação do parâmetro ridge. O estimador de máxima entropia de Leuven é baseado no método dos mínimos quadrados, na entropia de Shannon e em conceitos da eletrodinâmica quântica. Este estimador suplanta a principal crítica apontada ao estimador de máxima entropia generalizada, uma vez que prescinde dos suportes para os parâmetros e erros do modelo de regressão. Neste trabalho são apresentadas novas contribuições para a teoria de máxima entropia na estimação de modelos mal-postos, tendo por base o estimador de máxima entropia de Leuven, a teoria da informação e a regressão robusta. Os estimadores desenvolvidos revelam um bom desempenho em modelos de regressão linear com pequenas amostras, afetados por colinearidade e outliers. Por último, são apresentados alguns códigos computacionais para estimação com máxima entropia, contribuindo, deste modo, para um aumento dos escassos recursos computacionais atualmente disponíveis.

Contribution to the study of the Ria de Aveiro inlet morphodynamics

Over the years it was observed at the Ria de Aveiro lagoon inlet, near the head of the north breakwater, a depth increase that might threaten the stability of this structure. A trend of accretion in the navigation channel of this lagoon is observed, endangering the navigation in this region. In order to understand the origin of these and other trends observed, the knowledge of the sediment transport in the study area is imperative. The main aim of this work is understanding the dominant physical processes in the sediment transport of sediment at the Ria de Aveiro lagoon inlet and adjacent area, improving knowledge of this region morphodynamics. The methodology followed in this study consisted in the analyzes of the topohydrographic surveys performed by the Administration of the Aveiro Harbor, and in the numerical simulations results performed with the morphodynamic modeling system MORSYS2D. The analysis of the surveys was performed by studying the temporal evolution of the bathymetry. The numerical analysis was based on the implementation of the model at the study area, sensitivity analysis of the formulations used to compute the sediment transport to the variation of input parameters (e.g. depth, sediment size, tidal currents) and analysis of the sediment uxes and bathymetric changes predicted. The simulations considered as sediment transport forcing the tidal currents only and the coupled forcing of tides and waves. Considering the wave e ect as sediment transport forcing, both monochromatic waves and a wave regime were simulated. The results revealed that the observed residual sediment transport patterns are generated due to the channel con guration. Inside the lagoon the uxes are mainly induced by the tidal currents action, restricting the action of waves to the inlet and adjacent coast. In the navigation channel the residual sediment uxes predicted are directed o - shore with values between 7 and 40 m3=day generating accretions of approximately 10 m3=day for the shallower region and 35 m3=day for the region between the tidal gauge and the tri^angulo das mar es. At the inlet, the residual uxes are approximately 30 m3=day inducing trends of erosion of approximately 20 m3=day. At the North side of the nearshore accretion is predicted, while at the South side is predicted erosion, at the rates of 250 and 1500 m3=day, respectively. It was also concluded that the waves with higher contribution to the residual sediment uxes are those with heights between 4 and 5 m. However, the storm waves with heights bigger than 5 m, despite their 10% of frequency of occurrence are responsible for 25% of the observed sediment transport.

Single and joint effects of natural and chemical stressors to the terrestrial isopod Porcellionides pruinosus

Environmental contamination and climate changes constitute two of the most serious problems affecting soil ecosystems in agricultural fields. Agriculture is nowadays a highly optimized process that strongly relies on the application of multiple pesticides to reduce losses and increase yield production. Although constituting, per se, a serious problem to soil biota, pesticide mixtures can assume an even higher relevance in a context of unfavourable environmental conditions. Surprisingly, frameworks currently established for environmental risk assessments keep not considering environmental stressors, such as temperature, soil moisture or UV radiation, as factors liable to influence the susceptibility of organisms to pesticides, or pesticide mixtures, which is raising increasing apprehension regarding their adequacy to actually estimate the risks posed by these compounds to the environment. Albeit the higher attention received on the last few years, the influence of environmental stressors on the behaviour and toxicity of chemical mixtures remains still poorly understood. Aiming to contribute for this discussion, the main goal of the present thesis was to evaluate the single and joint effects of natural stressors and pesticides to the terrestrial isopod Porcellionides pruinosus. The first approach consisted on evaluating the effects of several abiotic factors (temperature, soil moisture and UV radiation) on the performance of P. pruinosus using several endpoints: survival, feeding parameters, locomotor activity and avoidance behaviour. Results showed that these stressors might indeed affect P. pruinosus at relevant environmental conditions, thus suggesting the relevance of their consideration in ecotoxicological assays. At next, a multiple biomarker approach was used to have a closer insight into the pathways of damage of UV radiation and a broad spectrum of processes showed to be involved (i.e. oxidative stress, neurotoxicity, energy). Furthermore, UV effects showed to vary with the environment medium and growth-stage. A similar biomarker approach was employed to assess the single and joint effects of the pesticides chlorpyrifos and mancozeb to P. pruinosus. Energy-related biomarkers showed to be the most differentiating parameters since age-classes seemed to respond differently to contamination stress and to have different metabolic costs associated. Finally, the influence of temperature and soil moisture on the toxicity of pesticide mixtures was evaluated using survival and feeding parameters as endpoints. Pesticide-induced mortality was found to be oppositely affected by temperature, either in single or mixture treatments. Whereas chlorpyrifos acute toxicity was raised under higher temperatures the toxicity of mancozeb was more prominent at lower temperatures. By the opposite, soil moisture showed no effects on the pesticide-induced mortality of isopods. Contrary to survival, both temperature and soil moisture showed to interact with pesticides to influence isopods’ feeding parameters. Nonetheless, was however the most common pattern. In brief, findings reported on this thesis demonstrated why the negligence of natural stressors, or multiple stressors in general, is not a good solution for risk assessment frameworks.