Os efeitos de borda e a alteração da estrutura das paisagens constituem consequências negativas da fragmentação florestal responsáveis por transformações nos processos ecológicos. Decorrentes da expansão desordenada de atividades antrópicas, estas alterações podem comprometer o futuro dos remanescentes florestais e a manutenção dos recursos naturais na superfície terrestre. Nesta dissertação a dinâmica da vegetação arbórea foi analisada em oito transectos perpendiculares às bordas de seis remanescentes florestais entre 1996 e 2012. As paisagens do entorno destes transectos foram caracterizadas a partir de imagens orbitais de 1995 e 2011 para a verificação das mudanças ocorridas no uso do solo e para a investigação da influência de seus parâmetros físicos e estruturais sobre as taxas de mortalidade e recrutamento de espécies. Os resultados indicaram que, ao longo do tempo, a influência das bordas se pronunciou em direção ao interior dos remanescentes florestais, enquanto que o contraste entre a borda e o interior se atenuou. A distância média da borda das espécies: pioneiras/iniciais, anemocóricas e de dossel foi significativamente maior em 2012 do que em 1996. A comunidade arbórea apresentou menor similaridade em sua composição ao longo do tempo a menores distâncias da borda. Apesar da dinâmica verificada no uso do solo, a proporcionalidade dos parâmetros físicos e estruturais das paisagens se manteve entre 1995 e 2011. De maneira geral, estes parâmetros apresentaram pouca influência sobre a dinâmica da comunidade arbórea. Apenas as taxas de mortalidade das espécies exóticas e as taxas de recrutamento das espécies pioneiras/inicias apresentam forte relação com o tamanho e o número dos fragmentos florestais nas paisagens. Estes resultados indicam que os efeitos de borda precisam ser atenuados e que o contexto das paisagens deve ser incorporado às estratégias conservacionistas para que estas sejam efetivas e o futuro dos remanescentes florestais não seja comprometido. / Edge effects and landscape structure alterations are among the negative consequences of forest fragmentation responsible for ecological process alterations on the earths surface. Originated from the disordered expansion of anthropogenic activities these alterations may endanger the remaining forest patches future and the maintenance of natural resources. This dissertation was pledged to analyze the vegetation dynamics at forest edges and its relations with landscape features. The vegetation dynamics was examined through eight perpendicular-to-edge transects within six forest patches and the alterations on the arboreal community distribution and composition were assessed between 1996 and 2012. The surrounding landscapes of the analyzed transects were characterized from 1995 and 2011 orbital images and its land use changes were evaluated. Landscape structure and physical parameters influence were analyzed over species recruitment and mortality. The results indicated that the distance of edge influence increased over time while its magnitude was attenuated. The average distance from the edge of pioneer/earlysuccessional species, wind-dispersed and canopy species in 2012 became significantly larger than in 1996. Over time lower similarities in species composition were found to be closer to the edges. Although the observed land use changes in the surrounding landscapes of the edge transects landscape structure and physical parameters proportionality was maintained between 1995 and 2011. Overall the arboreal community dynamics were poorly associated with landscape features. A strong relation of the variables was only found between the exotic and pioneer/early-successional species mortality and recruitment and the size and the amount of forest patches within the landscapes. These results indicate that to be effective conservation planning must tackled edge effects and incorporate the landscape context otherwise they will fail for the maintenance of the future of forest patches.

In this thesis we propose to use a penalized maximum conditional likelihood criterion to estimate the graph of a general discrete Markov random field. We prove the almost sure convergence of the estimator of the graph in the case of a finite or countable infinite set of variables. Our method requires minimal assumptions on the probability distribution and contrary to other approaches in the literature, the usual positivity condition is not needed. We present several examples with a finite set of vertices and study the performance of the estimator on simulated data from theses examples. We also introduce an empirical procedure based on k-fold cross validation to select the best value of the constant in the estimators definition and show the application of this method in two real datasets. / Nesta tese propomos um critério de máxima verossimilhança penalizada para estimar o grafo de dependência condicional de um campo aleatório Markoviano discreto. Provamos a convergência quase certa do estimador do grafo no caso de um conjunto finito ou infinito enumerável de variáveis. Nosso método requer condições mínimas na distribuição de probabilidade e contrariamente a outras abordagens da literatura, a condição usual de positividade não é necessária. Introduzimos alguns exemplos com um conjunto finito de vértices e estudamos o desempenho do estimador em dados simulados desses exemplos. Também propomos um procedimento empírico baseado no método de validação cruzada para selecionar o melhor valor da constante na definição do estimador, e mostramos a aplicação deste procedimento em dois conjuntos de dados reais.

A Regressão Robusta surge como uma alternativa ao ajuste por mínimos quadrados quando os erros são contaminados por pontos aberrantes ou existe alguma evidência de violação das suposições do modelo. Na regressão clássica existem critérios de seleção de modelos e medidas de diagnóstico que são muito conhecidos. O objetivo deste trabalho é apresentar os principais critérios robustos de seleção de modelos e medidas de detecção de pontos aberrantes, assim como analisar e comparar o desempenho destes de acordo com diferentes cenários para determinar quais deles se ajustam melhor a determinadas situações. Os critérios de validação cruzada usando simulações de Monte Carlo e o Critério de Informação Bayesiano são conhecidos por desenvolver-se de forma adequada na identificação de modelos. Na dissertação confirmou-se este fato e além disso, suas alternativas robustas também destacam-se neste aspecto. A análise de resíduos constitui uma forte ferramenta da análise diagnóstico de um modelo, no trabalho detectou-se que a análise clássica de resíduos sobre o ajuste do modelo de regressão linear robusta, assim como a análise das ponderações das observações, são medidas de detecção de pontos aberrantes eficientes. Foram aplicados os critérios e medidas analisados ao conjunto de dados obtido da Estação Meteorológica do Instituto de Astronomia, Geofísica e Ciências Atmosféricas da Universidade de São Paulo para detectar quais variáveis meteorológicas influem na temperatura mínima diária durante o ano completo, e ajustou-se um modelo que permite identificar os dias associados à entrada de sistemas frontais. / Robust Regression arises as an alternative to least squares method when errors are contaminated by outliers points or there are some evidence of violation of model assumptions. In classical regression there are several criteria for model selection and diagnostic measures that are well known. The objective of this work is to present the main robust criteria of model selection and outliers detection measures, as well as to analyze and compare their performance according to different stages to determine which of them fit better in certain situations. The cross-validation criteria using Monte Carlo simulations and Beyesian Information Criterion are known to be adequately developed in model identification. This fact was confirmed, and in addition, its robust alternatives also stand out in this aspect. The residual analysis is a strong tool for model diagnostic analysis, in this work it was detected that the classic residual analysis on the robust linear model regression fit, as well as the analysis of the observations weights, are efficient measures of outliers detection points. The analyzed criteria and measures were applied to the data set obtained from the Meteorological Station of the Astronomy, Geophysics and Atmospheric Sciences Institute of São Paulo University to detect which meteorological variables influence the daily minimum temperature during the whole year, and was fitted a model that allows identify the days associated with the entry of frontal systems.

nÃo hà / PropÃe-se nesta tese um mÃtodo de poda de pesos para redes Perceptron Multicamadas (MLP). TÃcnicas clÃssicas de poda convencionais, tais como Optimal Brain Surgeon(OBS) e Optimal Brain Damage(OBD), baseiam-se na anÃlise de sensibilidade de cada peso da rede, o que requer a determinaÃÃo da inversa da matriz Hessiana da funÃÃo-custo. A inversÃo da matriz Hessiana, alÃm de possuir um alto custo computacional, à bastante susceptÃvel a problemas numÃricos decorrentes do mal-condicionamento da mesma. MÃtodos de poda baseados na regularizaÃÃo da funÃÃo-custo, por outro lado, exigem a determinaÃÃo por tentativa-e-erro de um parÃmetro de regularizaÃÃo. Tendo em mente as limitaÃÃes dos mÃtodos de poda supracitados, o mÃtodo proposto baseia-se no "PrincÃpio da MÃxima CorrelaÃÃo dos Erros" (MAXCORE). A idÃia consiste em analisar a importÃncia de cada conexÃo da rede a partir da correlaÃÃo cruzada entre os erros em uma camada e os erros retropropagados para a camada anterior, partindo da camada de saÃda em direÃÃo à camada de entrada. As conexÃes que produzem as maiores correlaÃÃes tendem a se manter na rede podada. Uma vantagem imediata deste procedimento està em nÃo requerer a inversÃo de matrizes, nem um parÃmetro de regularizaÃÃo. O desempenho do mÃtodo proposto à avaliado em problemas de classificaÃÃo de padrÃes e os resultados sÃo comparados aos obtidos pelos mÃtodos OBS/OBD e por um mÃtodo de poda baseado em regularizaÃÃo. Para este fim, sÃo usados, alÃm de dados articialmente criados para salientar caracterÃsticas importantes do mÃtodo, os conjuntos de dados bem conhecidos da comunidade de aprendizado de mÃquinas: Iris, Wine e Dermatology. Utilizou-se tambÃm um conjunto de dados reais referentes ao diagnÃstico de patologias da coluna vertebral. Os resultados obtidos mostram que o mÃtodo proposto apresenta desempenho equivalente ou superior aos mÃtodos de poda convencionais, com as vantagens adicionais do baixo custo computacional e simplicidade. O mÃtodo proposto tambÃm mostrou-se bastante agressivo na poda de unidades de entrada (atributos), o que sugere a sua aplicaÃÃo em seleÃÃo de caracterÃsticas. / This thesis proposes a new pruning method which eliminates redundant weights in a multilayer perceptron (MLP). Conventional pruning techniques, like Optimal Brain Surgeon (OBS) and Optimal Brain Damage (OBD), are based on weight sensitivity analysis, which requires the inversion of the error Hessian matrix of the loss function (i.e. mean squared error). This inversion is specially susceptible to numerical problems due to poor conditioning of the Hessian matrix and demands great computational efforts. Another kind of pruning method is based on the regularization of the loss function, but it requires the determination of the regularization parameter by trial and error. The proposed method is based on "Maximum Correlation Errors Principle" (MAXCORE). The idea in this principle is to evaluate the importance of each network connection by calculating the cross correlation among errors in a layer and the back-propagated errors in the preceding layer, starting from the output layer and working through the network until the input layer is reached. The connections which have larger correlations remain and the others are pruned from the network. The evident advantage of this procedure is its simplicity, since matrix inversion or parameter adjustment are not necessary. The performance of the proposed method is evaluated in pattern classification tasks and the results are compared to those achieved by the OBS/OBD techniques and also by regularization-based method. For this purpose, artificial data sets are used to highlight some important characteristics of the proposed methodology. Furthermore, well known benchmarking data sets, such as IRIS, WINE and DERMATOLOGY, are also used for the sake of evaluation. A real-world biomedical data set related to pathologies of the vertebral column is also used. The results obtained show that the proposed method achieves equivalent or superior performance compared to conventional pruning methods, with the additional advantages of low computational cost and simplicity. The proposed method also presents eficient behavior in pruning the input units, which suggests its use as a feature selection method.

Nous présentons dans cette thèse une méthode générique et automatique pour la localisation et la caractérisation de lésions cérébrales telles que les tumeurs primaires à partir de multiples contrastes IRM. Grâce à une récente généralisation des lois de probabilités de mélange par l'échelle de distributions gaussiennes, nous pouvons modéliser une large variété d'interactions entre les paramètres IRM mesurés, et cela afin de capter l'hétérogénéité présent dans les tissus cérébraux sains et endommagés. En nous basant sur ces lois de probabilités, nous proposons un protocole complet pour l'analyse de données IRM multi-contrastes : à partir de données quantitatives, ce protocole fournit, s'il y a lieu, la localisation et le type des lésions détectées au moyen de modèles probabilistes. Nous proposons également deux extensions de ce protocole. La première extension concerne la sélection automatique du nombre de composantes au sein du modèle probabiliste, sélection réalisée via une représentation bayésienne des modèles utilisés. La seconde extension traite de la prise en compte de la structure spatiale des données IRM par l'ajout d'un champ de Markov latent au sein du protocole développé. / We present in this thesis a generic and automatic method for the localization and the characterization of brain lesions such as primary tumor using multi-contrast MRI. From the recent generalization of scale mixtures of Gaussians, we reach to model a large variety of interactions between the MRI parameters, with the aim of capturing the heterogeneity inside the healthy and damaged brain tissues. Using these probability distributions we propose an all-in-one protocol to analyze multi-contrast MRI: starting from quantitative MRI data this protocol determines if there is a lesion and in this case the localization and the type of the lesion based on probability models. We also develop two extensions for this protocol. The first one concerns the selection of mixture components in a Bayesian framework. The second one is about taking into account the spatial structure of MRI data by the addition of a random Markov field to our protocol.

Pela necessidade de reverter o atual quadro de degradação da Mata Atlântica, ações de restauração se fazem urgentes e devem ser pensadas a fim de restabelecer a biodiversidade nessas áreas, envolvendo as diversas formas de vida vegetal, animal e suas interações. O restabelecimento da relação planta-frugívoro e consequente dispersão de sementes certamente são essenciais não só para a conservação de uma floresta existente, mas também na aceleração do processo de restauração florestal. Portanto, a atração dos agentes dispersores de sementes deve fazer parte dos esforços empregados em ações restauradoras. Uma forma de avaliar a contribuição destes animais em áreas restauradas é através do estudo da chuva de sementes, mais especificamente aquela que é resultado dos eventos de dispersão pela fauna (zoocoria). Este estudo buscou caracterizar e comparar a composição da chuva de sementes zoocóricas em uma área em processo de restauração florestal na Mata Atlântica, submetidas a duas técnicas de manejo distintas, uma por meio de plantio de restauração em área total e outra, através da indução e condução da regeneração natural, originando uma área de capoeira. Ainda, utilizando a ferramenta de seleção de modelos pelo critério de Akaike, foram avaliadas se variáveis de estrutura e composição da vegetação arbustivo-arbórea influenciaram a riqueza e abundância da chuva de sementes zoocóricas total e imigrantes. O estudo foi conduzido em uma área em processo de restauração florestal, com seis anos de idade, que abrange 28,86 ha da Fazenda Intermontes (24°11\'17\" S, 42°24\'49\" O; 24°12\'47\" S, 42° 26\'15\" O), próximo ao município de Ribeirão Grande, SP. Propágulos depositados nos coletores foram retirados mensalmente pelo período de 1 ano. Utilizou-se um total de 100 coletores de sementes, de 1 m x 1 m. Para a caracterização da vegetação presente, foi realizado um levantamento dos indivíduos arbustivo-arbóreos, num raio de 5 metros no entorno de cada coletor de semente. Os resultados mostraram que a composição da comunidade da chuva de sementes zoocóricas diferiu entre os ambientes de capoeira e plantio, porém a riqueza e abundância médias das sementes não diferiram significativamente entre os ambientes. Apesar da composição da comunidade ter sido diferente, as categorias funcionais das sementes presentes na chuva, em ambas as áreas, foram semelhantes entre si. Avaliando se houve influência de variáveis relacionadas à estrutura e composição da vegetação arbustivo-arbórea na chuva de sementes zoocóricas, os modelos gerados e selecionados indicaram que as variáveis estudadas não influenciaram a riqueza e abundância da chuva de sementes zoocóricas total e imigrantes. O estudo concluiu também que o processo de chegada de propágulos alóctones a área já se iniciou, demonstrando um grande potencial de incremento de novas espécies, pertencentes a outras formas de vida e a diferentes funções ecológicas. Isto possibilita a aceleração do processo de restauração florestal, aumento da complexidade estrutural da vegetação e uma contribuição para a heterogeneidade da floresta implantada, fator este importante para o processo de retorno e incremento da fauna dispersora. / The need to reverse the current degradation of the Atlantic Forest requires urgent restoration actions aimed at reestablishing biodiversity in these areas, involving various plant and animal life forms and their interactions. The reestablishment of plant-frugivore interactions and subsequent seed dispersal are essential not only for the conservation of an existing forest, but also for the acceleration of forest restoration processes. Therefore, seed dispersal agents should be employed in restoration actions. One way to assess animals\' contribution in seed dispersion is through the study of seed rain, more specifically through results of dispersal events by fauna (zoochory). This study aimed to characterize and compare the composition of animal-dispersed seed rain in an area of the Atlantic Forest undergoing a restoration process using two different management techniques. One area comprised of tree planting and another comprising a \"capoeira\" through assisted natural regeneration. We also used an Akaike information criterion of model selection tool to evaluate whether structure and composition variables of arbustive-arboreal vegetation influenced the richness and abundance of total and immigrant animal-dispersed seed rain. The study was conducted in an area undergoing a forest restoration process with six years of age, covering 28.86 ha of the Intermontes Farm (24°11\'17\"S, 42°24\'49\"W; 24°12\'47\"S, 42°26\'15\"W), near Ribeirão Grande city, São Paulo State, Brazil. Propagules deposited in traps were removed monthly for a period of one year. We used 100 seed collectors 1 m x 1 m. To characterize the vegetation in the region, we surveyed the arbustive-arboreal species in a 5-meter radius around each seed collector. The results showed that the community composition of the animal-dispersed seed rain differed between tree planting and \"capoeira\" environments; however, the richness and abundance averages of seeds did not differ significantly between the environments. Although the community composition was different, functional categories of seeds in the rain in both areas were similar. Assessing whether there was influence of variables related to structure and composition of arbustive-arboreal species on animal-dispersed seed rain, generated and selected models indicated that these variables did not influence the richness and abundance of total and immigrant animal-dispersed seed rain. The results also showed the presence of alien propagules in the region, demonstrating great potential for the growth of new species belonging to other life forms with different ecological functions. This allows the acceleration of forest restoration processes, increased structural complexity of vegetation and contribution to heterogeneity of deployed forest, which is important for the return and increase of animal dispersers.

時間序列中對於模式階數的選取，一直是重要的課題。從過去文獻研究得 知，大多數的討論都局限於平穩的模式。然而近年來，非平穩型序列逐漸 成為各學者研究的方向。因此，一個能協助研究者適當處理資料的方法， 如採取適當的單位根檢定，是進行實證分析時所必需採行的程序。在本篇 文章中我們是採用單位根檢定來決定差分階數，然後再結合 Pukkila et al.(1990)所提出的選模方法決定p、q的階數(簡稱PKK選模法)經由本文模 擬結果所得之結論為當序列為平穩型時，直接用PKK選模法來進行階數的 選取，能得到較強的選模能力 。但當序列為非平穩型時，則建議先以單 位根檢定來決定差分階數，再佐以PKK選模法決定p、q階數。

The Support Vector (SV) machine is a novel type of learning machine, based on statistical learning theory, which contains polynomial classifiers, neural networks, and radial basis function (RBF) networks as special cases. In the RBF case, the SV algorithm automatically determines centers, weights and threshold such as to minimize an upper bound on the expected test error. The present study is devoted to an experimental comparison of these machines with a classical approach, where the centers are determined by $k$--means clustering and the weights are found using error backpropagation. We consider three machines, namely a classical RBF machine, an SV machine with Gaussian kernel, and a hybrid system with the centers determined by the SV method and the weights trained by error backpropagation. Our results show that on the US postal service database of handwritten digits, the SV machine achieves the highest test accuracy, followed by the hybrid approach. The SV approach is thus not only theoretically well--founded, but also superior in a practical application.

In this dissertation, we have developed and combined several statistical techniques in Bayesian factor analysis (BAYFA) and mixture of factor analyzers (MFA) to overcome the shortcoming of these existing methods. Information Criteria are brought into the context of the BAYFA model as a decision rule for choosing the number of factors m along with the Press and Shigemasu method, Gibbs Sampling and Iterated Conditional Modes deterministic optimization. Because of sensitivity of BAYFA on the prior information of the factor pattern structure, the prior factor pattern structure is learned directly from the given sample observations data adaptively using Sparse Root algorithm. Clustering and dimensionality reduction have long been considered two of the fundamental problems in unsupervised learning or statistical pattern recognition. In this dissertation, we shall introduce a novel statistical learning technique by focusing our attention on MFA from the perspective of a method for model-based density estimation to cluster the high-dimensional data and at the same time carry out factor analysis to reduce the curse of dimensionality simultaneously in an expert data mining system. The typical EM algorithm can get trapped in one of the many local maxima therefore, it is slow to converge and can never converge to global optima, and highly dependent upon initial values. We extend the EM algorithm proposed by cite{Gahramani1997} for the MFA using intelligent initialization techniques, K-means and regularized Mahalabonis distance and introduce the new Genetic Expectation Algorithm (GEM) into MFA in order to overcome the shortcomings of typical EM algorithm. Another shortcoming of EM algorithm for MFA is assuming the variance of the error vector and the number of factors is the same for each mixture. We propose Two Stage GEM algorithm for MFA to relax this constraint and obtain different numbers of factors for each population. In this dissertation, our approach will integrate statistical modeling procedures based on the information criteria as a fitness function to determine the number of mixture clusters and at the same time to choose the number factors that can be extracted from the data.

It is desirable to reduce the potential threats that result from the variability of nature, such as droughts or heat waves that lead to food shortage, or the other extreme, floods that lead to severe damage. To prevent such catastrophic events, it is necessary to understand, and to be capable of characterising, nature's variability. Typically one aims to describe the underlying dynamics of geophysical records with differential equations. There are, however, situations where this does not support the objectives, or is not feasible, e.g., when little is known about the system, or it is too complex for the model parameters to be identified. In such situations it is beneficial to regard certain influences as random, and describe them with stochastic processes. In this thesis I focus on such a description with linear stochastic processes of the FARIMA type and concentrate on the detection of long-range dependence. Long-range dependent processes show an algebraic (i.e. slow) decay of the autocorrelation function. Detection of the latter is important with respect to, e.g. trend tests and uncertainty analysis. Aiming to provide a reliable and powerful strategy for the detection of long-range dependence, I suggest a way of addressing the problem which is somewhat different from standard approaches. Commonly used methods are based either on investigating the asymptotic behaviour (e.g., log-periodogram regression), or on finding a suitable potentially long-range dependent model (e.g., FARIMA[p,d,q]) and test the fractional difference parameter d for compatibility with zero. Here, I suggest to rephrase the problem as a model selection task, i.e.comparing the most suitable long-range dependent and the most suitable short-range dependent model. Approaching the task this way requires a) a suitable class of long-range and short-range dependent models along with suitable means for parameter estimation and b) a reliable model selection strategy, capable of discriminating also non-nested models. With the flexible FARIMA model class together with the Whittle estimator the first requirement is fulfilled. Standard model selection strategies, e.g., the likelihood-ratio test, is for a comparison of non-nested models frequently not powerful enough. Thus, I suggest to extend this strategy with a simulation based model selection approach suitable for such a direct comparison. The approach follows the procedure of a statistical test, with the likelihood-ratio as the test statistic. Its distribution is obtained via simulations using the two models under consideration. For two simple models and different parameter values, I investigate the reliability of p-value and power estimates obtained from the simulated distributions. The result turned out to be dependent on the model parameters. However, in many cases the estimates allow an adequate model selection to be established. An important feature of this approach is that it immediately reveals the ability or inability to discriminate between the two models under consideration. Two applications, a trend detection problem in temperature records and an uncertainty analysis for flood return level estimation, accentuate the importance of having reliable methods at hand for the detection of long-range dependence. In the case of trend detection, falsely concluding long-range dependence implies an underestimation of a trend and possibly leads to a delay of measures needed to take in order to counteract the trend. Ignoring long-range dependence, although present, leads to an underestimation of confidence intervals and thus to an unjustified belief in safety, as it is the case for the return level uncertainty analysis. A reliable detection of long-range dependence is thus highly relevant in practical applications. Examples related to extreme value analysis are not limited to hydrological applications. The increased uncertainty of return level estimates is a potentially problem for all records from autocorrelated processes, an interesting examples in this respect is the assessment of the maximum strength of wind gusts, which is important for designing wind turbines. The detection of long-range dependence is also a relevant problem in the exploration of financial market volatility. With rephrasing the detection problem as a model selection task and suggesting refined methods for model comparison, this thesis contributes to the discussion on and development of methods for the detection of long-range dependence. / Die potentiellen Gefahren und Auswirkungen der natürlicher Klimavariabilitäten zu reduzieren ist ein wünschenswertes Ziel. Solche Gefahren sind etwa Dürren und Hitzewellen, die zu Wasserknappheit führen oder, das andere Extrem, Überflutungen, die einen erheblichen Schaden an der Infrastruktur nach sich ziehen können. Um solche katastrophalen Ereignisse zu vermeiden, ist es notwendig die Dynamik der Natur zu verstehen und beschreiben zu können. Typischerweise wird versucht die Dynamik geophysikalischer Datenreihen mit Differentialgleichungssystemen zu beschreiben. Es gibt allerdings Situationen in denen dieses Vorgehen nicht zielführend oder technisch nicht möglich ist. Dieses sind Situationen in denen wenig Wissen über das System vorliegt oder es zu komplex ist um die Modellparameter zu identifizieren. Hier ist es sinnvoll einige Einflüsse als zufällig zu betrachten und mit Hilfe stochastischer Prozesse zu modellieren. In dieser Arbeit wird eine solche Beschreibung mit linearen stochastischen Prozessen der FARIMA-Klasse angestrebt. Besonderer Fokus liegt auf der Detektion von langreichweitigen Korrelationen. Langreichweitig korrelierte Prozesse sind solche mit einer algebraisch, d.h. langsam, abfallenden Autokorrelationsfunktion. Eine verläßliche Erkennung dieser Prozesse ist relevant für Trenddetektion und Unsicherheitsanalysen. Um eine verläßliche Strategie für die Detektion langreichweitig korrelierter Prozesse zur Verfügung zu stellen, wird in der Arbeit ein anderer als der Standardweg vorgeschlagen. Gewöhnlich werden Methoden eingesetzt, die das asymptotische Verhalten untersuchen, z.B. Regression im Periodogramm. Oder aber es wird versucht ein passendes potentiell langreichweitig korreliertes Modell zu finden, z.B. aus der FARIMA Klasse, und den geschätzten fraktionalen Differenzierungsparameter d auf Verträglichkeit mit dem trivialen Wert Null zu testen. In der Arbeit wird vorgeschlagen das Problem der Detektion langreichweitiger Korrelationen als Modellselektionsproblem umzuformulieren, d.h. das beste kurzreichweitig und das beste langreichweitig korrelierte Modell zu vergleichen. Diese Herangehensweise erfordert a) eine geeignete Klasse von lang- und kurzreichweitig korrelierten Prozessen und b) eine verläßliche Modellselektionsstrategie, auch für nichtgenestete Modelle. Mit der flexiblen FARIMA-Klasse und dem Whittleschen Ansatz zur Parameterschätzung ist die erste Voraussetzung erfüllt. Hingegen sind standard Ansätze zur Modellselektion, wie z.B. der Likelihood-Ratio-Test, für nichtgenestete Modelle oft nicht trennscharf genug. Es wird daher vorgeschlagen diese Strategie mit einem simulationsbasierten Ansatz zu ergänzen, der insbesondere für die direkte Diskriminierung nichtgenesteter Modelle geeignet ist. Der Ansatz folgt einem statistischen Test mit dem Quotienten der Likelihood als Teststatistik. Ihre Verteilung wird über Simulationen mit den beiden zu unterscheidenden Modellen ermittelt. Für zwei einfache Modelle und verschiedene Parameterwerte wird die Verläßlichkeit der Schätzungen für p-Wert und Power untersucht. Das Ergebnis hängt von den Modellparametern ab. Es konnte jedoch in vielen Fällen eine adäquate Modellselektion etabliert werden. Ein wichtige Eigenschaft dieser Strategie ist, dass unmittelbar offengelegt wird, wie gut sich die betrachteten Modelle unterscheiden lassen. Zwei Anwendungen, die Trenddetektion in Temperaturzeitreihen und die Unsicherheitsanalyse für Bemessungshochwasser, betonen den Bedarf an verläßlichen Methoden für die Detektion langreichweitiger Korrelationen. Im Falle der Trenddetektion führt ein fälschlicherweise gezogener Schluß auf langreichweitige Korrelationen zu einer Unterschätzung eines Trends, was wiederum zu einer möglicherweise verzögerten Einleitung von Maßnahmen führt, die diesem entgegenwirken sollen. Im Fall von Abflußzeitreihen führt die Nichtbeachtung von vorliegenden langreichweitigen Korrelationen zu einer Unterschätzung der Unsicherheit von Bemessungsgrößen. Eine verläßliche Detektion von langreichweitig Korrelierten Prozesse ist somit von hoher Bedeutung in der praktischen Zeitreihenanalyse. Beispiele mit Bezug zu extremem Ereignissen beschränken sich nicht nur auf die Hochwasseranalyse. Eine erhöhte Unsicherheit in der Bestimmung von extremen Ereignissen ist ein potentielles Problem von allen autokorrelierten Prozessen. Ein weiteres interessantes Beispiel ist hier die Abschätzung von maximalen Windstärken in Böen, welche bei der Konstruktion von Windrädern eine Rolle spielt. Mit der Umformulierung des Detektionsproblems als Modellselektionsfrage und mit der Bereitstellung geeigneter Modellselektionsstrategie trägt diese Arbeit zur Diskussion und Entwicklung von Methoden im Bereich der Detektion von langreichweitigen Korrelationen bei.