Separata del curso de Estadística para Ingeniería 1 (CE54), que corresponde al ciclo 2013-1. Este curso es una asignatura destinada al análisis estadístico.

Barrier options are becoming more popular, mainly due to the reduced cost to hold a barrier option when compared to holding a standard call/put options, but exotic options are difficult to price since the payoff functions depend on the whole path of the underlying process, rather than on its value at a specific time instant. It is a path dependent option, which implies that the payoff depends on the path followed by the price of the underlying asset, meaning that barrier options prices are especially sensitive to volatility. For basic exchange traded options, analytical prices, based on the Black-Scholes formula, can be computed. These prices are influenced by supply and demand. There is not always an analytical solution for an exotic option. Hence it is advantageous to have methods that efficiently provide accurate numerical solutions. This study gives a literature overview and compares implementation of some available numerical methods applied to barrier options. The three numerical methods that will be adapted and compared for the pricing of barrier options are: • Binomial Tree Methods • Monte-Carlo Methods • Finite Difference Methods / Thesis (MSc (Applied Mathematics))--North-West University, Potchefstroom Campus, 2013

Barrier options are becoming more popular, mainly due to the reduced cost to hold a barrier option when compared to holding a standard call/put options, but exotic options are difficult to price since the payoff functions depend on the whole path of the underlying process, rather than on its value at a specific time instant. It is a path dependent option, which implies that the payoff depends on the path followed by the price of the underlying asset, meaning that barrier options prices are especially sensitive to volatility. For basic exchange traded options, analytical prices, based on the Black-Scholes formula, can be computed. These prices are influenced by supply and demand. There is not always an analytical solution for an exotic option. Hence it is advantageous to have methods that efficiently provide accurate numerical solutions. This study gives a literature overview and compares implementation of some available numerical methods applied to barrier options. The three numerical methods that will be adapted and compared for the pricing of barrier options are: • Binomial Tree Methods • Monte-Carlo Methods • Finite Difference Methods / Thesis (MSc (Applied Mathematics))--North-West University, Potchefstroom Campus, 2013

Lookback option is a well-known path-dependent option where its payoff depends on the historical extremum prices. The thesis focuses on the binomial pricing of the American floating strike lookback put options with payoff at time $t$ (if exercise) characterized by \[ \max_{k=0, \ldots, t} S_k - S_t, \] where $S_t$ denotes the price of the underlying stock at time $t$. Build upon the idea of \hyperlink{RBCV}{Reiner Babbs Cheuk and Vorst} (RBCV, 1992) who proposed a transformed binomial lattice model for efficient pricing of this class of option, this thesis extends and enhances their binomial recursive algorithm by exploiting the additional combinatorial properties of the lattice structure. The proposed algorithm is not only computational efficient but it also significantly reduces the memory constraint. As a result, the proposed algorithm is more than 1000 times faster than the original RBCV algorithm and it can compute a binomial lattice with one million time steps in less than two seconds. This algorithm enables us to extrapolate the limiting (American) option value up to 4 or 5 decimal accuracy in real time.

The planet is experiencing a dramatic loss of species. The majority of species are unknown to science, and it is usually infeasible to conduct a census of a region to acquire a complete inventory of all life forms. Therefore, it is important to estimate and conduct statistical inference on the total number of species in a region based on samples obtained from field observations. Such estimates may suggest the number of species new to science and at potential risk of extinction. In this thesis, we develop novel methodology to conduct statistical inference, based on abundance-based data collected from multiple sampling locations, on the number of species within a taxonomic group residing in a region. The primary contribution of this work is the formulation of novel statistical methodology for analysis in this setting, where abundances of species are recorded at multiple sampling units across a region. This particular area has received relatively little attention in the literature. In the first chapter, the problem of estimating the number of species is formulated in a broad context, one that occurs in several seemingly unrelated fields of study. Estimators are commonly developed from statistical sampling models. Depending on the organisms or objects under study, different sampling techniques are used, and consequently, a variety of statistical models have been developed for this problem. A review of existing estimation methods, categorized by the associated sampling model, is presented in the second chapter. The third chapter develops a new negative binomial mixture model. The negative binomial model is employed to account for the common tendency of individuals of a particular species to occur in clusters. An exponential mixing distribution permits inference on the number of species that exist in the region, but were in fact absent from the sampling units. Adopting a classical approach for statistical inference, we develop the maximum likelihood estimator, and a corresponding profile-log-likelihood interval estimate of species richness. In addition, a Gaussian-based confidence interval based on large-sample theory is presented. The fourth chapter further extends the hierarchical model developed in Chapter 3 into a Bayesian framework. The motivation for the Bayesian paradigm is explained, and a hierarchical model based on random effects and discrete latent variables is presented. Computing the posterior distribution in this case is not straight-forward. A data augmentation technique that indirectly places priors on species richness is employed to compute the model using a Metropolis-Hastings algorithm. The fifth chapter examines the performance of our new methodology. Simulation studies are used to examine the mean-squared error of our proposed estimators. Comparisons to several commonly-used non-parametric estimators are made. Several conclusions emerge, and settings where our approaches can yield superior performance are clarified. In the sixth chapter, we present a case study. The methodology is applied to a real data set of oribatid mites (a taxonomic order of micro-arthropods) collected from multiple sites in a tropical rainforest in Panama. We adjust our statistical sampling models to account for the varying masses of material sampled from the sites. The resulting estimates of species richness for the oribatid mites are useful, and contribute to a wider investigation, currently underway, examining the species richness of all arthropods in the rainforest. Our approaches are the only existing methods that can make full use of the abundance-based data from multiple sampling units located in a single region. The seventh and final chapter concludes the thesis with a discussion of key considerations related to implementation and modeling assumptions, and describes potential avenues for further investigation. / Graduate

Thesis (M. Sc.)--Carleton University, 2008. / Includes bibliographical references (p. 57-62). Also available in electronic format on the Internet.

Thesis (M.Sc.) - Carleton University, 2008. / Includes bibliographical references (p. 116-119). Also available in electronic format on the Internet.

Thesis--University of Oklahoma. / Bibliography: leaf 51.

Orientador: Liciana Vaz de Arruda Silveira / Banca: José Carlos de Figueiredo Pantoja / Banca: Maria Del Pilar Diaz / Resumo: O objetivo deste trabalho é propor, comparar e selecionar modelos estatísticos baseados na metodologia dos MLGMs e das EEGs. Analisar em que situações cada modelo pode ser melhor utilizado. Discorrer sobre as técnicas de estimação dos parâmetros, escolha da estrutura da matriz de covariância, definição e utilidade das razões de chances e a aplicação em um conjunto de dados da área de anestesiologia veterinária envolvendo equinos. Os dados utilizados neste trabalho foram obtidos por Taffarel (2013). Os vinte e quatro equinos utilizados no experimento foram agrupados da seguinte maneira: (1) animais anestesiados (tratamento 1), (2) animais anestesiados e que receberam analgesia prévia (tratamento 2), (3) animais anestesiados e submetidos à orquiectomia com administração de analgésico após o processo operatório (tratamento 3) e (4) animais anestesiados e submetidos à orquiectomia com administração de analgésico antes de serem operados (tratamento 4). Os animais foram observados por cinco avaliadores em diferentes momentos: uma hora antes do procedimento cirúrgico ou anestésico (M1), quatro horas após a recuperação anestésica e antes da aplicação de analgésicos nos animais do tratamento 3 (M2), duas horas após M2 (M3) e vinte e quatro horas após a cirurgia (M4). A variável resposta (com distribuição Bernoulli) era "olhar o flanco", um comportamento comum em equinos com dores abdominais. O tratamento 3 e o momento 2 foram os efeitos que apresentaram as maiores razões de chances de ocorrência da variável resposta (independente de qual metodologia estatística foi empregada na análise) quando comparados com os demais tratamentos e momentos. Ambos os modelos estatísticos ajustados aos dados (modelos 1 e 2) obtidos através das EEGs e dos MLGMs mostraram-se ser uma poderosa ferramenta para explicar a variável resposta "olhar o flanco" principalmente em relação a seleção das covariáveis... / Abstract: The objective of this work is to propose, compare and select statistical models based on the methodology of GLMMs and GEEs. Examine in which situations each model can be better used. Discuss about the techniques of parameter estimation, choice of the covariance matrix structure, definition and utility of the odds ratios and application in a set of data in the area of veterinary anesthesiology involving equines. The data used in this work were obtained by Taffarel (2013). The twentyfour equines used in the experiment were grouped as follows: (1) anesthetized animals (treatment 1), (2) animals anesthetized and that received prior analgesia (treatment 2), (3) animals anesthetized and underwent orchiectomy with administration of analgesics after surgery process (treatment 3) and (4) animals anesthetized and underwent orchiectomy with administration of analgesics before being operated (treatment 4). The animals were observed by five evaluators at different times: one hour before surgery or anesthetic (M1), four hours after recovery from anesthesia and before the application of analgesics in animals of treatment 3 (M2), two hours after M2 (M3) and twenty-four hours after surgery (M4). The response variable (with Bernoulli distribution) was "look the flank", a common behavior in equines with abdominal pain. The treatment 3 and the moment 2 were the effects with the highest occurrence of odds ratios of the response variable (regardless of what statistical methodology used in the analysis) compared to other treatments and moments. Both statistical models fitted to the data (models 1 and 2) obtained through the EEGs and MLGMs shown to be a powerful tool to explain the response variable "look flank" especially regarding the selection of statistically significant covariates. In the EEG, is not required as the specification of the distribution of vectors response, it became quite advantageous statistical methods, particularly for binary data as ... / Mestre

One of the greatest problems for sub-Saharan Africa is shortage of epidemiological data to support planning for provision of adequate public and animal health services. The overriding challenge is to provide the necessary resources to facilitate the process of regular data collection in support of disease surveillance and vector monitoring across target regions. Due to such circumstances, there is currently an increasing interest towards devising cheaper but yet significantly reliable means for availing the needed epidemiological and vector data for planning purpose. This study comes as a contribution towards solving such challenges. The study has three research components starting with a review of past Uganda national tsetse and trypanosomiasis control efforts as a means towards appreciating the dynamics of controlling the vector and disease. This is an analysis of what was applied, what worked, what didn't, and why it didn’t as linked to the broader vector and disease control system. Secondly through the use of remote sensing, geographical information systems and global positioning technologies tsetse species were sampled within Lake Victoria Basin. Only two species of tsetse were trapped, G. f. fG. f. fuscipes which was widely distributed across the surveyed area, and G. Pallidipes which was detected in a few isolated locations close to the border with Kenya in Eastern Uganda. The analysis of land cover with tsetse findings showed an important association between G. f. fuscipes and particular vegetation mosaics. Unfortunately, while the results are highly informative, approaches for data collection such as this one are costly and unlikely to be sustained by the already over-burdened health systems in the low developed countries of Africa. The third and main part of this study investigates, demonstrates and delivers the possibilities of applying spatial epidemiological modelling techniques to produce both tsetse distribution and abundance maps. Four spatial and non-spatial regression models (Logistic, Autologistic, Negative binomial and Auto-negative binomial), were constructed and used to predict tsetse fly presence and tsetse fly abundance for the study area. The product is an improved understanding of association between environmental variables and tsetse fly distribution/abundance and maps providing continuous representations of the probability of tsetse occurrence and predicted tsetse abundance across the study area. The results indicate that tsetse presence and abundance are influenced differently. Tsetse abundance is highly determined by river systems while tsetse presence is majorly influenced by forested landscapes. Therefore, efforts to control trypanosomiasis through vector control in the Lake Victoria basin will call for delineation of such clearly identified high tsetse accumulation zones for targeted tsetse control operations. This will ensure optimum utilization of the scarce resources and above all contribute to the protection of humans and animals against trypanosomiasis infection.