The analysis of big data is now very popular. Big data may be very important for companies, societies or even human beings if we can take full advantage of them. Data scientists defined big data with four Vs: volume, velocity, variety and veracity. In a short, the data have large volume, grow with high velocity, represent with numerous varieties and must have high quality. Here we analyze data from many sources (varieties). In small area estimation, the term ``big data' refers to numerous areas. We want to analyze binary for a large number of small areas. Then standard Markov Chain Monte Carlo methods (MCMC) methods do not work because the time to do the computation is prohibitive. To solve this problem, we use numerical approximations. We set up four methods which are MCMC, method based on Beta-Binomial model, Integrated Nested Normal Approximation Model (INNA) and Empirical Logistic Transform (ELT) method. We compare the processing time and accuracies of these four methods in order to find the fastest and reasonable accurate one. Last but not the least, we combined the empirical logistic transform method, the fastest and accurate method, with time series to explore the sales data over time.

The Slovenian Public Opinion survey (SPOS), which carried out in 1990, was used by the government of Slovenia as a benchmark to prepare for an upcoming plebiscite, which asked the respondents whether they support independence from Yugoslavia. However, the sample size was large and it is quite likely that the respondents and nonrespondents had divergent viewpoints. We first develop an ignorable nonresponse model which is an extension of a bivariate binomial model. In order to accommodate the nonrespondents, we then develop a nonignorable nonresponse model which is an extension of the ignorable model. Our methodology uses an EM algorithm to fit both the ignorable and nonignorable nonresponse models, and estimation is carried out using the bootstrap mechanism. We also perform sensitivity analysis to study different degrees of departures of the nonignorable nonresponse model from the ignorable nonresponse model. We found that the nonignorable nonresponse model is mildly sensitive to departures from the ignorable nonresponse model. In fact, our finding based on the nonignorable model is better than an earlier conclusion about another nonignorable nonresponse model fitted to these data.

Promover a segurança viária no entorno escolar é uma estratégia que contribui para que sejam construídas cidades seguras, saudáveis e sustentáveis. Nesse sentido, este estudo é dedicado a identificar a influência das características da estrutura urbana na frequência e na severidade dos acidentes no entorno de escolas de educação básica de Porto Alegre. A análise da frequência e da severidade de acidentes foi conduzida através da estimação de modelos econométricos: binomial negativo e logit ordenado, respectivamente. Para esses, foram calculados os efeitos marginais, permitindo a observação da magnitude dos impactos das variáveis explicativas sobre as variáveis dependentes. As variáveis dependentes frequência e severidade foram extraídas dos acidentes registrados em Porto Alegre entre 2012 e 2014. Foram incluídas, simultaneamente, variáveis da estrutura urbana, das escolas, socioeconômicas e dos acidentes (para a severidade). A partir do geoprocessamento dos dados existentes, os entornos escolares puderam ser caracterizados para três diferentes áreas circulares de análise (buffer ring) de raios de 100, 150 e 200 metros, permitindo a comparação do uso das diferentes áreas. O conjunto de estimativas indica que áreas menores produzem modelos de melhor desempenho para ambas as técnicas empregadas. No entanto, áreas maiores permitem a análise de maior quantidade de variáveis relativas à estrutura urbana. Essa relação sugere os benefícios da escolha a partir do trade-off entre ajuste do modelo e sua capacidade de propiciar análises de variáveis. Foi identificado que a frequência e a severidade de acidentes podem estar relacionadas a uma única variável explicativa de formas opostas – a partir de sinais contrários. Essa diferença de resultados para frequência e severidade de acidentes indica que há maiores benefícios em analisá-las em conjunto. Identificou-se ainda que existem benefícios para a segurança viária em áreas de estrutura urbana com quarteirões menores e maior quantidade de interseções de quatro vias, em frequência e severidade, respectivamente. Já as áreas mais arborizadas tendem a apresentar acidentes de menor severidade nos casos de usuários de modos ativos. / Fostering road safety nearby schools is a strategy that contributes to build safe, healthy and sustainable cities. The aim of this study is to identify the influence of the built environment characteristics in the frequency and severity of accidents nearby elementary and secondary schools in Porto Alegre. The frequency and severity of the accidents were analyzed using econometric models: negative binomial and ordered logit, respectively. The evaluation of their marginal effects allowed the magnitude of the impact caused by the explanatory variable on the dependent variables to be observed. The measured variables frequency and severity were extracted from accidents registered in Porto Alegre from 2012 and 2014. Built environment, socioeconomic and school variables were also included, as well as accident data (for severity). Data geoprocessing allowed school surroundings to be characterized for three different buffer rings, measuring 100, 150 and 200 meters of radius. Thereby it was possible to compare the inclusion of different areas in the study. The estimations indicates that models based on smaller areas have better performances for both employed techniques, whereas larger areas allow the study of a bigger quantity of urban infrastructure variables. That indicates the benefits of choosing based on a trade-off between model adjustment and capacity to engender the analysis of variables. It was shown that frequency and severity of accidents could be related to a single explanatory variable in opposite ways – based on contrary signs. This difference in the results found for frequency and severity indicates that there are more benefits when analyzing them together. Moreover, there are benefits for road safety in areas where the city blocks are shorter and where there are more four-way intersections, in frequency and severity of accidents, respectively. Also, areas of more important afforestation tend to decrease the severity of accidents involving users of active modes.

Orientador: José Carlos Barbosa / Banca: Marcelo Francisco Arantes Pereira / Banca: Marilia Gregolin Costa de Castro / Banca: Arlindo Leal Boiça Junior / Banca: Antônio Carlos Busoli / Resumo: Com a expansão dos seringais na região Noroeste do Estado de São Paulo, o percevejo-de-renda da seringueira, Leptopharsa heveae, alcançou níveis populacionais que provocaram e têm provocado danos à heveicultura em geral, reduzindo de forma significativa a produção de látex nos seringais. Com o objetivo de conhecer a distribuição espacial para basear ações de controle desta praga, instalaram-se experimentos em 3 áreas de seringueira plantadas com o clone RRIM 600, com idades de 4, 8 e 12 anos, em uma fazenda localizada no município de Guapiaçu-SP. Em cada área foram consideradas 100 parcelas, cada uma composta por uma linha de 3 plantas sendo amostrado 1 ramo da parte externa do terço inferior da copa da planta central de cada parcela onde foram contadas ninfas e adultos, em 27 amostragens. O nível de agregação da praga foi estudado, para cada amostragem, segundo os índices de dispersão: razão variância/média, índice de Morisita, coeficiente de Green, lei de potência de Taylor e expoente k da binomial negativa e constatou-se que, na maioria das amostragens, a população de L. heveae apresentou distribuição agregada tanto para ninfas quanto para adultos e também para a população total (ninfas + adultos) da praga. Estudou-se o ajuste às distribuições de probabilidade através do teste qui-quadrado de aderência e o modelo mais adequado para representar a distribuição espacial foi a distribuição binomial negativa para ninfas, adultos e para o total da praga. Foi construído um plano de amostragem sequencial para a população total de L. heveae e o número máximo esperado é de 21 ramos para decidir se há a necessidade ou não do controle. As maiores médias populacionais de ninfas e adultos de L. heveae ocorreram no período de julho a outubro, e verificou-se que a população de L. heveae foi significativamente influenciada pelas chuvas, independente das idades ... / Abstract: With the expansion of rubber trees in the northwestern region of São Paulo state, Brazil, the rubber-tree lacebug, Leptopharsa heveae, reached population levels that caused and continues to cause damages to heveiculture, reducing significantly the rubber production in these trees. To determine the spatial distribution of the lace bug and devise measures to control this pest, experiments were established in 3 areas where RRIM 600 rubber tree clones had been planted (ages 4, 8, and 12 years old), in a farm in the city of Guapiaçu, São Paulo. In each area, 100 parcels were considered, each one made by a line of 3 plants, being sampled 1 branch from the outer section of the lower-third of the canopy of the central plant in each parcel where the number of lacebug nymphs and adults was counted in 27 sampling dates. In each sample, the level of pest aggregation was studied by the dispersion indexes: variance/mean relationship, Morisita's index, Green's coefficient, Taylor's Power Law, and k exponent of the negative binomial; thus, it was verified that, in most samples, the L. heveae population presents aggregate distribution both for nymphs and adults, as well as the pest population as a whole (nymphs plus adults). The adjustment to the probability's distributions was studied through the chi-square test; the binomial negative distribution was the most appropriate model to represent the spatial distribution of the nymphs, adults, and the total population in the 3 areas. A sequential sampling plan was developed for the whole L. heveae population, with an expected maximum of 21 branches being sampled to determine whether preventive measures are necessary. The highest population averages of nymphs and adults of L. heveae occurred from July to October. It was found that the population of L. heveae was significantly influenced by rainfall, regardless of the age of the rubber trees / Doutor

This thesis investigates the relationship between conflict, economic growth, state capacity and natural resources in Sub-Saharan Africa. It contributes to the limited research in this area and empirically examines these relationships using different econometric models. The first empirical chapter uses a panel dataset that covers the period 1997 - 2013 to analyse the effects of economic growth on conflict in Nigeria using the negative binomial model. The findings support the direct relationship between economic growth and conflict in Nigeria. Controlling for other factors, the results indicate that increase in growth rate - measured by annual growth rate of GDP per capita - decreases the expected number of conflicts. The study finds no evidence of a relationship between levels of wealth in a state and the incidence of conflicts. The analysis controls for factors such as spill-over effects from other states and year and state effects. Finally, to address potential concerns that economic growth could be a cause of conflict or that other unobserved factors could confound the relationship between economic growth and conflict, the chapter employs instrumental variable (IV) estimation using percentage change in rainfall as an instrument. The results with the IV estimation are similar to the results without IV in terms of both sign and significance, indicating that the negative effect of economic growth on conflicts is not due to reverse causality or omitted variables. For robustness checks, a Panel Autoregressive model (PVAR) is also employed. The second empirical chapter analyses the effect of conflict on state capacity in Sub-Saharan Africa. State capacity is measured in terms of fiscal and legal capacity. It also looks at the effects of internal and external conflicts on state capacity. The chapter adopts the Ordinary least squared (OLS) and the system generalised methods of moments (GMM) estimation methods to analyse the panel data consisting of 49 Sub-Saharan countries over the period 2000 - 2015. The results suggest that conflicts have a negative and significant effect on state capacity. However, when military expenditure is used as a proxy for state capacity it is found that conflict strengthens state capacity. The results are consistent with theoretical argument that internal conflicts polarise societies and make it more difficult for governments to reach a consensus in investing in state capacity, while external conflicts mobilise domestic population against a common enemy thereby helping in state capacity building. Finally, the third empirical chapter examines the effect of natural resources on conflict onset and duration using discrete choice models with a dataset covering the period 1980 -2016. The results on the duration analysis show that natural resources prolong duration of conflicts. However, it is found that not all natural resources prolong duration of conflicts. Oil production does not seem to affect duration, whereas oil reserves and gas production lengthens the duration. The findings from the onset analysis show that both production and reserves of natural resources increase the risk of conflict onset.

In the development of any product to perform a specific function the first concern of the engineer is to design for satisfactory operation. Engineers originally approached the reliability problem by using excessive safety factors to be assured the structure or material would withstand the calculated loads and stresses. The engineer also learned from operating or testing the equipment until failures occurred and then redesigning as mistakes became apparent. These methods were time consuming and often resulted in bulky over designed products. These approaches became impractical with the advent of new technological advancements. The accelerated industrial development of aircraft, missiles, and modern electronics coupled with a need for a drastic reduction in weight and size magnified the problem. As products became more complex the problem of building a reliable product was intensified. An appreciation for the increase in complexity can be gained from considering that in a period of fifteen years the requirements for electronic tubes on a U.S. Navy destroyer changed from sixty to thirty-six hundred (14). During World War II new equipment was developed that had to be operational for extended period of time if the military mission was to be accomplished. The addition of a time requirement added to the already difficult problem caused by the increasing complexity of equipment. It soon became obvious that new techniques had to be developed that would assist the manufacturer in designing a reliable product.

關於描述兩個觀察地A和B相似的程度而言，生物品種是否相同是其中的一個切入點，因此品種重複（species overlap）便為描述兩觀察地相似度的一種指標。就一般的生物或生態研究而言，較常使用的品種重複指數為以品種數為計算基礎的 Jaccard index，公式為 ，其中 和 分別為觀察地A和B的總品種數，而 則為兩地的共同品種數，這樣的計算方式為Gower(1985) 歸類描述兩單位（unit）的相似度（similarity）中的一種。在我們的研究中，將令依觀察到的品種數及品種重複數所計算出的 Jaccard index 視為估計值，記為 ；若描述相似度時僅以品種為計算單位，而忽略個別品種的數量未免有資訊流失的情形，因此我們延伸 Jaccard index 指數而另立以個別品種數為計算單位的 N 指數，並以無母數最大概似估計法（Nonparametric Maximum Likelihood Estimator, NPMLE）估計 N 指數，記為 。另外，Smith, Solow 和 Preston (1996) 也提出利用 delta-beta-binomial 模型修正 Jaccard index 的低估（underestimate）情形，我們將此模型所推估的品種重複記為 ，因此我們的研究重點便在於以模擬實驗比較 、 和 在估計真正參數時的行為。 在模擬實驗中，根據蒙地卡羅（Monte-Carlo）模擬法則，我們設計6種品種發生機率相等的平衡母體，及12種品種發生機率服從幾何分配的不平衡母體，以500次抽樣所得的平均數及標準差決定估計的好壞。根據研究結果，若在已知母體為平衡母體的情形之下， 和 有不錯的估計；而 則是不管在平衡母體或不平衡母體皆有不錯的估計，但 和 在某些不平衡母體時，卻有極偏差的估計。 除了模擬實驗之外，我們並推導出 的期望值和變異數，並證明其為 N 指數的大樣本不偏估計值（asymptotic unbiased estimator），並以台灣西北部濕地的鳥類記錄為實例，計算出三個估計值，並以跋靴法（Bootstrapping）計算出三個估計量的標準差估計值，發現NPMLE 有最小的變異程度。 / In describing the similarity between communities A and B, species overlap is one kind of measure. In ecology and biology, the Jaccard index (Gower, 1985) ,denoted , for species overlap is widely used and is useded as an estimation in our research. However, the Jaccard index is simply the proportion of overlapping species, that is those species appearing in more than one community, to unique species, that is those species appearing in only one community. However, this index ignores species proportion information, assigning equal weight to all species. We propose a new index, N, which includes proportion information and is estimated by a Nonparametric Maximum Likelihood Estimator (NPMLE), denoted . Smith et al. (1996) proposed a delta-beta-binomial model to improve underestimation of the Jaccard index, we denoted this estimator . In our Monte-Carlo simulations, we design 6 balanced populations in which every species has an equal proportion and 12 unbalanced populations in which species proportions follow a geometric distribution. We found that and are accurate for balanced populations but overestimate or underestimate the true value for some unbalanced populations. However, is robust for both balanced and unbalanced populations. In addition to simulation results, we also give theoretical results, which prove some asymptotic properties of NPMLE .For example, species abundance of wild birds communications occurred at two locations in north-western Taiwan.Via bootstrapping, has smaller standard error than and .

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.

"none"

Developing sound or reliable statistical models for analyzing vehicle crashes is very important in highway safety studies. A difficulty arises when crash data exhibit overdispersion. Over-dispersion caused by unobserved heterogeneity is a serious problem and has been addressed in a variety ways within the negative binomial (NB) modeling framework. However, the true factors that affect heterogeneity are often unknown to researchers, and failure to accommodate such heterogeneity in the model can undermine the validity of the empirical results. Given the limitations of the NB regression model for addressing over-dispersion of crash data due to heterogeneity, this research examined an alternative model formulation that could be used for capturing heterogeneity through the use of finite mixture regression models. A Finite mixture of Poisson or NB regression models is especially useful when the count data were generated from a heterogeneous population. To evaluate these models, Poisson and NB mixture models were estimated using both simulated and empirical crash datasets, and the results were compared to those from a single NB regression model. For model parameter estimation, a Bayesian approach was adopted, since it provides much richer inference than the maximum likelihood approach. Using simulated datasets, it was shown that the single NB model is biased if the underlying cause of heterogeneity is due to the existence of multiple counting processes. The implications could be poor prediction performance and poor interpretation. Using two empirical datasets, the results demonstrated that a two-component finite mixture of NB regression models (FMNB-2) was quite enough to characterize the uncertainty about the crash occurrence, and it provided more opportunities for interpretation of the dataset which are not available from the standard NB model. Based on the models from the empirical dataset (i.e., FMNB-2 and NB models), their relative performances were also examined in terms of hotspot identification and accident modification factors. Finally, using a simulation study, bias properties of the posterior summary statistics for dispersion parameters in FMNB-2 model were characterized, and the guidelines on the choice of priors and the summary statistics to use were presented for different sample sizes and sample-mean values.