Sunken oil is difficult to locate because remote sensing techniques cannot as yet provide views of sunken oil over large areas. Moreover, the oil may re-suspend and sink with changes in salinity, sediment load, and temperature, making deterministic fate models difficult to deploy and calibrate when even the presence of sunken oil is difficult to assess. For these reasons, together with the expense of field data collection, there is a need for a statistical technique integrating limited data collection with stochastic transport modeling. Predictive Bayesian modeling techniques have been developed and demonstrated for exploiting limited information for decision support in many other applications. These techniques brought to a multi-modal Lagrangian modeling framework, representing a near-real time approach to locating and tracking sunken oil driven by intrinsic physical properties of field data collected following a spill after oil has begun collecting on a relatively flat bay bottom. Methods include (1) development of the conceptual predictive Bayesian model and multi-modal Gaussian computational approach based on theory and literature review; (2) development of an object-oriented programming and combinatorial structure capable of managing data, integration and computation over an uncertain and highly dimensional parameter space; (3) creating a new bi-dimensional approach of the method of images to account for curved shoreline boundaries; (4) confirmation of model capability for locating sunken oil patches using available (partial) real field data and capability for temporal projections near curved boundaries using simulated field data; and (5) development of a stand-alone open-source computer application with graphical user interface capable of calibrating instantaneous oil spill scenarios, obtaining sets maps of relative probability profiles at different prediction times and user-selected geographic areas and resolution, and capable of performing post-processing tasks proper of a basic GIS-like software. The result is a predictive Bayesian multi-modal Gaussian model, SOSim (Sunken Oil Simulator) Version 1.0rc1, operational for use with limited, randomly-sampled, available subjective and numeric data on sunken oil concentrations and locations in relatively flat-bottomed bays. The SOSim model represents a new approach, coupling a Lagrangian modeling technique with predictive Bayesian capability for computing unconditional probabilities of mass as a function of space and time. The approach addresses the current need to rapidly deploy modeling capability without readily accessible information on ocean bottom currents. Contributions include (1) the development of the apparently first pollutant transport model for computing unconditional relative probabilities of pollutant location as a function of time based on limited available field data alone; (2) development of a numerical method of computing concentration profiles subject to curved, continuous or discontinuous boundary conditions; (3) development combinatorial algorithms to compute unconditional multimodal Gaussian probabilities not amenable to analytical or Markov-Chain Monte Carlo integration due to high dimensionality; and (4) the development of software modules, including a core module containing the developed Bayesian functions, a wrapping graphical user interface, a processing and operating interface, and the necessary programming components that lead to an open-source, stand-alone, executable computer application (SOSim - Sunken Oil Simulator). Extensions and refinements are recommended, including the addition of capability for accepting available information on bathymetry and maybe bottom currents as Bayesian prior information, the creation of capability of modeling continuous oil releases, and the extension to tracking of suspended oil (3-D).

In the field of cognitive science, as well as the area of Artificial Intelligence (AI), the role of context has been investigated in many forms, and for many purposes. It is clear in both areas that consideration of contextual information is important. However, the significance of context has not been emphasized in the Bayesian networks literature. We suggest that consideration of context is necessary for acquiring knowledge about a situation and for refining current representational models that are potentially erroneous due to hidden independencies in the data.<p>In this thesis, we make several contributions towards the automation of contextual consideration by discovering useful contexts from probability distributions. We show how context-specific independencies in Bayesian networks and discovery algorithms, traditionally used for efficient probabilistic inference can contribute to the identification of contexts, and in turn can provide insight on otherwise puzzling situations. Also, consideration of context can help clarify otherwise counter intuitive puzzles, such as those that result in instances of Simpson's paradox. In the social sciences, the branch of attribution theory is context-sensitive. We suggest a method to distinguish between <i>dispositional causes</i> and <i>situational factors</i> by means of contextual models. Finally, we address the work of Cheng and Novick dealing with causal attribution by human adults. Their <i>probabilistic contrast model</i> makes use of contextual information, called focal sets, that must be determined by a human expert. We suggest a method for discovering complete <i>focal sets</i> from probabilistic distributions, without the human expert.

In the field of cognitive science, as well as the area of Artificial Intelligence (AI), the role of context has been investigated in many forms, and for many purposes. It is clear in both areas that consideration of contextual information is important. However, the significance of context has not been emphasized in the Bayesian networks literature. We suggest that consideration of context is necessary for acquiring knowledge about a situation and for refining current representational models that are potentially erroneous due to hidden independencies in the data.<p>In this thesis, we make several contributions towards the automation of contextual consideration by discovering useful contexts from probability distributions. We show how context-specific independencies in Bayesian networks and discovery algorithms, traditionally used for efficient probabilistic inference can contribute to the identification of contexts, and in turn can provide insight on otherwise puzzling situations. Also, consideration of context can help clarify otherwise counter intuitive puzzles, such as those that result in instances of Simpson's paradox. In the social sciences, the branch of attribution theory is context-sensitive. We suggest a method to distinguish between <i>dispositional causes</i> and <i>situational factors</i> by means of contextual models. Finally, we address the work of Cheng and Novick dealing with causal attribution by human adults. Their <i>probabilistic contrast model</i> makes use of contextual information, called focal sets, that must be determined by a human expert. We suggest a method for discovering complete <i>focal sets</i> from probabilistic distributions, without the human expert.

In this study, the semi-empirical approach is introduced to accurately estimate the probability distribution of complex non-linear random variables in the field of wavestructure interaction. The structural form of the semi-empirical distribution is developed based on a mathematical representation of the process and the model parameters are estimated directly from utilization of the sample data. Here, three probability distributions are developed based on the quadratic transformation of the linear random variable. Assuming that the linear process follows a standard Gaussian distribution, the three-parameter Gaussian-Stokes model is derived for the second-order variables. Similarly, the three-parameter Rayleigh-Stokes model and the four-parameter Weibull- Stokes model are derived for the crests, troughs, and heights of non-linear process assuming that the linear variable has a Rayleigh distribution or a Weibull distribution. The model parameters are empirically estimated with the application of the conventional method of moments and the newer method of L-moments. Furthermore, the application of semi-empirical models in extreme analysis and estimation of extreme statistics is discussed. As a main part of this research study, the sensitivity of the model statistics to the variability of the model parameters as well as the variability in the samples is evaluated. In addition, the sample size effects on the performance of parameter estimation methods are studied. Utilizing illustrative examples, the application of semi-empirical probability distributions in the estimation of probability distribution of non-linear random variables is studied. The examples focused on the probability distribution of: wave elevations and wave crests of ocean waves and waves in the area close to an offshore structure, wave run-up over the vertical columns of an offshore structure, and ocean wave power resources. In each example, the performance of the semi-empirical model is compared with appropriate theoretical and empirical distribution models. It is observed that the semi-empirical models are successful in capturing the probability distribution of complex non-linear variables. The semi-empirical models are more flexible than the theoretical models in capturing the probability distribution of data and the models are generally more robust than the commonly used empirical models.

Reliability worth analysis is an important tool for distribution systems planning and operations. The interruption cost model used in the analysis directly affects the accuracy of the reliability worth evaluation. In this dissertation, the reliability worth analysis was dealt with two interruption cost models including an average or aggregated model (AAM), and a probabilistic distribution model (PDM) in two phases. In the first phase, the dissertation presents a reliability cost model based AAM for distribution system planning. The reliability cost model has been derived as a linear function of line flows for evaluating the outages. The objective is to minimize the total cost including the outage cost, feeder resistive loss, and fixed investment cost. The Evolutionary Programming (EP) was used to solve the very complicated mixed-integer, highly non-linear, and non-differential problem. A real distribution network was modeled as the sample system for tests. There is also a higher opportunity to obtain the global optimum during the EP process. In the second phase, the interruption cost model PDM was proposed by using the radial basis function (RBF) neural network with orthogonal least-squares (OLS) learning method. The residential and industrial interruption costs in PDM were integrated by the proposed neural network technique. A Monte-Carlo time sequential simulation technique was adopted for worth assessment. The technique is tested by evaluating the reliability worth of a Taipower system for the installation of disconnected switches, lateral fuses, transformers and alternative supplies. The results show that the two cost models result in very different interruption costs, and PDM may be more realistic in modeling the system.

Growth rate of prostate cancer tumor is an important aspect of understanding the natural history of prostate cancer. Using real prostate cancer data from the SEER database with tumor size as a response variable, we have clustered the cancerous tumor sizes into age groups to enhance its analytical behavior. The rate of change of the response variable as a function of age is given for each cluster. Residual analysis attests to the quality of the analytical model and the subject estimates. In addition, we have identified the probability distribution that characterize the behavior of the response variable and proceeded with basic parametric analysis. There are several remarkable treatment options available for prostate cancer patients. In this present study, we have considered the three commonly used treatment for prostate cancer: radiation therapy, surgery, and combination of surgery and radiation therapy. The study uses data from the SEER database to evaluate and rank the effectiveness of these treatment options using survival analysis in conjunction with basic parametric analysis. The evaluation is based on the stage of the prostate cancer classification. Improvement in prostate cancer disease can be measured by improvement in its mortality. Also, mortality projection is crucial for policy makers and the financial stability of insurance business. Our research applies a parametric model proposed by Renshaw et al. (1996) to project the force of mortality for prostate cancer. The proposed modeling structure can pick up both age and year effects.

As the cost of designing and building new highway pavements increases and the number of new construction and major rehabilitation projects decreases, the importance of ensuring that a given pavement design performs as expected in the field becomes vital. To address this issue in other fields of civil engineering, reliability analysis has been used extensively. However, in the case of pavement structural design, the reliability component is usually neglected or overly simplified. To address this need, the current dissertation proposes a framework for estimating the reliability of a given pavement structure regardless of the pavement design or analysis procedure that is being used. As part of the dissertation, the framework is applied with the Mechanistic-Empirical Pavement Design Guide (MEPDG) and failure is considered as a function of rutting of the hot-mix asphalt (HMA) layer. The proposed methodology consists of fitting a response surface, in place of the time-demanding implicit limit state functions used within the MEPDG, in combination with an analytical approach to estimating reliability using second moment techniques: First-Order and Second-Order Reliability Methods (FORM and SORM) and simulation techniques: Monte Carlo and Latin Hypercube Simulation. In order to demonstrate the methodology, a three-layered pavement structure is selected consisting of a hot-mix asphalt (HMA) surface, a base layer, and subgrade. Several pavement design variables are treated as random; these include HMA and base layer thicknesses, base and subgrade modulus, and HMA layer binder and air void content. Information on the variability and correlation between these variables are obtained from the Long-Term Pavement Performance (LTPP) program, and likely distributions, coefficients of variation, and correlation between the variables are estimated. Additionally, several scenarios are defined to account for climatic differences (cool, warm, and hot climatic regions), truck traffic distributions (mostly consisting of single unit trucks versus mostly consisting of single trailer trucks), and the thickness of the HMA layer (thick versus thin). First and second order polynomial HMA rutting failure response surfaces with interaction terms are fit by running the MEPDG under a full factorial experimental design consisting of 3 levels of the aforementioned design variables. These response surfaces are then used to analyze the reliability of the given pavement structures under the different scenarios. Additionally, in order to check for the accuracy of the proposed framework, direct simulation using the MEPDG was performed for the different scenarios. Very small differences were found between the estimates based on response surfaces and direct simulation using the MEPDG, confirming the accurateness of the proposed procedure. Finally, sensitivity analysis on the number of MEPDG runs required to fit the response surfaces was performed and it was identified that reducing the experimental design by one level still results in response surfaces that properly fit the MEPDG, ensuring the applicability of the method for practical applications. / text

Technological improvements along with falling prices on photovoltaic (PV) panels and electric vehicles (EVs) suggest that they might become more common in the future. The introduction of distributed PV power production and EV charging has a considerable impact on the power system, in particular at the end-user in the electricity grid. In this PhD thesis PV power production, household electricity use and EV charging are investigated on different system levels. The methodologies used in this thesis are interdisciplinary but the main contributions are mathematical modeling, simulations and data analysis of these three components and their interactions. Models for estimating PV power production, household electricity use, EV charging and their combination are developed using data and stochastic modeling with Markov chains and probability distributions. Additionally, data on PV power production and EV charging from eight solar charging stations is analyzed. Results show that the clear-sky index for PV power production applications can be modeled via a bimodal Normal probability distribution, that household electricity use can be modeled via either Weibull or Log-normal probability distributions and that EV charging can be modeled by Bernoulli probability distributions. Complete models of PV power production, household electricity use and EV home-charging are developed with both Markov chain and probability distribution modeling. It is also shown that EV home-charging can be modeled as an extension to the Widén Markov chain model for generating synthetic household electricity use patterns. Analysis of measurements from solar charging stations show a wide variety of EV charging patterns. Additionally an alternative approach to modeling the clear-sky index is introduced and shown to give a generalized Ångström equation relating solar irradiation to the duration of bright sunshine. Analysis of the total power consumption/production patterns of PV power production, household electricity use and EV home-charging at the end-user in the grid highlights the dependency between the components, which quantifies the mismatch issue of distributed intermittent power production and consumption. At an aggregate level of households the level of mismatch is shown to be lower.

O planejamento de curto prazo em minas a céu aberto exige a definição de poligonais, que representam os sucessivos avanços de lavra. As poligonais, tradicionalmente, são desenhadas em um processo laborioso na tentativa de delinear como minério em qualidade e quantidade de acordo com os limites determinados. O minério delimitado deve apresentar a menor variabilidade em qualidade possível, com o objetivo de maximizar a recuperação na usina de processamento. Essa dissertação visa desenvolver um fluxo do trabalho para definir poligonais de curto prazo de forma automática, além disso, sequenciar todos os blocos de minério de cada polígono de modo a definir uma sequência interconectada lavrável de poligonais. O fluxo do trabalho foi aplicada à incerteza de teores, obtida através de simulações estocásticas. Algoritmos genéticos foram desenvolvidos em linguagem de programação Python e implementados na forma de plug-in no software geoestatístico Ar2GeMS. Múltiplas iterações são criadas para cada avanço individual, gerando regiões (ou poligonais). Então, a região que apresenta menor variabilidade de teores é selecionada. A distribuição de probabilidade dos teores dos blocos em cada avanço é comparada com a distribuição global de teores, calculada a partir de todos os blocos do corpo de minério. Os resultados mostraram que os teores dos blocos abrangidos pelas poligonais criadas dessa forma apresentam teores similares à distribuição de referência, permitindo o sequenciamento de lavra com distribuição de teores mais próximo possível da distribuição global. Modelos equiprováveis permitem avaliar a incerteza associada à solução proposta. / Open-pit short-term planning requieres the definition of polygons identifying the successive mining advances. These polygons are drawn in a labour intensive task attempting to delineate ore with the quantity and quality within established ranges. The ore delineated by the polygons should have the least possible quality variability among them, helping in maximizing ore recovery at the processing plant. This thesis aims at developíng a workflow for drawing short-term polygons automatically, sequencing all ore blocks within each polygon and leading to a mineable and connected sequence of polygons. This workflow is also tested under grade uncertainty obtained through multiple syochastic simulated models. For this, genetics algorithms were developed in Python programming language and pluged in Ar2GeMS geostatistical software. Multiple iterations were generated for each of the individual advances, generating regions or polygons, and selecting the regions of lower grade variability. The blocks probability distribution within each advance were compared to the global distribution, including all blocks within the ore body. Results show that the polygons generated are comprised by block grades similar to the ones from the reference distribution, leading to mining sequence as close as possible to the global maintaining a quasi-satationarity. Equally probable models provide the means to access the uncertainy in the solution provided.

Este trabalho tem como objetivo estudar as origens dos estudos ligados à gestão do risco e suas aplicações no mercado de capitais, incluindo o mercado brasileiro. São destacadas importantes características estatísticas desses estudos, algumas premissas probabilísticas básicas e o questionamento do uso indiscriminado dos modelos matemáticos desenvolvidos para Finanças. Apresentamos alguns tipos de distribuições estatísticas que podem ser aplicadas ao mercado de capitais. Esta pesquisa apresenta, também, características de sistemas complexos, da Teoria da Utilidade de Bernoulli, da Teoria da Utilidade Esperada (TUE) de Von Neumann e Morgenstern (1944), da Hipótese de Mercados Eficientes (HME) organizado/sistematizado por Eugene Fama (1970), da Racionalidade Limitada, estudada por Simon (1959), das Finanças Comportamentais, tratada por Kahneman e Tverski (1979) e do uso de modelos, apresentado por Merton, (1994). É feito um estudo empírico, a título de ilustração, contemplando o mercado brasileiro, representado pelo índice BOVESPA (Ibovespa), comparado com resultados obtidos por Gabaix (2003), em estudo realizado no mercado americano, a fim de verificar a distribuição de probabilidade do retorno. Esta realização empírica é realizada no intento de reforçar a importância da reflexão acerca do uso indiscriminado dos modelos e das quebras de suas premissas. / The objective of this work is to study the origins of the research related to risk and its implications to capital markets, including the Brazilian market. Important statistical characteristics, several basic probabilistic premises and the questioning of indiscriminate use of mathematical models developed by accountants and analysts in finances had been highlighted. There had been shown some kinds of statistical distribution which can be applied to capital markets. This research also presents characteristics of complex systems, Utility Theory, studied by Von Neumann and Morgenstern (1944), Efficient Markets Hypothesis (EMH), organized/systematized by Eugene Fama (1970), Limited Rationality, studied by Simon (1959), Behavioral Finance, dealt by Kahneman and Tveski (1979) and model\'s use by Merton (1994). In order to illustrate the work, there had been made an empirical study, contemplating Brazilian market and comparing it to Garbaix\'s (2003) results, obtained by American market study. This was made in order to verify the market return probability distribution to reinforce the importance of reflection in indiscriminate usage of models and its premises crack.