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In many applications, it is common to have multiple diagnostic tests on each subject. When there are multiple tests available, combining tests to incorporate information from various aspects in subjects may be necessary in order to obtain a better diagnostic. For continuous tests, in the presence of a gold standard, we could combine the tests linearly (Su and Liu, 1993) or sequentially (Thompson, 2003), or using the risk score as studied by McIntosh and Pepe (2002). The gold standard, however, is not always available in practice. This dissertation concentrates on deriving classification methods based on multiple tests in the absence of a gold standard. Motivated by a lab data set consisting of two tests testing for an antibody in 100 blood samples, we first develop a mixture model of four bivariate normal distributions with the mixture probabilities depending on a two-stage latent structure. The proposed two-stage latent structure is based on the biological mechanism of the tests. A Bayesian classification method incorporating the available prior information is derived utilizing Bayesian decision theory. The proposed method is illustrated by the motivating example, and the properties of the estimation and the classification are described via simulation studies. Sensitivity to the choice of the prior distribution is also studied. We also investigate a general problem of combining multiple continuous tests without any gold standard or a reference test. We thoroughly study the existing methods for combining multiple tests and develop optimal classification rules corresponding to the methods accommodating the situation without a gold standard. We justify the proposed methods both theoretically and numerically through exten- sive simulation studies and illustrate the methods with the motivating example. In the end, we conclude the thesis with remarks and some interesting open questions extended from the dissertation.

A segmentação de imagens consiste em urna tarefa de fundamental importância para diferentes aplicações em visão computacional, tais como por exemplo, o reconhecimento e o rastreamento de objetos, a segmentação de tomores/lesões em aplicações médicas, podendo também servir de auxílio em sistemas de reconhecimento facial. Embora exista uma extensa literatora abordando o problema de segmentação de imagens, tal tópico ainda continua em aberto para pesquisa. Particularmente, a tarefa de segmentar imagens coloridas é desafiadora devido as diversas inomogeneidades de cor, texturas e formas presentes nas feições descritivas das imagens. Este trabalho apresenta um novo método de clustering para abordar o problema da segmentação de imagens coloridas. Nós desenvolvemos uma abordagem Bayesiana para procura de máximos de densidade em urna distribuição discreta de dados, e representamos os dados de forma hierárquica originando clusters adaptativos a cada nível da hierarquia. Nós aplicamos o método de clustering proposto no problema de segmentação de imagens coloridas, aproveitando sua estrutura hierárquica, baseada em propriedades de árvores direcionadas, para representar hierarquicamente uma imagem colorida. Os experimentos realizados revelaram que o método de clustering proposto, aplicado ao problema de segmentação de imagens coloridas, obteve para a medida de performance Probabilistic Rand lndex (PRI) o valor de 0.8148 e para a medida Global Consistency Error (GCE) o valor 0.1701, superando um total de vinte e um métodos previamente propostos na literatura para o banco de dados BSD300. Comparações visuais confirmaram a competitividade da nossa abordagem em relação aos demais métodos testados. Estes resultados enfatizam a potencialidade do nosso método de clustering para abordar outras aplicações no domínio de Visão Computacional e Reconhecimento de Padrões. / Image segmentation is an essential task for several computer vision applications, such as object recognition, tracking and image retrieval. Although extensively studied in the literature, the problem of image segmentation remains an open topic of research. Particularly, the task of segmenting color images is challenging due to the inhomogeneities in the color regions encountered in natural scenes, often caused by the shapes of surfaces and their interactions with the illumination sources (e.g. causing shading and highlights) This work presents a novel non-supervised classification method. We develop a Bayesian framework for seeking modes on the underlying discrete distribution of data and we represent data hierarchically originating adaptive clusters at each levei of hierarchy. We apply the prnposal clustering technique for tackling the problem of color irnage segmentation, taking advantage of its hierarchical structure based on hierarchy properties of directed trees for representing fine to coarse leveis of details in an image. The experiments herein conducted revealed that the proposed clustering method applied to the color image segmentation problem, achieved for the Probabilistic Rand Index (PRI) performance measure the value of 0.8148 and for the Global Consistency Error (GCE) the value of 0.1701, outperforming twenty-three methods previously proposed in the literature for the BSD300 dataset. Visual comparison confirmed the competitiveness of our approach towards state-of-art methods publicly available in the literature. These results emphasize the great potential of our proposed clustering technique for tackling other applications in computer vision and pattem recognition.

A segmentação de imagens consiste em urna tarefa de fundamental importância para diferentes aplicações em visão computacional, tais como por exemplo, o reconhecimento e o rastreamento de objetos, a segmentação de tomores/lesões em aplicações médicas, podendo também servir de auxílio em sistemas de reconhecimento facial. Embora exista uma extensa literatora abordando o problema de segmentação de imagens, tal tópico ainda continua em aberto para pesquisa. Particularmente, a tarefa de segmentar imagens coloridas é desafiadora devido as diversas inomogeneidades de cor, texturas e formas presentes nas feições descritivas das imagens. Este trabalho apresenta um novo método de clustering para abordar o problema da segmentação de imagens coloridas. Nós desenvolvemos uma abordagem Bayesiana para procura de máximos de densidade em urna distribuição discreta de dados, e representamos os dados de forma hierárquica originando clusters adaptativos a cada nível da hierarquia. Nós aplicamos o método de clustering proposto no problema de segmentação de imagens coloridas, aproveitando sua estrutura hierárquica, baseada em propriedades de árvores direcionadas, para representar hierarquicamente uma imagem colorida. Os experimentos realizados revelaram que o método de clustering proposto, aplicado ao problema de segmentação de imagens coloridas, obteve para a medida de performance Probabilistic Rand lndex (PRI) o valor de 0.8148 e para a medida Global Consistency Error (GCE) o valor 0.1701, superando um total de vinte e um métodos previamente propostos na literatura para o banco de dados BSD300. Comparações visuais confirmaram a competitividade da nossa abordagem em relação aos demais métodos testados. Estes resultados enfatizam a potencialidade do nosso método de clustering para abordar outras aplicações no domínio de Visão Computacional e Reconhecimento de Padrões. / Image segmentation is an essential task for several computer vision applications, such as object recognition, tracking and image retrieval. Although extensively studied in the literature, the problem of image segmentation remains an open topic of research. Particularly, the task of segmenting color images is challenging due to the inhomogeneities in the color regions encountered in natural scenes, often caused by the shapes of surfaces and their interactions with the illumination sources (e.g. causing shading and highlights) This work presents a novel non-supervised classification method. We develop a Bayesian framework for seeking modes on the underlying discrete distribution of data and we represent data hierarchically originating adaptive clusters at each levei of hierarchy. We apply the prnposal clustering technique for tackling the problem of color irnage segmentation, taking advantage of its hierarchical structure based on hierarchy properties of directed trees for representing fine to coarse leveis of details in an image. The experiments herein conducted revealed that the proposed clustering method applied to the color image segmentation problem, achieved for the Probabilistic Rand Index (PRI) performance measure the value of 0.8148 and for the Global Consistency Error (GCE) the value of 0.1701, outperforming twenty-three methods previously proposed in the literature for the BSD300 dataset. Visual comparison confirmed the competitiveness of our approach towards state-of-art methods publicly available in the literature. These results emphasize the great potential of our proposed clustering technique for tackling other applications in computer vision and pattem recognition.

A segmentação de imagens consiste em urna tarefa de fundamental importância para diferentes aplicações em visão computacional, tais como por exemplo, o reconhecimento e o rastreamento de objetos, a segmentação de tomores/lesões em aplicações médicas, podendo também servir de auxílio em sistemas de reconhecimento facial. Embora exista uma extensa literatora abordando o problema de segmentação de imagens, tal tópico ainda continua em aberto para pesquisa. Particularmente, a tarefa de segmentar imagens coloridas é desafiadora devido as diversas inomogeneidades de cor, texturas e formas presentes nas feições descritivas das imagens. Este trabalho apresenta um novo método de clustering para abordar o problema da segmentação de imagens coloridas. Nós desenvolvemos uma abordagem Bayesiana para procura de máximos de densidade em urna distribuição discreta de dados, e representamos os dados de forma hierárquica originando clusters adaptativos a cada nível da hierarquia. Nós aplicamos o método de clustering proposto no problema de segmentação de imagens coloridas, aproveitando sua estrutura hierárquica, baseada em propriedades de árvores direcionadas, para representar hierarquicamente uma imagem colorida. Os experimentos realizados revelaram que o método de clustering proposto, aplicado ao problema de segmentação de imagens coloridas, obteve para a medida de performance Probabilistic Rand lndex (PRI) o valor de 0.8148 e para a medida Global Consistency Error (GCE) o valor 0.1701, superando um total de vinte e um métodos previamente propostos na literatura para o banco de dados BSD300. Comparações visuais confirmaram a competitividade da nossa abordagem em relação aos demais métodos testados. Estes resultados enfatizam a potencialidade do nosso método de clustering para abordar outras aplicações no domínio de Visão Computacional e Reconhecimento de Padrões. / Image segmentation is an essential task for several computer vision applications, such as object recognition, tracking and image retrieval. Although extensively studied in the literature, the problem of image segmentation remains an open topic of research. Particularly, the task of segmenting color images is challenging due to the inhomogeneities in the color regions encountered in natural scenes, often caused by the shapes of surfaces and their interactions with the illumination sources (e.g. causing shading and highlights) This work presents a novel non-supervised classification method. We develop a Bayesian framework for seeking modes on the underlying discrete distribution of data and we represent data hierarchically originating adaptive clusters at each levei of hierarchy. We apply the prnposal clustering technique for tackling the problem of color irnage segmentation, taking advantage of its hierarchical structure based on hierarchy properties of directed trees for representing fine to coarse leveis of details in an image. The experiments herein conducted revealed that the proposed clustering method applied to the color image segmentation problem, achieved for the Probabilistic Rand Index (PRI) performance measure the value of 0.8148 and for the Global Consistency Error (GCE) the value of 0.1701, outperforming twenty-three methods previously proposed in the literature for the BSD300 dataset. Visual comparison confirmed the competitiveness of our approach towards state-of-art methods publicly available in the literature. These results emphasize the great potential of our proposed clustering technique for tackling other applications in computer vision and pattem recognition.

Decision support systems have emerged over five decades ago to serve decision makers in uncertain conditions and usually rapidly changing and unstructured problems. Most decision support approaches, such as Bayesian decision theory and computing with words, compare and analyze the consequences of different decision alternatives. Bayesian decision methods use probabilities to handle uncertainty and have been widely used in different areas for estimating, predicting, and offering decision supports. On the other hand, computing with words (CW) and approximate reasoning apply fuzzy set theory to deal with imprecise measurements and inexact information and are most concerned with propositions stated in natural language. The concept of a Z-number [69] has been recently introduced to represent propositions and their reliability in natural language. This work proposes a methodology that integrates Z-numbers and Bayesian decision theory to provide decision support when precise measurements and exact values of parameters and probabilities are not available. The relationships and computing methods required for such integration are derived and mathematically proved. The proposed hybrid methodology benefits from both approaches and combines them to model the expert knowledge and its certainty (reliability) in natural language and apply such model to provide decision support. To the best of our knowledge, so far there has been no other decision support methodology capable of using the reliability of propositions in natural language. In order to demonstrate the proof of concept, the proposed methodology has been applied to a realistic case study on breast cancer diagnosis and a daily life example of choosing means of transportation.

This thesis considers two related problems that has application in the field of experimental design for clinical trials: • fixed sample size determination for parallel arm, double-blind survival data analysis to test the hypothesis of no difference in survival functions, and • blinded sample size re-estimation for the same. For the first problem of fixed sample size determination, a method is developed generally for testing of hypothesis, then applied particularly to survival analysis; for the second problem of blinded sample size re-estimation, a method is developed specifically for survival analysis. In both problems, the exponential survival model is assumed. The approach we propose for sample size determination is Bayesian decision theoretical, using explicitly a loss function and a prior distribution. The loss function used is the intrinsic discrepancy loss function introduced by Bernardo and Rueda (2002), and further expounded upon in Bernardo (2011). We use a conjugate prior, and investigate the sensitivity of the calculated sample sizes to specification of the hyper-parameters. For the second problem of blinded sample size re-estimation, we use prior predictive distributions to facilitate calculation of the interim test statistic in a blinded manner while controlling the Type I error. The determination of the test statistic in a blinded manner continues to be nettling problem for researchers. The first problem is typical of traditional experimental designs, while the second problem extends into the realm of adaptive designs. To the best of our knowledge, the approaches we suggest for both problems have never been done hitherto, and extend the current research on both topics. The advantages of our approach, as far as we see it, are unity and coherence of statistical procedures, systematic and methodical incorporation of prior knowledge, and ease of calculation and interpretation. / Statistics

A 2009 report published by the National Research Council addressed the need for improvements in the field of forensic science. In the report emphasis was placed on the need for more rigorous scientific analysis within many forensic science disciplines and for established limitations and determination of error rates from statistical analysis. This research focused on multivariate statistical techniques for the analysis of spectral data obtained for multiple forensic applications which include samples from: automobile float glasses and paints, bones, metal transfers, ignitable liquids and fire debris, and organic compounds including explosives. The statistical techniques were used for two types of data analysis: classification and discrimination. Statistical methods including linear discriminant analysis and a novel soft classification method were used to provide classification of forensic samples based on a compiled library. The novel soft classification method combined three statistical steps: Principal Component Analysis (PCA), Target Factor Analysis (TFA), and Bayesian Decision Theory (BDT) to provide classification based on posterior probabilities of class membership. The posterior probabilities provide a statistical probability of classification which can aid a forensic analyst in reaching a conclusion. The second analytical approach applied nonparametric methods to provide the means for discrimination between samples. Nonparametric methods are performed as hypothesis test and do not assume normal distribution of the analytical figures of merit. The nonparametric iv permutation test was applied to forensic applications to determine the similarity between two samples and provide discrimination rates. Both the classification method and discrimination method were applied to data acquired from multiple instrumental methods. The instrumental methods included: Laser Induced-Breakdown Spectroscopy (LIBS), Fourier Transform Infrared Spectroscopy (FTIR), Raman spectroscopy, and Gas Chromatography-Mass Spectrometry (GC-MS). Some of these instrumental methods are currently applied to forensic applications, such as GC-MS for the analysis of ignitable liquid and fire debris samples; while others provide new instrumental methods to areas within forensic science which currently lack instrumental analysis techniques, such as LIBS for the analysis of metal transfers. The combination of the instrumental techniques and multivariate statistical techniques is investigated in new approaches to forensic applications in this research to assist in improving the field of forensic science.

From the Proceedings of the 1975 Meetings of the Arizona Section - American Water Resources Assn. and the Hydrology Section - Arizona Academy of Science - April 11-12, 1975, Tempe, Arizona / Bayesian decision theory is a method for comparing expected utilities of alternative actions given various possible states of nature. The method treats uncertainty as to the true state of nature by determining the expected utility of each action in terms of the probabilities of the various possible states. The decision rule is to choose the action having the best expected utility. This paper illustrates an application of Bayesian decision theory in a well field design problem where a decision had to be made regarding capacity-density combination for wells located in an extensive uniform grid. The uncertainty lay in anticipating the frequencies of transmissivity values among the wells.

The reported research provides a rough guide to the best practice of decision modeling concerning urban pipeline systems’ rehabilitation. The thesis aims to bring attention to the fact that a proper decision-making model is a cornerstone for efficient infrastructure management. More precisely, this thesis aims to increase the knowledge about applicable decision support methods by identifying relevant factors that should be considered in the decision-making process. This can, facilitate future rehabilitation attempts of existing urban infrastructure. A utility-based decision model was adopted for a water distribution network in Sweden to locate and rehabilitate leakages as an ultimate sign of failure. This was performed by implementing and evaluating a Bayesian decision model including the treatment of uncertainties in evaluating the best decision from a short-term perspective. Despite its simplicity, the result showed that the proposed model could facilitate problem-solving approaches when uncertainty is an issue. Considering the several interacting factors of services and the availability of information, the importance of problem structuring before applying a decision model was extensively acknowledged. As a result, a conceptual decision model was proposed to choose the most appropriate decision model applicable for a particular problem in the essence of deciding how to decide. The presented model illustrated the first steps of developing a theoretical framework for a rational yet practical decisionmaking. This approach, which is aimed to be further employed in rehabilitation strategies of urban pipelines, ensures that the chosen decision technique has explicitly considered different levels of uncertainty and would be the best-established solution for a particular type of problem, organization, and stakeholder. This effort may help the decision analysts define the problem and elicit objectives and values relatively early in the decision-making to ensure that decisions to be selected would support the desired outcomes, actions, and core values. Then, a critical evaluation of the decision strategy was presented by comparing the performed Bayesian approach with the proposed conceptual model. Then so, it was shown that the choice of the decision model is dissimilar if the presented specific basic components vary. This was performed by presenting two semi-fictitious case studies, exemplifying the framework’s importance in structuring the assessment of available means. / Forskningen som redovisas i denna uppsats utgör en översiktlig guide till en praktisktillämpning av beslutsmodellering gällande underhåll av urbana ledningssystem.Syftet med licentiatuppsatsen är att betona att en korrekt modell för beslutsfat-tande är nödvändig för en effektiv förvaltning av infrastruktur. Mer specifikt ärmålet att öka kunskapen om tillämpbara beslutsstödsmetoder genom att identifiera relevanta faktorer som bör beaktas i beslutsprocessen. Det förväntas underlätta framtida underhållsaktiveter för befintlig urban infrastruktur. En nyttobaserad beslutsmodell för åtgärdsplanering har applicerats på en del av ettsvenskt vattenledningssystem, där läckage är den kritiska händelse som hanteras.Modellen baserad på Bayesiansk beslutsteori har implementerats och utvärderatsmed avseende på hantering av osäkerheter och beslutsoptimering ur ett korttidsper-spektiv. Trots modellens enkelhet visar resultatet att den kan underlätta metodvalför problemlösning när det råder osäkerheter i förutsättningarna. Vikten av en tydlig och strukturerad problembeskrivning inför tillämpningen av enbeslutsmodell bekräftas, där beaktande av interaktioner mellan ibland flera faktoreri systemets funktion och den tillgängliga informationen är viktig. Som ett resultatföreslås en konceptuell metod för att välja den mest lämpliga beslutsmodellen förett specifikt problem med syftet att besluta hur man bör besluta. Den presenter-ade metoden utgör ett första steg i utvecklingen av ett teoretiskt ramverk för ettrationellt och samtidigt praktiskt beslutsfattande. Arbetet hjälper beslutsfattarenatt strukturera problemet och lyfta syftet och värden tidigt i beslutsfattandet föratt säkerställa att tagna beslut stödjer eftersökta utfall, åtgärder och kärnvärden. Vidare har en kritisk utvärdering av beslutsstrategier presenterats som en jämförelsemellan den Bayesianska beslutsmodellen och den konceptuella metoden. Den visaratt valet av beslutsmodell skiljer sig om de grundläggande förutsättningarna ärolika. Utvärderingen baseras på två semifiktiva fallstudier som visar på vikten avstrukturering i bedömningen av tillgänglig information och tillgängliga resurser. / <p>2022-10-24</p> / Mistra InfraMaint