Traditional clinical trials have been inefficient in their methods of dose finding and dose allocation. In this paper a four-parameter logistic equation is used to model the outcome of Bernoulli-response clinical trials. A Bayesian adaptive design is used to fit the logistic equation to the dose-response curve of Phase II and Phase III clinical trials. Because of inherent restrictions in the logistic model, symmetric candidate densities cannot be used, thereby creating asymmetric jumping rules inside the Markov chain Monte Carlo algorithm. An order restricted Metropolis-Hastings algorithm is implemented to account for these limitations. Modeling clinical trials in a Bayesian framework allows the experiment to be adaptive. In this adaptive design batches of subjects are assigned to doses based on the posterior probability of success for each dose, thereby increasing the probability of receiving advantageous doses. Good posterior fitting is demonstrated for typical dose-response curves and the Bayesian design is shown to properly stop drug trials for clinical futility or clinical success. In this paper we demonstrate that an adaptive Bayesian approach to dose-response studies increases both the statistical and medicinal effectiveness of clinical research.

Each year, billions of dollars are spent on missiles and munitions by the United States government. It is therefore vital to have a dependable method to estimate the reliability of these missiles. It is important to take into account the age of the missile, the reliability of different components of the missile, and the impact of different launch phases on missile reliability. Additionally, it is of importance to estimate the missile performance under a variety of test conditions, or modalities. Bayesian logistic regression is utilized to accurately make these estimates. This project presents both previously proposed methods and ways to combine these methods to accurately estimate the reliability of the Cruise Missile.

Автором рассматриваются различные подходы к изучению предпринимательства, классифицируются типы мотивов предпринимателя. Доказывается высокий уровень потенциала молодёжного предпринимательства в мегаполисе, предопределяемый как характерными чертами молодежи, так и особенностями социально-экономической среды мегаполиса. Эмпирическое исследование было проведено в мегаполисе Челябинск с использованием статистических данных, методов глубинного интервью и количественного опроса предпринимателей. На основе анализа статистических данных делается вывод о том, что с 2018 г. и по настоящее время наблюдается негативная тенденция – снижение количества субъектов малого и среднего бизнеса. Результаты глубинных интервью показали, что предпринимателям свойственны характерные черты, позволяющие работать в условиях данной тенденции (позитивное мышление, стремление решать сложные задачи, интерес к социо-политическому контексту). Результаты количественного опроса показали доминирование «материальной» мотивации: подавляющее большинство опрошенных предпринимателей стремится с помощью бизнеса улучшить уровень жизни. Однако даже при условии сохранения дохода предприниматели не готовы перейти на наёмную работу, поскольку важными мотивами предпринимательской деятельности являются реализация творческого потенциала и ощущение независимости. / The author examines various approaches to the study of entrepreneurship, classifies the types of entrepreneur's motives. The high level of potential of youth entrepreneurship in the metropolis is proved, which is predetermined by both the characteristic features of youth and the peculiarities of the socio-economic environment of the metropolis. An empirical study was conducted in Chelyabinsk using statistical data, in-depth interview methods and a quantitative survey of entrepreneurs. Based on the analysis of statistical data, it is concluded that from 2018 to the present, there has been a negative trend - a decrease in the number of small and medium-sized businesses. The results of in-depth interviews showed that entrepreneurs have characteristic features that allow them to work in this conditions (positive thinking, the desire to solve complex problems, interest in the socio-political context). The results of the quantitative survey showed the dominance of “material” motivation: the overwhelming majority of the interviewed entrepreneurs strive to improve their living standards with the help of business. However, even if income is preserved, entrepreneurs are not ready to switch to hired work, since the realization of creative potential and a sense of independence are important motives for entrepreneurial activity.

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This study is generally concerned with the assumption that the contemporary global flows of people, capital, and commodities, which accelerated dramatically in the age of globalization, have significant impacts on the land use patterns of global cities. With this assumption, the study further questions in the context of polycentric US metropolis, whether or not the distribution of transnational advanced producer service firms define a new form of centrality, in which the traditional central business districts and suburban centers differ from each other in terms of spatial clustering patterns and sectoral distributions of transnational advanced producer service firms. Spatial clustering patterns of advanced producer service firms are evaluated according to high-rise and high-density criteria. In ten selected cities, clusters of advanced producer service firms and high-rise office buildings are identified through the Nearest Neighbor Hierarchical Clustering Method in CrimeStat. To define the polycentric US metropolis, the research employs Lang et al's (2006) classification of metropolitan office space. The results show significant differences between former manufacturing belt cities and Sunbelt cities. / Ph. D.

The advent of various types of high-throughput genomic data has enabled researchers to investigate complex biological systems in a systemic way and started to shed light on the underlying molecular mechanisms in cancers. To analyze huge amounts of genomic data, effective statistical and machine learning tools are clearly needed; more importantly, integrative approaches are especially needed to combine different types of genomic data for a network or pathway view of biological systems. Motivated by such needs, we make efforts in this dissertation to develop integrative framework for pathway analysis. Specifically, we dissect the molecular pathway into two parts: protein-DNA interaction network and protein-protein interaction network. Several novel approaches are proposed to integrate gene expression data with various forms of biological knowledge, such as protein-DNA interaction and protein-protein interaction for reliable molecular network identification. The first part of this dissertation seeks to infer condition-specific transcriptional regulatory network by integrating gene expression data and protein-DNA binding information. Protein-DNA binding information provides initial relationships between transcription factors (TFs) and their target genes, and this information is essential to derive biologically meaningful integrative algorithms. Based on the availability of this information, we discuss the inference task based on two different situations: (a) if protein-DNA binding information of multiple TFs is available: based on the protein-DNA data of multiple TFs, which are derived from sequence analysis between DNA motifs and gene promoter regions, we can construct initial connection matrix and solve the network inference using a constraint least-squares approach named motif-guided network component analysis (mNCA). However, connection matrix usually contains a considerable amount of false positives and false negatives that make inference results questionable. To circumvent this problem, we propose a knowledge based stability analysis (kSA) approach to test the conditional relevance of individual TFs, by checking the discrepancy of multiple estimations of transcription factor activity with respect to different perturbations on the connections. The rationale behind stability analysis is that the consistency of observed gene expression and true network connection shall remain stable after small perturbations are applied to initial connection matrix. With condition-specific TFs prioritized by kSA, we further propose to use multivariate regression to highlight condition-specific target genes. Through simulation studies comparing with several competing methods, we show that the proposed schemes are more sensitive to detect relevant TFs and target genes for network inference purpose. Experimentally, we have applied stability analysis to yeast cell cycle experiment and further to a series of anti-estrogen breast cancer studies. In both experiments not only biologically relevant regulators are highlighted, the condition-specific transcriptional regulatory networks are also constructed, which could provide further insights into the corresponding cellular mechanisms. (b) if only single TF's protein-DNA information is available: this happens when protein-DNA binding relationship of individual TF is measured through experiments. Since original mNCA requires a complete connection matrix to perform estimation, an incomplete knowledge of single TF is not applicable for such approach. Moreover, binding information derived from experiments could still be inconsistent with gene expression levels. To overcome these limitations, we propose a linear extraction scheme called regulatory component analysis (RCA), which can infer underlying regulation relationships, even with partial biological knowledge. Numerical simulations show significant improvement of RCA over other traditional methods to identify target genes, not only in low signal-to-noise-ratio situations and but also when the given biological knowledge is incomplete and inconsistent to data. Furthermore, biological experiments on Escherichia coli regulatory network inferences are performed to fairly compare traditional methods, where the effectiveness and superior performance of RCA are confirmed. The second part of the dissertation moves from protein-DNA interaction network up to protein-protein interaction network, to identify dys-regulated protein sub-networks by integrating gene expression data and protein-protein interaction information. Specifically, we propose a statistically principled method, namely Metropolis random walk on graph (MRWOG), to highlight condition-specific PPI sub-networks in a probabilistic way. The method is based on the Markov chain Monte Carlo (MCMC) theory to generate a series of samples that will eventually converge to some desired equilibrium distribution, and each sample indicates the selection of one particular sub-network during the process of Metropolis random walk. The central idea of MRWOG is built upon that the essentiality of one gene to be included in a sub-network depends on not only its expression but also its topological importance. Contrasted to most existing methods constructing sub-networks in a deterministic way and therefore lacking relevance score for each protein, MRWOG is capable of assessing the importance of each individual protein node in a global way, not only reflecting its individual association with clinical outcome but also indicating its topological role (hub, bridge) to connect other important proteins. Moreover, each protein node is associated with a sampling frequency score, which enables the statistical justification of each individual node and flexible scaling of sub-network results. Based on MRWOG approach, we further propose two strategies: one is bootstrapping used for assessing statistical confidence of detected sub-networks; the other is graphic division to separate a large sub-network to several smaller sub-networks for facilitating interpretations. MRWOG is easy to use with only two parameters need to be adjusted, one is beta value for performing random walk and another is Quantile level for calculating truncated posteriori mean. Through extensive simulations, we show that the proposed scheme is not sensitive to these two parameters in a relatively wide range. We also compare MRWOG with deterministic approaches for identifying sub-network and prioritizing topologically important proteins, in both cases MRWG outperforms existing methods in terms of both precision and recall. By utilizing MRWOG generated node/edge sampling frequency, which is actually posteriori mean of corresponding protein node/interaction edge, we illustrate that condition-specific nodes/interactions can be better prioritized than the schemes based on scores of individual node/interaction. Experimentally, we have applied MRWOG to study yeast knockout experiment for galactose utilization pathways to reveal important components of corresponding biological functions; we also applied MRWSOG to study breast cancer patient prognostics problems, where the sub-network analysis could lead to an understanding of the molecular mechanisms of antiestrogen resistance in breast cancer. Finally, we conclude this dissertation with a summary of the original contributions, and the future work for deepening the theoretical justification of the proposed methods and broadening their potential biological applications such as cancer studies. / Ph. D.

Mathematical models of viral infections have been informing virology research for years. Estimating parameter values for these models can lead to understanding of biological values. This has been successful in HIV modeling for the estimation of values such as the lifetime of infected CD8 T-Cells. However, estimating these values is notoriously difficult, especially for highly complex models. We use Bayesian inference and Monte Carlo Markov Chain methods to estimate the underlying densities of the parameters (assumed to be continuous random variables) for three models of influenza. We discuss the advantages and limitations of parameter estimation using these methods. The data and influenza models used for this project are from the lab of Dr. Amber Smith in Memphis, Tennessee. / Master of Science / Mathematical models of viral infections have been informing virology research for years. Estimating parameter values for these models can lead to understanding of biological values. This has been successful in HIV modeling for the estimation of values such as the lifetime of infected CD8 T-Cells. However, estimating these values is notoriously difficult, especially for highly complex models. We use Bayesian inference and Monte Carlo Markov Chain methods to perform parameter estimation for three models of influenza. We discuss the advantages and limitations of these methods. The data and influenza models used for this project are from the lab of Dr. Amber Smith in Memphis, Tennessee.

Les titres financiers sont souvent modélisés par des équations différentielles stochastiques (ÉDS). Ces équations peuvent décrire le comportement de l'actif, et aussi parfois certains paramètres du modèle. Par exemple, le modèle de Heston (1993), qui s'inscrit dans la catégorie des modèles à volatilité stochastique, décrit le comportement de l'actif et de la variance de ce dernier. Le modèle de Heston est très intéressant puisqu'il admet des formules semi-analytiques pour certains produits dérivés, ainsi qu'un certain réalisme. Cependant, la plupart des algorithmes de simulation pour ce modèle font face à quelques problèmes lorsque la condition de Feller (1951) n'est pas respectée. Dans ce mémoire, nous introduisons trois nouveaux algorithmes de simulation pour le modèle de Heston. Ces nouveaux algorithmes visent à accélérer le célèbre algorithme de Broadie et Kaya (2006); pour ce faire, nous utiliserons, entre autres, des méthodes de Monte Carlo par chaînes de Markov (MCMC) et des approximations. Dans le premier algorithme, nous modifions la seconde étape de la méthode de Broadie et Kaya afin de l'accélérer. Alors, au lieu d'utiliser la méthode de Newton du second ordre et l'approche d'inversion, nous utilisons l'algorithme de Metropolis-Hastings (voir Hastings (1970)). Le second algorithme est une amélioration du premier. Au lieu d'utiliser la vraie densité de la variance intégrée, nous utilisons l'approximation de Smith (2007). Cette amélioration diminue la dimension de l'équation caractéristique et accélère l'algorithme. Notre dernier algorithme n'est pas basé sur une méthode MCMC. Cependant, nous essayons toujours d'accélérer la seconde étape de la méthode de Broadie et Kaya (2006). Afin de réussir ceci, nous utilisons une variable aléatoire gamma dont les moments sont appariés à la vraie variable aléatoire de la variance intégrée par rapport au temps. Selon Stewart et al. (2007), il est possible d'approximer une convolution de variables aléatoires gamma (qui ressemble beaucoup à la représentation donnée par Glasserman et Kim (2008) si le pas de temps est petit) par une simple variable aléatoire gamma. / Financial stocks are often modeled by stochastic differential equations (SDEs). These equations could describe the behavior of the underlying asset as well as some of the model's parameters. For example, the Heston (1993) model, which is a stochastic volatility model, describes the behavior of the stock and the variance of the latter. The Heston model is very interesting since it has semi-closed formulas for some derivatives, and it is quite realistic. However, many simulation schemes for this model have problems when the Feller (1951) condition is violated. In this thesis, we introduce new simulation schemes to simulate price paths using the Heston model. These new algorithms are based on Broadie and Kaya's (2006) method. In order to increase the speed of the exact scheme of Broadie and Kaya, we use, among other things, Markov chains Monte Carlo (MCMC) algorithms and some well-chosen approximations. In our first algorithm, we modify the second step of the Broadie and Kaya's method in order to get faster schemes. Instead of using the second-order Newton method coupled with the inversion approach, we use a Metropolis-Hastings algorithm. The second algorithm is a small improvement of our latter scheme. Instead of using the real integrated variance over time p.d.f., we use Smith's (2007) approximation. This helps us decrease the dimension of our problem (from three to two). Our last algorithm is not based on MCMC methods. However, we still try to speed up the second step of Broadie and Kaya. In order to achieve this, we use a moment-matched gamma random variable. According to Stewart et al. (2007), it is possible to approximate a complex gamma convolution (somewhat near the representation given by Glasserman and Kim (2008) when T-t is close to zero) by a gamma distribution.

Submitted by Marlene Santos (marlene.bc.ufg@gmail.com) on 2016-08-05T17:38:42Z No. of bitstreams: 2 Dissertação - Alexandre Barbosa de Almeida - 2016.pdf: 11943401 bytes, checksum: 94f2e941bbde05e098c40f40f0f2f69c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2016-08-09T11:57:53Z (GMT) No. of bitstreams: 2 Dissertação - Alexandre Barbosa de Almeida - 2016.pdf: 11943401 bytes, checksum: 94f2e941bbde05e098c40f40f0f2f69c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2016-08-09T11:57:53Z (GMT). No. of bitstreams: 2 Dissertação - Alexandre Barbosa de Almeida - 2016.pdf: 11943401 bytes, checksum: 94f2e941bbde05e098c40f40f0f2f69c (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-06-17 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / Proteins are vital for the biological functions of all living beings on Earth. However, they only have an active biological function in their native structure, which is a state of minimum energy. Therefore, protein functionality depends almost exclusively on the size and shape of its native conformation. However, less than 1% of all known proteins in the world has its structure solved. In this way, various methods for determining protein structures have been proposed, either in vitro or in silico experiments. This work proposes a new in silico method called Monte Carlo with Dominance, which addresses the problem of protein structure prediction from the point of view of ab initio and multi-objective optimization, considering both protein energetic and structural aspects. The software GROMACS was used for the ab initio treatment to perform Molecular Dynamics simulations, while the framework ProtPred-GROMACS (2PG) was used for the multi-objective optimization problem, employing genetic algorithms techniques as heuristic solutions. Monte Carlo with Dominance, in this sense, is like a variant of the traditional Monte Carlo Metropolis method. The aim is to check if protein tertiary structure prediction is improved when structural aspects are taken into account. The energy criterion of Metropolis and energy and structural criteria of Dominance were compared using RMSD calculation between the predicted and native structures. It was found that Monte Carlo with Dominance obtained better solutions for two of three proteins analyzed, reaching a difference about 53% in relation to the prediction by Metropolis. / As proteínas são vitais para as funções biológicas de todos os seres na Terra. Entretanto, somente apresentam função biológica ativa quando encontram-se em sua estrutura nativa, que é o seu estado de mínima energia. Portanto, a funcionalidade de uma proteína depende, quase que exclusivamente, do tamanho e da forma de sua conformação nativa. Porém, de todas as proteínas conhecidas no mundo, menos de 1% tem a sua estrutura resolvida. Deste modo, vários métodos de determinação de estruturas de proteínas têm sido propostos, tanto para experimentos in vitro quanto in silico. Este trabalho propõe um novo método in silico denominado Monte Carlo com Dominância, o qual aborda o problema da predição de estrutura de proteínas sob o ponto de vista ab initio e de otimização multiobjetivo, considerando, simultaneamente, os aspectos energéticos e estruturais da proteína. Para o tratamento ab initio utiliza-se o software GROMACS para executar as simulações de Dinâmica Molecular, enquanto que para o problema da otimização multiobjetivo emprega-se o framework ProtPred-GROMACS (2PG), o qual utiliza algoritmos genéticos como técnica de soluções heurísticas. O Monte Carlo com Dominância, nesse sentido, é como uma variante do tradicional método de Monte Carlo Metropolis. Assim, o objetivo é o de verificar se a predição da estrutura terciária de proteínas é aprimorada levando-se em conta também os aspectos estruturais. O critério energético de Metropolis e os critérios energéticos e estruturais da Dominância foram comparados empregando o cálculo de RMSD entre as estruturas preditas e as nativas. Foi verificado que o método de Monte Carlo com Dominância obteve melhores soluções para duas de três proteínas analisadas, chegando a cerca de 53% de diferença da predição por Metropolis.