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Dissertations / Theses on the topic 'Statistical Theory'
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Liang, Annie. "Economic Theory and Statistical Learning." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493561.
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This dissertation presents three independent essays in microeconomic theory. Chapter 1 suggests an alternative to the common prior assumption, in which agents form beliefs by learning from data, possibly interpreting the data in different ways. In the limit as agents observe increasing quantities of data, the model returns strict solutions of a limiting complete information game, but predictions may diverge substantially for small quantities of data. Chapter 2 (with Jon Kleinberg and Sendhil Mullainathan) proposes use of machine learning algorithms to construct benchmarks for “achievable" predictive accuracy. The paper illustrates this approach for the problem of predicting human-generated random sequences. We find that leading models explain approximately 10-15% of predictable variation in the problem. Chapter 3 considers the problem of how to interpret inconsistent choice data, when the observed departures from the standard model (perfect maximization of a single preference) may emerge either from context-dependencies in preference or from stochastic choice error. I show that if preferences are “simple" in the sense that they consist only of a small number of context-dependencies, then the analyst can use a proposed optimization problem to recover the true number of underlying context-dependent preferences.Economics
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Lu, Adonis. "Statistical Theory Through Differential Geometry." Scholarship @ Claremont, 2019. https://scholarship.claremont.edu/cmc_theses/2181.
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This thesis will take a look at the roots of modern-day information geometry and some applications into statistical modeling. In order to truly grasp this field, we will first provide a basic and relevant introduction to differential geometry. This includes the basic concepts of manifolds as well as key properties and theorems. We will then explore exponential families with applications of probability distributions. Finally, we select a few time series models and derive the underlying geometries of their manifolds.
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Leroux, Brian Gilbert. "Likelihood ratios in asymptotic statistical theory." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/24843.
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This thesis deals with two topics in asymptotic statistics. A concept of asymptotic optimality for sequential tests of statistical hypotheses is introduced. Sequential Probability Ratio Tests are shown to have asymptotic optimality properties corresponding to their usual optimality properties. Secondly, the asymptotic power of Pearson's chi-square test for goodness of fit is derived in a new way.
The main tool for evaluating asymptotic performance of tests is the likelihood ratio of two hypotheses. In situations examined here the likelihood ratio based on a sample of size ⁿ has a limiting distribution as ⁿ → ∞ and the limit is also a likelihood ratio. To calculate limiting values of various performance criteria of statistical tests the calculations can be made using the limiting likelihood ratio.Science, Faculty of
Statistics, Department of
Graduate
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Rasmussen, H. O. "The statistical theory of stationery turbulence." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363346.
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Thomas, Kuryan. "A statistical theory of the epilepsies." Diss., Virginia Polytechnic Institute and State University, 1988. http://hdl.handle.net/10919/87673.
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A new physical and mathematical model for the epilepsies is proposed, based on the theory of bond percolation on finite lattices. Within this model, the onset of seizures in the brain is identified with the appearance of spanning clusters of neurons engaged in the spurious and uncontrollable electrical activity characteristic of seizures. It is proposed that the fraction of excitatory to inhibitory synapses can be identified with a bond probability, and that the bond probability is a randomly varying quantity displaying Gaussian statistics. The consequences of the proposed model to the treatment of the epilepsies is explored.
The nature of the data on the epilepsies which can be acquired in a clinical setting is described. It is shown that such data can be analyzed to provide preliminary support for the bond percolation hypothesis, and to quantify the efficacy of anti-epileptic drugs in a treatment program. The results of a battery of statistical tests on seizure distributions are discussed.
The physical theory of the electroencephalogram (EEG) is described, and extant models of the electrical activity measured by the EEG are discussed, with an emphasis on their physical behavior. A proposal is made to explain the difference between the power spectra of electrical activity measured with cranial probes and with the EEG. Statistical tests on the characteristic EEG manifestations of epileptic activity are conducted, and their results described.
Computer simulations of a correlated bond percolating system are constructed. It is shown that the statistical properties of the results of such a simulation are strongly suggestive of the statistical properties of clinical data.
The study finds no contradictions between the predictions of the bond percolation model and the observed properties of the available data. Suggestions are made for further research and for techniques based on the proposed model which may be used for tuning the effects of anti-epileptic drugs.Ph. D.
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Lee, Yun-Soo. "On some aspects of distribution theory and statistical inference involving order statistics." Virtual Press, 1991. http://liblink.bsu.edu/uhtbin/catkey/834141.
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Statistical methods based on nonparametric and distribution-free procedures require the use of order statistics. Order statistics are also used in many parametric estimation and testing problems. With the introduction of modern high speed computers, order statistics have gained more importance in recent years in statistical inference - the main reason being that ranking a large number of observations manually was difficult and time consuming in the past, which is no longer the case at present because of the availability of high speed computers. Also, applications of order statistics require in many cases the use of numerical tables and computer is needed to construct these tables.In this thesis, some basic concepts and results involving order statistics are provided. Typically, application of the Theory of Permanents in the distribution of order statistics are discussed. Further, the correlation coefficient between the smallest observation (Y1) and the largest observation (Y,,) of a random sample of size n from two gamma populations, where (n-1) observations of the sample are from one population and the remaining observation is from the other population, is presented.Department of Mathematical Sciences
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Grigo, Alexander. "Billiards and statistical mechanics." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29610.
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Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009.Committee Chair: Bunimovich, Leonid; Committee Member: Bonetto, Federico; Committee Member: Chow, Shui-Nee; Committee Member: Cvitanovic, Predrag; Committee Member: Weiss, Howard. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Jeng, Tian-Tzer. "Some contributions to asymptotic theory on hypothesis testing when the model is misspecified /." The Ohio State University, 1987. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487332636473942.
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Weston, Robert Andrew. "Lattice field theory and statistical-mechanical models." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315971.
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Jiang, Xiao. "Contributions to statistical distribution theory with applications." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/contributions-to-statistical-distribution-theory-with-applications(fa612f53-1950-48c2-9cdf-135b2d145587).html.
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The whole thesis contains 10 chapters. Chapter 1 is the introductory chapter of my thesis and the main contributions are presented in Chapter 2 through to Chapter 9. Chapter 10 is the conclusion chapter. These chapters are motivated by applications to new and existing problems in finance, healthcare, sports, and telecommunications. In recent years, there has been a surge in applications of generalized hyperbolic distributions in finance. Chapter 2 provides a review of generalized hyperbolic and related distributions, including related programming packages. A real data application is presented which compares some of the distributions reviewed. Chapter 3 and Chapter 4 derive conditions for stochastic, hazard rate, likelihood ratio, reversed hazard rate, increasing convex and mean residual life orderings of Pareto distributed variables and Weibull distributed variables, respectively. A real data application of the conditions is presented in each chapter. Motivated by Lee and Cha [The American Statistician 69 (2015) 221-230], Chapter 5 introduces seven new families of discrete bivariate distributions. We reanalyze the football data in Lee and Cha (2015) and show that some of the newly proposed distributions provide better fits than the two families proposed by Lee and Cha (2015). Chapter 6 derives the distribution of amplitude, its moments and the distribution of phase for thirty-four flexible bivariate distributions. The results in part extend those given in Coluccia [IEEE Communications Letters, 17, 2013, 2364-2367]. Motivated by Schoenecker and Luginbuhl [IEEE Signal Processing Letters, 23, 2016, 644-647], Chapter 7 studies the characteristic function of products of two independent random variables. One follows the standard normal distribution and the other follows one of forty other continuous distributions. In this chapter, we give explicit expressions for the characteristic function of products, and some of the results are verified by simulations. Cossette, Marceau, and Perreault [Insurance: Mathematics and Economics, 64, 2015, 214-224] derived formulas for aggregation and capital allocation based on risks following two bivariate exponential distributions. Chapter 8 derives formulas for aggregation and capital allocation for thirty-three commonly known families of bivariate distributions. This collection of formulas could be a useful reference for financial risk management. Chapter 9 derives expressions for the kth moment of the dependent random sum using copulas. It also extends Mao and Zhao[IMA Journal of Management Mathematics, 25, 2014, 421-433]âs results to the case where the components of the sum are not identically distributed. The practical usefulness of the results in terms of computational time and computational accuracy is demonstrated by simulation.
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Chu, Jeffrey. "Statistical distribution theory with applications to finance." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/statistical-distribution-theory-with-applications-to-finance(415d8a76-64d1-4c78-a299-a931f7e1b48c).html.
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The whole thesis comprises six chapters, where the running theme focuses on the development of statistical methods and distribution theory, with applications to finance. It begins with Chapter 1, which provides the introduction and background to my thesis. This is then followed by Chapters 2 through to 6, which provide the main contributions. The exact distribution of the sum of more than two independent beta random variables is not a known result. Even in terms of approximations, only the normal approximation is known for the sum. Motivated by Murakami (2014), Chapter 2 derives a saddlepoint approximation for the distribution of the sum. An extensive simulation study shows that it always gives better performance than the normal approximation. Jin et al. (2016) proposed a novel moments based approximation based on the gamma distribution for the compound sum of independent and identical random variables, and illustrated their approximation through the use of six examples. Chapter 3 revisits four of their examples, and it is shown that moments based approximations based on simpler distributions can be good competitors. The moments based approximations are also shown to be more accurate than the truncated versions of the exact distribution of the compound sum. Results regarding the performances of the approximations are provided, which could be useful in determining which approximation should be used given a real data set. The estimation of the size of large populations can often be a significant problem. Chapter 4 proposes a new population size estimator and provides a comparison of its performance with two recent estimators known in the literature. The comparison is based on a simulation study and applications to two real big data sets from the Twitter and LiveJournal social networks. The proposed estimator is shown to outperform the known estimators, at least for small sample sizes. In recent years, with a growing interest in big or large datasets, there has been a rise in the application of large graphs and networks to financial big data. Much of this research has focused on the construction and analysis of the network structure of stock markets, based on the relationships between stock prices. Motivated by Boginski et al. (2005), who studied the characteristics of a network structure of the US stock market, Chapter 5 constructs network graphs of the UK stock market using the same method. Four distributions are fitted to the degree density of the vertices from these graphs: the Pareto I, Frechet, lognormal, and generalised Pareto distributions, and their goodness of fits are assessed. Results show that the degree density of the complements of the market graphs, constructed using a negative threshold value close to zero, can be fitted well with the Frechet and lognormal distributions. Chapter 6 analyses statistical properties of the largest cryptocurrencies (determined by market capitalisation), of which Bitcoin is the most prominent example. The analysis characterises their exchange rates versus the US Dollar by fitting parametric distributions to them. It is shown that cryptocurrency returns are clearly non-normal, however, no single distribution fits well jointly to all of the cryptocurrencies analysed. We find that for the most popular cryptocurrencies, such as Bitcoin and Litecoin, the generalised hyperbolic distribution gives the best fit, whilst for the smaller cryptocurrencies the normal inverse Gaussian distribution, generalised t distribution, and Laplace distribution give good fits. The results are important for investment and risk management purposes.
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Acharya, Anirudh. "Quantum tomography : asymptotic theory and statistical methodology." Thesis, University of Nottingham, 2018. http://eprints.nottingham.ac.uk/49998/.
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Recent experimental progress in the preparation and control of quantum systems has brought to light the importance of Quantum State Tomography (QST) in validating the results. In this thesis we investigate several aspects of QST, whose central problem is to devise estimation schemes for the recovery of an unknown state, given an ensemble of n independent identically prepared systems. The key issues in tackling QST for large dimensional systems is the construction of physically relevant low dimensional state models, and the design of appropriate measurements. Inspired by compressed sensing tomography, in chapters 4, 5 we consider the statistical problem of estimating low rank states (r ≪ d) in the set-up of Multiple Ions Tomography (MIT), where r and d are the rank and the dimension of the state respectively. We investigate how the estimation error behaves with a reduction in the number of measurement settings, compared to ‘full’ QST in two setups - Pauli and random bases measurement designs. We study the estimation errors in this ‘incomplete’ measurement setup in terms of a concentration of the Fisher information matrix. For the random bases design we demonstrate that O(r logd) settings suffice for the mean square error w.r.t the Frobenius norm to achieve the optimal O(1/n) rate of estimation. When the error functions are locally quadratic, like the Frobenius norm, then the expected error (or risk) of standard procedures achieves this optimal rate. However, for fidelity based errors such as the Bures distance we show that no ‘compressive’ recovery exists for states close to the boundary, and it is known that even with conventional ‘full’ tomography schemes the risk scales as O(1/√n) for such states and error functions. For qubit states this boundary is the surface of the Bloch sphere. Several estimators have been proposed to improve this scaling with ‘adaptive’ tomography. In chapter 6 we analyse this problem from the perspective of the maximum Bures risk over all qubit states. We propose two adaptive estimation strategies, one based on local measurements and another based on collective measurements utilising the results of quantum local asymptotic normality. We demonstrate a scaling of O(1/n) for the maximum Bures risk with both estimation strategies, and also discuss the construction of a minimax optimal estimator. In chapter 7 we return to the MIT setup and systematically compare several tomographic estimators in an extensive simulation study. We present and analyse results from this study, investigating the performance of the estimators across various states, measurement designs and error functions. Along with commonly used estimators like maximum likelihood, we propose and evaluate a few new ones. We finally introduce two web-based applications designed as tools for performing QST simulations online.
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Herath, H. M. A. C. "Statistical databases within a relational framework." Thesis, Keele University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386218.
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Deng, Xinwei. "Contributions to statistical learning and statistical quantification in nanomaterials." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29777.
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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.Committee Chair: Wu, C. F. Jeff; Committee Co-Chair: Yuan, Ming; Committee Member: Huo, Xiaoming; Committee Member: Vengazhiyil, Roshan Joseph; Committee Member: Wang, Zhonglin. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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Dugarte, Edgar José Candales. "Partitions theory in physics : some applications on string theory and statistical mechanics." Universidade Estadual de Londrina. Centro de Ciências Exatas. Programa de Pós-Graduação em Física, 2018. http://www.bibliotecadigital.uel.br/document/?code=vtls000217536.
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O poder combinatório da teoria de partições permite calcular os parâmetros termodinâmicos dos sistemas físicos. Em particular, a teoria das partições é especialmente útil para contar os estados que são especificados pela aplicação dos operadores de criação. Também derivamos e refinamos a fórmula de Hardy-Ramanujan através da Mecânica Estatística.The combinatorial power of the Partitions theory allows to calculate thermodynamical parameters of physical systems. In particular, Partitions theory is especially useful to count states that are specified by the application of creation-operators. Also we derived and refined the formula of Hardy-Ramanujan via Statistical Mechanics.
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Kuchler, Ryan J. "Theory of multirate statistical signal processing and applications." Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 2005. http://library.nps.navy.mil/uhtbin/hyperion/05Sep%5FKuchler%5FPhD.pdf.
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Itami, Masato. "Non-equilibrium Statistical Theory for Singular Fluid Stresses." 京都大学 (Kyoto University), 2016. http://hdl.handle.net/2433/215285.
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Fang, Gang. "Rate of liquid evaporation, statistical rate theory approach." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape17/PQDD_0001/NQ35153.pdf.
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Munsaka, Melvin Slaighter. "Some integral equations connected with statistical distribution theory." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60056.
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This thesis looks at certain integral equations which are used to obtain statistical distributions, particularly in the multivariate case. In all, seven integral equations are considered. Two of the integral equations were introduced by Wilks (1932) and these are known as type A and type B integral equations. The other five known as type C to type G were introduced by Mathai (1984). Some statistical distributions associated with the solutions to these integral equations will also be discussed.
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Choy, Siu Kai. "Statistical histogram characterization and modeling : theory and applications." HKBU Institutional Repository, 2008. http://repository.hkbu.edu.hk/etd_ra/913.
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McCabe, Clare. "Statistical mechanics of chain molecules." Thesis, University of Sheffield, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.287724.
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屠烈偉 and Lit-wai Tao. "Statistical inference on a mixture model." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1993. http://hub.hku.hk/bib/B31977480.
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Tao, Lit-wai. "Statistical inference on a mixture model." [Hong Kong] : University of Hong Kong, 1993. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13781479.
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Lesser, Elizabeth Rochelle. "A New Right Tailed Test of the Ratio of Variances." UNF Digital Commons, 2016. http://digitalcommons.unf.edu/etd/719.
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It is important to be able to compare variances efficiently and accurately regardless of the parent populations. This study proposes a new right tailed test for the ratio of two variances using the Edgeworth’s expansion. To study the Type I error rate and Power performance, simulation was performed on the new test with various combinations of symmetric and skewed distributions. It is found to have more controlled Type I error rates than the existing tests. Additionally, it also has sufficient power. Therefore, the newly derived test provides a good robust alternative to the already existing methods.
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Elliott, Janet Anne Wade. "Advancements in the statistical rate theory treatment of adsorption." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ27917.pdf.
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Hill, S. "Applications of statistical learning theory to signal processing problems." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604048.
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The dissertation focuses on the applicability of Support Vector Regression (SVR) in signal processing contexts. This is shown to be particularly well-suited to filtering in alpha-stable noise environments, and a further slight modification is proposed to this end. The main work in this dissertation on SVR is on the application to audio filtering based on perceptual criteria. This appears an ideal solution to the problem due to the fact that the loss function typically used by perceptual audio filtering practitioners incorporates a region of zero loss, as does SVR. SVR is extended to the problem of complex-valued regression, for application in the audio filtering problem to the frequency domain. This is with regions of zero loss that are both square and circular, and the circular case is extended to the problem of vector-valued regression. Three experiments are detailed with a mix of both good and poor results, and further refinements are proposed. Polychotomous, or multi-category classification is then studied. Many previous attempts are reviewed, and compared. A new approach is proposed, based on a geometrical structure. This is shown to overcome many of the problems identified with previous methods in addition to being very flexible and efficient in its implementation. This architecture is also derived, for just the three-class case, using a complex-valued kernel function. The general architecture is used experimentally in three separate implementations to give a demonstration of the overall approach. The methodology is shown to achieve results comparable to those of many other methods, and to include many of them as special cases. Further possible refinements are proposed which should drastically reduce optimisation times for so-called 'all-together' methods.
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Vladikas, A. "An analogue statistical mechanical approach in quantum field theory." Thesis, Imperial College London, 1985. http://hdl.handle.net/10044/1/37887.
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Hu, Qiao Ph D. Massachusetts Institute of Technology. "Application of statistical learning theory to plankton image analysis." Thesis, Massachusetts Institute of Technology, 2006. http://hdl.handle.net/1721.1/39206.
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Thesis (Ph. D.)--Joint Program in Applied Ocean Science and Engineering (Massachusetts Institute of Technology, Dept. of Mechanical Engineering; and the Woods Hole Oceanographic Institution), 2006.Includes bibliographical references (leaves 155-173).
A fundamental problem in limnology and oceanography is the inability to quickly identify and map distributions of plankton. This thesis addresses the problem by applying statistical machine learning to video images collected by an optical sampler, the Video Plankton Recorder (VPR). The research is focused on development of a real-time automatic plankton recognition system to estimate plankton abundance. The system includes four major components: pattern representation/feature measurement, feature extraction/selection, classification, and abundance estimation. After an extensive study on a traditional learning vector quantization (LVQ) neural network (NN) classifier built on shape-based features and different pattern representation methods, I developed a classification system combined multi-scale cooccurrence matrices feature with support vector machine classifier. This new method outperforms the traditional shape-based-NN classifier method by 12% in classification accuracy. Subsequent plankton abundance estimates are improved in the regions of low relative abundance by more than 50%. Both the NN and SVM classifiers have no rejection metrics. In this thesis, two rejection metrics were developed.
(cont.) One was based on the Euclidean distance in the feature space for NN classifier. The other used dual classifier (NN and SVM) voting as output. Using the dual-classification method alone yields almost as good abundance estimation as human labeling on a test-bed of real world data. However, the distance rejection metric for NN classifier might be more useful when the training samples are not "good" ie, representative of the field data. In summary, this thesis advances the current state-of-the-art plankton recognition system by demonstrating multi-scale texture-based features are more suitable for classifying field-collected images. The system was verified on a very large real-world dataset in systematic way for the first time. The accomplishments include developing a multi-scale occurrence matrices and support vector machine system, a dual-classification system, automatic correction in abundance estimation, and ability to get accurate abundance estimation from real-time automatic classification. The methods developed are generic and are likely to work on range of other image classification applications.
by Qiao Hu.
Ph.D.
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Florêncio, Dinei Alfonso Ferreira. "A new sampling theory and a framework for nonlinear filter banks." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/15792.
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Deel, Troy A. "A statistical study of graph algorithms." Virtual Press, 1985. http://liblink.bsu.edu/uhtbin/catkey/424871.
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The object of this paper is to investigate the behavior of some important graph properties and to statistically analyze the execution times of certain graph are the average degree of a vertex, connectivity of a graph, the existence of Hamilton cycles, Euler tours, and bipartitions in graphs. This study is unique in that it is based on statistical rather than deterministic methods.
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Cheng, Dunlei Stamey James D. "Topics in Bayesian sample size determination and Bayesian model selection." Waco, Tex. : Baylor University, 2007. http://hdl.handle.net/2104/5039.
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Ho, Man Wai. "Bayesian inference for models with monotone densities and hazard rates /." View Abstract or Full-Text, 2002. http://library.ust.hk/cgi/db/thesis.pl?ISMT%202002%20HO.
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Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2002.Includes bibliographical references (leaves 110-114). Also available in electronic version. Access restricted to campus users.
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Fung, Wing-kam Tony. "Analysis of outliers using graphical and quasi-Bayesian methods /." [Hong Kong] : University of Hong Kong, 1987. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1236146X.
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Guo, Yawen. "On Some Test Statistics for Testing the Population Skewness and Kurtosis: An Empirical Study." FIU Digital Commons, 2016. http://digitalcommons.fiu.edu/etd/3045.
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The purpose of this thesis is to propose some test statistics for testing the skewness and kurtosis parameters of a distribution, not limited to a normal distribution. Since a theoretical comparison is not possible, a simulation study has been conducted to compare the performance of the test statistics. We have compared both parametric methods (classical method with normality assumption) and non-parametric methods (bootstrap in Bias Corrected Standard Method, Efron’s Percentile Method, Hall’s Percentile Method and Bias Corrected Percentile Method). Our simulation results for testing the skewness parameter indicate that the power of the tests differs significantly across sample sizes, the choice of alternative hypotheses and methods we chose. For testing the kurtosis parameter, the simulation results suggested that the classical method performs well when the data are from both normal and beta distributions and bootstrap methods are useful for uniform distribution especially when the sample size is large.
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Antal, Laszlo. "Statistical disclosure control for frequency tables." Thesis, University of Manchester, 2016. https://www.research.manchester.ac.uk/portal/en/theses/statistical-disclosure-control-for-frequency-tables(cfee4921-b2a9-49ea-a1b5-9f04e7476131).html.
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Disclosure risk assessment of statistical data, such as frequency tables, is a prerequisite for data dissemination. This thesis investigates the problem of disclosure risk assessment of frequency tables from the perspective of a statistical institute. In the research reported here, disclosure risk is measured by a mathematical function designed for the data according to a disclosure risk scenario. Such functions are called disclosure risk measures. A disclosure risk measure is defined for frequency tables based on the entire population using information theory. If the disclosure risk of a population based frequency table is high, a statistical institute will apply a statistical disclosure control (SDC) method possibly perturbing the table. It is known that the application of any SDC method lowers the disclosure risk. However, measuring the disclosure risk of the perturbed frequency table is a difficult problem. The disclosure risk measure proposed in the first paper of the thesis is also extended to assess the disclosure risk of perturbed frequency tables. SDC methods can be applied to either the microdata from which the frequency table is generated or directly to the frequency table. The two classes of methods are called pre- and post-tabular methods accordingly. It is shown that the two classes are closely related and that the proposed disclosure risk measure can account for both methods. In the second paper, the disclosure risk measure is extended to assess the disclosure risk of sample based frequency tables. Probabilistic models are used to estimate the population frequencies from sample frequencies which can then be used in the proposed disclosure risk measures. In the final paper of the thesis, we investigate an application of building a flexible table generator where disclosure risk and data utility measures must be calculated on-the-fly. We show that the proposed disclosure risk measure and a related information loss measure are adaptable to these settings. An example implementation of the disclosure risk and data utility assessment using the proposed disclosure risk measure is given.
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Magnello, Eileen. "Karl Pearson : evolutionary biology and the emergence of a modern theory of statistics (1884-1936)." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:e3fe747f-3879-42f6-80b0-f50016460dc2.
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This thesis examines the development of modern statistical theory and its emergence as a highly specialised mathematical discipline at the end of the nineteenth century. The statistical work of the mathematician and statistician Karl Pearson (1857-1936), who almost singularly created the modern theory of statistics, is the focus of the thesis. The impact of the statistical and experimental work of the Darwinian zoologist W.F.R. Weldon (1860-1906), on the emergence and construction of Pearsonian statistical innovation, is central to the arguments developed in this thesis. Contributions to the Pearsonian corpus from such statisticians as Francis Ysidro Edgeworth (1845-1926), Francis Galton (1822-1911), and George Udny Yule (1871- 1951) are also addressed. The scope of the thesis does not involve a detailed account of every technical contribution that Pearson made to statistics. Instead, it provides a unifying assessment of Pearson's most seminal and innovative contributions to modern statistical theory devised in the Biometric School, at University College London, from 1892 to 1903. An assessment of Pearson's statistical contributions also entails a comprehensive examination of the two separate methodologies he developed in the Drapers' Biometric Laboratory (from 1903 to 1933) and in the Galton Eugenics Laboratory (from 1907 to 1933). This thesis arises, in part, from a desire to reassess the state of the historiography of Pearsonian statistics over the course of the last half century. Some of the earliest work on Pearson came from his former students who emphasised his achievements as a statistician usually from the perspective of the state of the discipline in their tune. The conventional view has presumed that Pearson's relationship with Galton and thus to Gallon's work on simple correlation, simple regression, inheritance and eugenics provided the impetus to Pearson's own statistical work. This approach, which focuses on a part of Pearson's statistical work, has provided minimal insight into the complexity of the totality of Pearsonian statistics. Another approach, derived from the sociology of knowledge in the 1970s, espoused this conventional view and linked Pearson's statistical work to eugenics by placing his work in a wider context of social and political ideologies. This has usually entailed frequent recourse to Pearson's social and political views vis-a-vis his popular writings on eugenics. This approach, whilst indicating the political and social dimensions of science, has produced a rather mono-causal or uni-dimensional view of history. The crucial question of the relation between his technical contributions and his ideology in the construction of his statistical methods has not yet been adequately considered. This thesis argues that the impetus to Pearson's earliest statistical work was given by his efforts to tackle the problems of asymmetrical biological distributions (arising from Weldon's dimorphic distribution of the female shore crab in the Bay of Naples). Furthermore, it argues that the fundamental developments and construction of Pearsonian statistics arose from the Darwinian biological concepts at the centre of Weldon's statistical and experimental work on marine organisms in Naples and in Plymouth. Charles Darwin's recognition that species comprised different sets of 'statistical' populations (rather than consisting of 'types' or 'essences') led to a reconceptualisation of statistical populations by Pearson and Weldon which, in turn, led to their attempts to find a statistical resolution of the pre-Darwinian Aristotelian essentialistic concept of species. Pearson's statistical developments thus involved a greater consideration of speciation and of Darwin's theory of natural selection than hitherto considered. This has, therefore, entailed a reconstruction of the totality of Pearsonian statistics to identify the mathematical and biological developments that underpinned his work and to determine other sources of influence in this development. Pearson's writings are voluminous: as principal author he published more than 540 papers and books of which 361 are statistical. The other publications include 67 literary and historical writings, 49 eugenics publications, 36 pure mathematics and physics papers and 27 reports on university matters. He also published at least 111 letters, notes and book reviews. His collected papers and letters at University College London consist of 235 boxes of family papers, scientific manuscripts and 14,000 letters. One of the most extensive sets of letters in the collection are those of W.F.R. Weldon and his wife, Florence Joy Weldon, which consists of nearly 1,000 pieces of correspondence. No published work on Pearson to date has properly utilised the correspondence between Pearson and the Weldons. Particular emphasis has been given to this collection as these letters indicate (in tandem with Pearson's Gresham lectures and the seminal statistical published papers) that Pearson's earliest statistical work started in 1892 (rather than 1895-1896) and that Weldon's influence and work during these years was decisive in the development and advancement of Pearsonian statistics. The approach adopted in this thesis is essentially that of an intellectual biography which is thematic and is broadly chronological. This approach has been adopted to make greater use of primary sources in an attempt to provide a more historically sensitive interpretation of Pearson's work than has been used previously. It has thus been possible to examine these three (as yet unexamined) key Pearsonian developments: (1) his earliest statistical work (from 1892 to 1895), (2) his joint biometrical projects with Weldon (from 1898-1906) and a shift in the focus of research in the Drapers' Biometric Laboratory following Weldon's death in 1906 and (3) the later work in the twentieth century when he established the two laboratories which were underpinned by two separate methodologies. The arguments, which follow a chronological progression, have been built around Darwin's ideas of biological variation, 'statistical' populations, his theory of natural selection and Galton's law of ancestral inheritance. The first two chapters provide background material to the arguments developed in the thesis. Weldon's use of correlation (for the identification of species) in 1889 is examined in Chaper III. It is argued, that Pearson's analysis of Weldon's dimorphic distribution led to their work on speciation which led on to Pearson's earliest innovative statistical work. Weldon's most productive research with Pearson, discussed in Chapter IV, came to fruition when he showed empirical evidence of natural selection by detecting disturbances (or deviations) in the distribution from normality as a consequence of differential mortality rates. This research enabled Pearson to further develop his theory of frequency distributions. The central part of the thesis broadens out to examine further issues not adequately examined. Galton's statistical approach to heredity is addressed in Chapter V, and it is shown that Galton adumbrated Pearson's work on multiple correlation and multiple regression with his law of ancestral heredity. This work, in conjunction with Weldon's work on natural selection, led to Pearson's introduction of the use of determinantal matrix algebra into statistical theory in 1896: this (much neglected) development was pivotal in the professionalisation of the emerging discipline of mathematical statistics. Pearson's work on goodness of fit testing provided the machinery for reconstructing his most comprehensive statistical work which spanned four decades and encompassed his entire working life as a statistician. Thus, a greater part of Pearsonian statistics has been examined than in previous studies.
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Zhang, Zuoshun. "Proper posterior distributions for some hierarchical models and roundoff effects in the Gibbs sampler /." Digital version accessible at:, 2000. http://wwwlib.umi.com/cr/utexas/main.
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Wang, Hongyan. "Analysis of statistical learning algorithms in data dependent function spaces /." access full-text access abstract and table of contents, 2009. http://libweb.cityu.edu.hk/cgi-bin/ezdb/thesis.pl?phd-ma-b23750534f.pdf.
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Thesis (Ph.D.)--City University of Hong Kong, 2009."Submitted to Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy." Includes bibliographical references (leaves [87]-100)
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Vigneaux, Juan Pablo. "Topology of statistical systems : a cohomological approach to information theory." Thesis, Sorbonne Paris Cité, 2019. http://www.theses.fr/2019USPCC070.
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Cette thèse étend dans plusieurs directions l’étude cohomologique de la théorie de l’information initiée par Baudot et Bennequin. On introduit une notion d'espace statistique basée sur les topos, puis on étudie plusieurs invariants cohomologiques. Les fonctions d’information et quelques objets associés apparaissent comme des classes de cohomologie distinguées ; les équations de cocycle correspondantes codent les propriétés récursives de ces fonctions. L'information a donc une signification topologique et la topologie sert de cadre unificateur.La première partie traite des fondements géométriques de la théorie. Les structures d’information sont présentées sous forme de catégories qui codent les relations de raffinement entre différents observables statistiques. On étudie les produits et coproduits des structures d’information, ainsi que leur représentation par des fonctions mesurables ou des opérateurs hermitiens. Chaque structure d’information donne lieu à un site annelé ; la cohomologie de l'information est introduite avec les outils homologiques développés par Artin, Grothendieck, Verdier et leurs collaborateurs.La deuxième partie étudie la cohomologie des variables aléatoires discrètes. Les fonctions d'information — l'entropie de Shannon, l'alpha-entropie de Tsallis, et la divergence de Kullback-Leibler — apparaissent sous la forme de 1-cocycles pour certains modules de coefficients probabilistes (fonctions de lois de probabilité). Dans le cas combinatoire (fonctions des histogrammes), le seul 0-cocycle est la fonction exponentielle, et les 1-cocycles sont des coefficients multinomiaux généralisés (Fontené-Ward). Il existe une relation asymptotique entre les cocycles combinatoires et probabilistes.La troisième partie étudie en détail les coefficients q-multinomiaux, en montrant que leur taux de croissance est lié à la 2-entropie de Tsallis (entropie quadratique). Lorsque q est une puissance première, ces coefficients q-multinomiaux comptent les drapeaux d'espaces vectoriels finis de longueur et de dimensions prescrites. On obtient une explication combinatoire de la non-additivité de l'entropie quadratique et une justification fréquentiste du principe de maximisation d'entropie quadratique. On introduit un processus stochastique à temps discret associé à la distribution de probabilité q-binomial qui génère des espaces vectoriels finis (drapeaux de longueur 2). La concentration de la mesure sur certains sous-espaces typiques permet d'étendre la théorie de Shannon à ce cadre.La quatrième partie traite de la généralisation de la cohomologie de l'information aux variables aléatoires continues. On étudie les propriétés de fonctorialité du conditionnement (vu comme désintégration) et sa compatibilité avec la marginalisation. Les calculs cohomologiques sont limités aux variables réelles gaussiennes. Lorsque les coordonnées sont fixées, les 1-cocycles sont l’entropie différentielle ainsi que les moments généralisés. Les catégories grassmanniennes permettent de traiter les calculs canoniquement et retrouver comme seuls classes de cohomologie de degré 1 l'entropie et la dimension. Ceci constitue une nouvelle caractérisation algébrique de l'entropie différentielleThis thesis extends in several directions the cohomological study of information theory pioneered by Baudot and Bennequin. We introduce a topos-theoretical notion of statistical space and then study several cohomological invariants. Information functions and related objects appear as distinguished cohomology classes; the corresponding cocycle equations encode recursive properties of these functions. Information has thus topological meaning and topology serves as a unifying framework.Part I discusses the geometrical foundations of the theory. Information structures are introduced as categories that encode the relations of refinement between different statistical observables. We study products and coproducts of information structures, as well as their representation by measurable functions or hermitian operators. Every information structure gives rise to a ringed site; we discuss in detail the definition of information cohomology using the homological tools developed by Artin, Grothendieck, Verdier and their collaborators.Part II studies the cohomology of discrete random variables. Information functions—Shannon entropy, Tsallis alpha-entropy, Kullback-Leibler divergence—appear as 1-cocycles for appropriate modules of probabilistic coefficients (functions of probability laws). In the combinatorial case (functions of histograms), the only 0-cocycle is the exponential function, and the 1-cocycles are generalized multinomial coefficients (Fontené-Ward). There is an asymptotic relation between the combinatorial and probabilistic cocycles.Part III studies in detail the q-multinomial coefficients, showing that their growth rate is connected to Tsallis 2-entropy (quadratic entropy). When q is a prime power, these q-multinomial coefficients count flags of finite vector spaces with prescribed length and dimensions. We obtain a combinatorial explanation for the nonadditivity of the quadratic entropy and a frequentist justification for the maximum entropy principle with Tsallis statistics. We introduce a discrete-time stochastic process associated to the q-binomial probability distribution that generates finite vector spaces (flags of length 2). The concentration of measure on certain typical subspaces allows us to extend Shannon's theory to this setting.Part IV discusses the generalization of information cohomology to continuous random variables. We study the functoriality properties of conditioning (seen as disintegration) and its compatibility with marginalization. The cohomological computations are restricted to the real valued, gaussian case. When coordinates are fixed, the 1-cocycles are the differential entropy as well as generalized moments. When computations are done in a coordinate-free manner, with the so-called grassmannian categories, we recover as the only degree-one cohomology classes the entropy and the dimension. This constitutes a novel algebraic characterization of differential entropy
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Louf, Rémi. "Wandering in cities : a statistical physics approach to urban theory." Thesis, Paris 6, 2015. http://www.theses.fr/2015PA066359/document.
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Les données disponibles au sujet des villes ne cessent de croître en quantité et en précision. Cependant, malgré l'explosion de la quantité d'information disponible, notre compréhension des processus qui régissent les villes et le phénomène d'urbanisation restent mal compris. Dans cette thèse, nous nous proposons d'étudier les villes en adoptant une démarche inspirée de la physique statistique. Dans un premier temps, nous présentons un modèle stochastique et hors-équilibre de croissance des villes qui décrit la structure du réseau de mobilité. Ce modèle conduit à une prédiction sur la croissance du nombre de centres d'activités avec la population. Cette prédiction est vérifiée de façon indépendante sur des données concernant les villes américaines et espagnoles. Dans le cadre de ce modèle, nous sommes également capables de prédire la valeur de l'exposant des lois d'échelle qui relient la longueur totale des navettes, la longueur totale du réseau viaire, le retard total dû aux embouteillages, la quantité de dioxyde de carbone émis, la surface totale des villes à leur population. Ces prédictions sont elles aussi vérifiées sur des données concernant les villes américaines. Dans une troisième partie distincte, nous nous intéressons à la ségrégation résidentielle. En proposant une nouvelle définition de ce qu'est la ségrégation, nous dérivons naturellement une mesure d'attraction/répulsion entre les différentes catégories. Nous présentons de surcroît une méthode qui permet de diviser de façon non-ambigue et reproductible la distribution des revenus en un nombre discret de classes. Enfin, nous revisitons la dichotomie traditionnelle entre centre-ville et banlieue en construisant une mesure adaptée aux villes anisotropes et polycentriques. Finalement, dans un quatrième temps, nous reproduisons succinctement les résultats que nous avons obtenus dans le cadre de l'étude empirique et théorique des réseaux spatiaux. Dans cette thèse, nous avons essayé de démontrer que la complexité des villes est -- presque paradoxalement -- mieux comprise par des approches simples telles que l'on en trouve en physique. Les méthodes qui sont propres à cette dernière, c'est-à-dire chercher de la structure dans les données, essayer d'isoler les processus les plus importants, construire des modèles simples et ne garder que ceux dont les prédictions sont en accord avec les données, sont en effet pertinentes pour l'étude des systèmes urbainsThe amount of data that is being gathered about cities is increasing in size and specificity. However, despite this wealth of information, we still have little understanding of the processes that drive cities. In this thesis we apply some ideas from statistical physics to the study of cities. We first present a stochastic, out-of-equilibrium model of city growth that describes the structure of the mobility pattern of individuals. The model explains the appearance of secondary subcenters as an effect of traffic congestion. We are also able to predict the sublinear increase of the number of centers with population size, a prediction that is verified on American and Spanish data. Within the framework of this model, we are further able to give a prediction for the scaling exponent of the total distance commuted daily, the total length of the road network, the total delay due to congestion, the quantity of CO2 emitted, and the surface area with the population size of cities. Predictions that agree with data gathered for U.S. cities. In the third part, we focus on the quantitative description of the patterns of residential segregation. We propose a unifying theoretical framework in which segregation can be empirically characterised. We propose a measure of interaction between the different categories. Building on the information about the attraction and repulsion between categories, we are able to define classes in a quantitative, unambiguous way. Finally, we revisit the traditional dichotomy between poor city centers and rich suburbs; we provide a measure that is adapted to anisotropic, polycentric cities. In the fourth and last part, we succinctly present the most important theoretical and empirical results of our studies on spatial networks. Throughout this thesis, we try to convey the idea that the complexity of cities is almost paradoxically better comprehended through simple approaches. Looking for structure in data, trying to isolate the most important processes, building simple models and only keeping those which agree with data, constitute a universal method that is also relevant to the study of urban systems
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Abu-Samreh, Mohammad Mahmud. "Thermalization theory in heavy ion collisions by nonequilibrium statistical mechanics." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185391.
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This dissertation presents a semiclassical microscopic approach based on the Uehling-Uhlenbeck equation for studying the equilibration processes due to nucleon-nucleon collisions during the collision of two heavy ions in the low and intermediate energy domain (5-100 MeV/nucleon). The state formed in the early stages of a heavy-ion collision can be characterized by a highly excited non-equilibrium system of nucleons. Equilibration processes then take place resulting in a system for which a temperature can be defined at least locally. The single-nucleon distribution function for the nucleons during the early stage of the ion-ion collision is represented in momentum-space either by two Fermi-spheres separated by the relative momentum of the impacting ions or by a deformed Fermi-sphere. The equilibration (thermalization) of this initial distribution in momentum-space is studied by calculating the collision term as a function of time. The relaxation-times are investigated through a microscopic model that incorporates the UU collision term with the relaxation-time approximation. Relaxation-times for the equilibration are obtained as a function of density and temperature. The temperature dependence is strong at low temperatures and this is a consequence of the Fermi statistics. The mode dependence of the relaxation-times is also calculated by expanding the angular dependence of the distribution in spherical harmonics. The RTA is also tested against thermalization of the Fermi-sphere systems and is found to be reasonable. Transport coefficients for viscosity, thermal conductivity and diffusion are also calculated as well as their temperature and density dependencies. Their relation to relaxation-times are derived. The mean free path of nucleons in hot nuclear matter is also studied in the same frame of work. The numerical calculations of the collision term are an important part of this investigation. They involve five-dimensional integrations carried out using Gaussian and Simpson's numerical methods.
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Gianvecchio, Steven. "Application of information theory and statistical learning to anomaly detection." W&M ScholarWorks, 2010. https://scholarworks.wm.edu/etd/1539623563.
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In today's highly networked world, computer intrusions and other attacks area constant threat. The detection of such attacks, especially attacks that are new or previously unknown, is important to secure networks and computers. A major focus of current research efforts in this area is on anomaly detection.;In this dissertation, we explore applications of information theory and statistical learning to anomaly detection. Specifically, we look at two difficult detection problems in network and system security, (1) detecting covert channels, and (2) determining if a user is a human or bot. We link both of these problems to entropy, a measure of randomness information content, or complexity, a concept that is central to information theory. The behavior of bots is low in entropy when tasks are rigidly repeated or high in entropy when behavior is pseudo-random. In contrast, human behavior is complex and medium in entropy. Similarly, covert channels either create regularity, resulting in low entropy, or encode extra information, resulting in high entropy. Meanwhile, legitimate traffic is characterized by complex interdependencies and moderate entropy. In addition, we utilize statistical learning algorithms, Bayesian learning, neural networks, and maximum likelihood estimation, in both modeling and detecting of covert channels and bots.;Our results using entropy and statistical learning techniques are excellent. By using entropy to detect covert channels, we detected three different covert timing channels that were not detected by previous detection methods. Then, using entropy and Bayesian learning to detect chat bots, we detected 100% of chat bots with a false positive rate of only 0.05% in over 1400 hours of chat traces. Lastly, using neural networks and the idea of human observational proofs to detect game bots, we detected 99.8% of game bots with no false positives in 95 hours of traces. Our work shows that a combination of entropy measures and statistical learning algorithms is a powerful and highly effective tool for anomaly detection.
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Jankowitz, Maria Dorothea. "Some statistical aspects of LULU smoothers." Thesis, Link to the online version, 2007. http://hdl.handle.net/10019.1/1124.
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Hu, Zhiji. "Statistical approach toward designing expert system." Virtual Press, 1988. http://liblink.bsu.edu/uhtbin/catkey/539812.
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Inference under uncertainty plays a crucial role in expert system and receives growing attention from artificial intelligence experts, statisticians, and psychologists. In searching for new satisfactory ways to model inference under uncertainty, it will be necessary to combine the efforts of researchers from different areas. It is expected that with deep insight into this crucial problem, it will not only have enormous impact on development of AI and expert system, but also bring classical areas like statistics into a new stage. This research paper gives a precise synopsis of present work in the field and explores the mechanics of statistical inference to a new depth by combining efforts of computer scientists, statisticians, and psychologists. One important part of the paper is the comparison of different paradigms, including the difference between statistical and logical views. Special attentions, which need to be paid when combining various methods, are considered in the paper. Also, some examples and counterexamples will be given to illustrate the availability of individual model which describes human behavior. Finally, a new framework to deal with uncertainty is proposed, and future trends of uncertainty management are projected.Department of Mathematical Sciences
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Leung, Denis H. Y. "Robust estimation : efficiency and bias, in theory and practice." Thesis, University of Oxford, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.236163.
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李建德 and Kin-tak Christopher Li. "Statistical problems involving compositions in a covariate role." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1986. http://hub.hku.hk/bib/B31207777.
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Li, Kin-tak Christopher. "Statistical problems involving compositions in a covariate role /." [Hong Kong] : University of Hong Kong, 1986. http://sunzi.lib.hku.hk/hkuto/record.jsp?B12326227.
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Shen, Zhiyuan. "EMPIRICAL LIKELIHOOD AND DIFFERENTIABLE FUNCTIONALS." UKnowledge, 2016. http://uknowledge.uky.edu/statistics_etds/14.
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Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. It has been shown by Owen (1988,1990) and many others that empirical likelihood ratio (ELR) method can be used to produce nice confidence intervals or regions. Owen (1988) shows that -2logELR converges to a chi-square distribution with one degree of freedom subject to a linear statistical functional in terms of distribution functions. However, a generalization of Owen's result to the right censored data setting is difficult since no explicit maximization can be obtained under constraint in terms of distribution functions. Pan and Zhou (2002), instead, study the EL with right censored data using a linear statistical functional constraint in terms of cumulative hazard functions. In this dissertation, we extend Owen's (1988) and Pan and Zhou's (2002) results subject to non-linear but Hadamard differentiable statistical functional constraints. In this purpose, a study of differentiable functional with respect to hazard functions is done. We also generalize our results to two sample problems. Stochastic process and martingale theories will be applied to prove the theorems. The confidence intervals based on EL method are compared with other available methods. Real data analysis and simulations are used to illustrate our proposed theorem with an application to the Gini's absolute mean difference.
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Ounpraseuth, Songthip T. Young Dean M. "Selected topics in statistical discriminant analysis." Waco, Tex. : Baylor University, 2006. http://hdl.handle.net/2104/4883.
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Yan, Yujie yy. "A General Approach to Buhlmann Credibility Theory." Thesis, University of North Texas, 2017. https://digital.library.unt.edu/ark:/67531/metadc1011812/.
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Credibility theory is widely used in insurance. It is included in the examination of the Society of Actuaries and in the construction and evaluation of actuarial models. In particular, the Buhlmann credibility model has played a fundamental role in both actuarial theory and practice. It provides a mathematical rigorous procedure for deciding how much credibility should be given to the actual experience rating of an individual risk relative to the manual rating common to a particular class of risks. However, for any selected risk, the Buhlmann model assumes that the outcome random variables in both experience periods and future periods are independent and identically distributed. In addition, the Buhlmann method uses sample mean-based estimators to insure the selected risk, which may be a poor estimator of future costs if only a few observations of past events (costs) are available. We present an extension of the Buhlmann model and propose a general method based on a linear combination of both robust and efficient estimators in a dependence framework. The performance of the proposed procedure is demonstrated by Monte Carlo simulations.