published_or_final_version / Medical Sciences / Master / Master of Medical Sciences

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

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Eucalypt trees are one of tree species used for the manufacturing of papers in South Africa. The manufacturing of paper consists of cooking the wood with chemicals until obtaining a pulp. The wood is made of different cells. The shape and structure of these cells, called wood anatomical characteristics are important for the quality of paper. In addition, the anatomical characteristics of wood are influenced by environmental factors like climatic factors, soil compositions etc…. In this study we investigated the effects of the climatic factors (temperature, rainfall, solar radiation, relative humidity, and wind speed) on wood anatomical characteristics of two Eucalyptus clones, a GC (Eucalyptus grandis × camuldulensis) and a GU (Eucalyptus grandis × urophylla). Nine trees per clone have been selected. Two sets of data have been collected for this study. The first set of data was eleven anatomical characteristics of the wood formed daily over a period of five years. The second set of data was the daily measurement of temperature, rainfall, solar radiation, relative humidity and wind speed in the experimental area. Wood is made of two kinds of cell, the fibres and the vessels. The fibres are used for the strength and support of the tree and the vessels for the nutrition. Eleven characteristics related to those cells have been measured (diameter, wall thickness, frequency). These characteristics are highly correlated. To reduce the number of response variables, the principal component analysis was used and the first four principal components accounts for about 95% of the total variation. Based on the weights associated with each component the first four principal components were labelled as vessel dimension (VD), fibre dimension (FD), fibre wall (FW) and vessel frequency (VF). The longitudinal linear mixed model with age, season, temperature, rainfall, solar radiation, relative humidity and wind speed as the fixed effects factors and tree as random effect factor was fitted to the data. From time series modelling result, lagged order of climatic variables were identified and these lagged climatic variables were included in the model. To account for the physical characteristic of the trees we included the effect of diameter at breast height, stem radius, daily radial increment, and the suppression or dominance of the tree in the model. It was found that wood anatomical characteristics of the two clones were more affected by climatic variables when the tree was on juvenile stage as compared to mature stage. / Thesis (M.Sc.)-University of KwaZulu-Natal, Pietermaritzburg, 2010.

Time-series data that reflect a periodic pattern are often used in psychology. In personality psychology, Brown and Moskowitz (1998) used spectral analysis to study whether fluctuations in the expression of four interpersonal behaviors show a cyclical pattern. Spline smoothing had also been used in the past to track the non-periodic trend, but no research has yet been done that combines spectral analysis and spline smoothing. The present thesis describes a new model which combines these two techniques to capture both periodic and non-periodic trends in the data. / The new model is then applied to Brown and Moskowitz's time-series data to investigate the long-term evolution to the four interpersonal behaviors, and to the GDP data to examine the periodic and non-periodic pattern for the GDP values of the 16 countries. Finally, the extent to which the model is accurate is tested using simulated data.

For reasoning under uncertainty the Bayesian network has become the representation of choice. However, except where models are considered 'simple' the task of construction and inference are provably NP-hard. For modelling larger 'real' world problems this computational complexity has been addressed by methods that approximate the model. The Naive Bayes classifier, which has strong assumptions of independence among features, is a common approach, whilst the class of trees is another less extreme example. In this thesis we propose the use of an information theory based technique as a mechanism for inference in Singly Connected Networks. We call this a Mutual Information Measure classifier, as it corresponds to the restricted class of trees built from mutual information. We show that the new approach provides for both an efficient and localised method of classification, with performance accuracies comparable with the less restricted general Bayesian networks. To improve the performance of the classifier, we additionally investigate the possibility of expanding the class Markov blanket by use of a Wrapper approach and further show that the performance can be improved by focusing on the class Markov blanket and that the improvement is not at the expense of increased complexity. Finally, the two methods are applied to the task of diagnosing the 'real' world medical domain, Acute Abdominal Pain. Known to be both a different and challenging domain to classify, the objective was to investigate the optiniality claims, in respect of the Naive Bayes classifier, that some researchers have argued, for classifying in this domain. Despite some loss of representation capabilities we show that the Mutual Information Measure classifier can be effectively applied to the domain and also provides a recognisable qualitative structure without violating 'real' world assertions. In respect of its 'selective' variant we further show that the improvement achieves a comparable predictive accuracy to the Naive Bayes classifier and that the Naive Bayes classifier's 'overall' performance is largely due the contribution of the majority group Non-Specific Abdominal Pain, a group of exclusion.

No description available.

A research report submitted in partial fulfilment of Mathematical Statistics Masters by Coursework and Research Report to the Faculty of Science, University of the Witwatersrand, Johannesburg, 2019 / The growing demand for generic drugs has led to an increase in the generic drug industry. As a result, there has been a growing demand for bioequivalence studies. The challenges with the bioequivalence studies arose with the method used to quantify bioavailability. Bioavailability is commonly estimated by the area under the concentration-time curve (AUC), which is traditionally estimated by Non-Compartmental Analysis (NCA) such as interpolation in aid of the trapezoidal rule. However, when the number of samples per subject is insufficient, the NCA estimates may be biased and this can result in incorrect conclusions about bioequivalence. Alternatively, AUC can be estimated by the Non-Linear Mixed Effect Model (NLMEM). The objective of this study is to evaluate bioequivalence on lnAUC estimated by using a NCA approach to those based on the lnAUC estimated by the NLMEM approach. The NCA and NLMEM approaches are compared on the resulting bias when the linear mixed effect model is used to analyse the lnAUC data estimated by each method. The methods are evaluated on simulated and real data. The 2x2 crossover designs of different sample sizes and sampling time intensities are simulated using two null hypotheses. In each crossover design, concentration profiles are simulated with different levels of between-subject variability, within-subject variability and residual error variance. A higher bias is obtained with the lnAUC estimated by the NCA approach for trials with a limited number of samples per subject. The NCA estimates provide satisfactory global TypeI-error results. The NLMEM fails to distinguish between the existing formulation differences when the residual variability is high. / TL (2020)

The efforts addressed in this thesis refer to applying nonlinear risk predictive techniques based on logistic regression to medical diagnostic test data. This study is motivated and pursued to address the following: 1. To extend logistic regression model of biostatistics to medical informatics 2. Computational preemptive and predictive testing to determine the probability of occurrence (p) of an event by fitting a data set to a (logit function) logistic curve: Finding upper and lower bounds on p based on stochastical considerations 3. Using the model developed on available (clinical) data to illustrate the bounds-limited performance of the prediction. Relevant analytical methods, computational efforts and simulated results are presented. Using the results compiled, the risk evaluation in medical diagnostics is discussed with real-world examples. Conclusions are enumerated and inferences are made with directions for future studies. / by Alice Horn Dupont. / Thesis (M.S.C.S.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

因果分析由于可以刻画随机事件之间的关系而被关注，而图模型则是描述因果关系的重要工具。在图模型框架中，数据集中隐含的因果关系被表示为定义在这个数据集上的贝叶斯网络，通过贝叶斯网络学习就可以完成数据集上的因果关系挖掘。因此,贝叶斯网络学习在因果分析中具有非常重要的作用。在本文中，我们提出了一种二段式的贝叶斯网络学习算法。在第一阶段，此算法从数据中构建出马尔可夫随机场。在第二阶段，此算法根据学习到的条件随机场构造出贝叶斯网络。本文中提出的二段式贝叶斯网络学习算法具有比现有算法更高的准确率，而且这种二段式算法中的一些技术可以很容易的被应用于其他贝叶斯网络学习算法当中。此外，通过与其他的时间序列中的因果分析模型（例如向量自回归和结构向量自回归模型）做比较，我们可以看出二段式的贝叶斯网络学习算法可以被用于时间序列的因果分析。 通过在真实数据集上的实验，我们证明的二段式贝叶斯网络学习算法在实际问题中的可用性。 / 本文开始介绍了基于约束的贝叶斯网络学习框架，其中的代表作是SGS 算法。在基于约束的贝叶斯网络学习框架中，如何减小测试条件独立的搜索空间是提高算法性能的关键步骤。二段式贝叶斯网络学习算法的核心即是研究如何减小条件独立测试的搜索空间。为此，我们证明了通过马尔可夫随机场来确定贝叶斯网络的结构可以有效的减小条件独立测试的计算复杂性以及增加算法的稳定性。在本文中，偏相关系数被用来度量条件独立。这种方法可用于基于约束的贝叶斯网络学习算法。具体来说，本文证明了在给定数据集的生成模型为线性的条件下，偏相关系数可被用于度量条件独立。而且本文还证明了高斯模型是线性结构方程模型的一个特例。本文比较了二段式的贝叶斯网络学习算法与当前性能最佳的贝叶斯算法在一系列真实贝叶斯网络上的表现。 / 文章的最后一部分研究了二段式的贝叶斯网络学习算法在时间序列因果分析中的应用。在这部分工作中，我们首先证明了结构向量自回归模型模型在高斯过程中不能发现同时期的因果关系。失败的原因是结构向量自回归模型不能满足贝叶斯网络的忠实性条件。因此，本文的最后一部分提出了一种区别于现有工作的基于贝叶斯网络的向量自回归和结构向量自回归模型学习算法。并且通过实验证明的算法在实际问题中的可用性。 / Causal analysis has drawn a lot of attention because it provides with deep insight of relations between random events. Graphical model is a dominant tool to represent causal relations. Under graphical model framework, causal relations implied in a data set are captured by a Bayesian network defined on this data set and causal discovery is achieved by constructing a Bayesian network from the data set. Therefore, Bayesian network learning plays an important role in causal relation discovery. In this thesis, we develop a Two-Phase Bayesian network learning algorithm that learns Bayesian network from data. Phase one of the algorithm learns Markov random fields from data, and phase two constructs Bayesian networks based on Markov random fields obtained. We show that the Two-Phase algorithm provides state-of-the-art accuracy, and the techniques proposed in this work can be easily adopted by other Bayesian network learning algorithms. Furthermore, we present that Two-Phase algorithm can be used for time series analysis by evaluating it against a series of time series causal learning algorithms, including VAR and SVAR. Its practical applicability is also demonstrated through empirical evaluation on real world data set. / We start by presenting a constraint-based Bayesian network learning framework that is a generalization of SGS algorithm [86]. We show that the key step in making Bayesian networks to learn efficiently is restricting the search space of conditioning sets. This leads to the core of this thesis: Two-Phase Bayesian network learning algorithm. Here we show that by learning Bayesian networks fromMarkov random fields, we efficiently reduce the computational complexity and enhance the reliability of the algorithm. Besides the proposal of this Bayesian network learning algorithm, we use zero partial correlation as an indicator of conditional independence. We show that partial correlation can be applied to arbitrary distributions given that data are generated by linear models. In addition, we prove that Gaussian distribution is a special case of linear structure equation model. We then compare our Two-Phase algorithm to other state-of-the-art Bayesian network algorithms on several real world Bayesian networks that are used as benchmark by many related works. / Having built an efficient and accurate Bayesian network learning algorithm, we then apply the algorithm for causal relation discovering on time series. First we show that SVAR model is incapable of identifying contemporaneous causal orders for Gaussian process because it fails to discover the structures faithful to the underlying distributions. We also develop a framework to learn true SVAR and VAR using Bayesian network, which is distinct from existing works. Finally, we show its applicability to a real world problem. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Zhenxing. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 184-195). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Abstract --- p.i / Acknowledgement --- p.v / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Causal Relation and Directed Graphical Model --- p.1 / Chapter 1.2 --- A Brief History of Bayesian Network Learning --- p.3 / Chapter 1.3 --- Some Important Issues for Causal BayesianNetwork Learning --- p.5 / Chapter 1.3.1 --- Learning Bayesian network locally --- p.6 / Chapter 1.3.2 --- Conditional independence test --- p.7 / Chapter 1.3.3 --- Causation discovery for time series --- p.8 / Chapter 1.4 --- Road Map of the Thesis --- p.10 / Chapter 1.5 --- Summary of the Remaining Chapters --- p.12 / Chapter 2 --- Background Study --- p.14 / Chapter 2.1 --- Notations --- p.14 / Chapter 2.2 --- Formal Preliminaries --- p.15 / Chapter 2.3 --- Constraint-Based Bayesian Network Learning --- p.24 / Chapter 3 --- Two-Phase Bayesian Network Learning --- p.33 / Chapter 3.1 --- Two-Phase Bayesian Network Learning Algorithm --- p.35 / Chapter 3.1.1 --- Basic Two-Phase algorithm --- p.37 / Chapter 3.1.2 --- Two-Phase algorithm with Markov blanket information --- p.59 / Chapter 3.2 --- Correctness Proof and Complexity Analysis --- p.73 / Chapter 3.2.1 --- Correctness proof --- p.73 / Chapter 3.2.2 --- Complexity analysis --- p.81 / Chapter 3.3 --- Related Works --- p.83 / Chapter 3.3.1 --- Search-and-score algorithms --- p.84 / Chapter 3.3.2 --- Constraint-based algorithms --- p.85 / Chapter 3.3.3 --- Other algorithms --- p.86 / Chapter 4 --- Measuring Conditional Independence --- p.88 / Chapter 4.1 --- Formal Definition of Conditional Independence --- p.88 / Chapter 4.2 --- Measuring Conditional Independence --- p.96 / Chapter 4.2.1 --- Measuring independence with partial correlation --- p.96 / Chapter 4.2.2 --- Measuring independence with mutual information --- p.104 / Chapter 4.3 --- Non-Gaussian Distributions and Equivalent Class --- p.108 / Chapter 4.4 --- Heuristic CI Tests UnderMonotone Faithfulness Condition --- p.116 / Chapter 5 --- Empirical Results of Two-Phase Algorithms --- p.125 / Chapter 5.1 --- Experimental Setup --- p.126 / Chapter 5.2 --- Structure Error After Each Phase of Two-Phase Algorithms --- p.129 / Chapter 5.3 --- Maximal and Average Sizes of Conditioning Sets --- p.131 / Chapter 5.4 --- Comparison of the Number of CI Tests Required by Dependency Analysis Approaches --- p.133 / Chapter 5.5 --- Reason forWhich Number of CI Tests Required Grow with Sample Size --- p.135 / Chapter 5.6 --- Two-Phase Algorithms on Linear Gaussian Data --- p.136 / Chapter 5.7 --- Two-phase Algorithms on Linear Non-Gaussian Data --- p.139 / Chapter 5.8 --- Compare Two-phase Algorithms with Search-and-Score Algorithms and Lasso Regression --- p.142 / Chapter 6 --- Causal Mining in Time Series Data --- p.146 / Chapter 6.1 --- A Brief Review of Causation Discovery in Time Series --- p.146 / Chapter 6.2 --- Limitations of Constructing SVAR from VAR --- p.150 / Chapter 6.3 --- SVAR Being Incapability of Identifying Contemporaneous Causal Order for Gaussian Process --- p.152 / Chapter 6.4 --- Estimating the SVARs by Bayesian Network Learning Algorithm --- p.157 / Chapter 6.4.1 --- Represent SVARs by Bayesian networks --- p.158 / Chapter 6.4.2 --- Getting back SVARs and VARs fromBayesian networks --- p.159 / Chapter 6.5 --- Experimental Results --- p.162 / Chapter 6.5.1 --- Experiment on artificial data --- p.162 / Chapter 6.5.2 --- Application in finance --- p.172 / Chapter 6.6 --- Comparison with Related Works --- p.174 / Chapter 7 --- Concluding Remarks --- p.178 / Bibliography --- p.184