The main contribution of this thesis is the introduction of Bayesian quantile regression for hidden Markov models, especially when we have to deal with extreme quantile regression analysis, as there is a limited research to inference conditional quantiles for hidden Markov models, under a Bayesian approach. The first objective is to compare Bayesian extreme quantile regression and the classical extreme quantile regression, with the help of simulated data generated by three specific models, which only differ in the error term’s distribution. It is also investigated if and how the error term’s distribution affects Bayesian extreme quantile regression, in terms of parameter and confidence intervals estimation. Bayesian extreme quantile regression is performed by implementing a Metropolis-Hastings algorithm to update our parameters, while the classical extreme quantile regression is performed by using linear programming. Moreover, the same analysis and comparison is performed on a real data set. The results provide strong evidence that our method can be improved, by combining MCMC algorithms and linear programming, in order to obtain better parameter and confidence intervals estimation. After improving our method for Bayesian extreme quantile regression, we extend it by including hidden Markov models. First, we assume a discrete time finite state-space hidden Markov model, where the distribution associated with each hidden state is a) a Normal distribution and b) an asymmetric Laplace distribution. Our aim is to explore the number of hidden states that describe the extreme quantiles of our data sets and check whether a different distribution associated with each hidden state can affect our estimation. Additionally, we also explore whether there are structural changes (breakpoints), by using break-point hidden Markov models. In order to perform this analysis we implement two new MCMC algorithms. The first one updates the parameters and the hidden states by using a Forward-Backward algorithm and Gibbs sampling (when a Normal distribution is assumed), and the second one uses a Forward-Backward algorithm and a mixture of Gibbs and Metropolis-Hastings sampling (when an asymmetric Laplace distribution is assumed). Finally, we consider hidden Markov models, where the hidden state (latent variables) are continuous. For this case of the discrete-time continuous state-space hidden Markov model we implement a method that uses linear programming and the Kalman filter (and Kalman smoother). Our methods are used in order to analyze real interest rates by assuming hidden states, which represent different financial regimes. We show that our methods work very well in terms of parameter estimation and also in hidden state and break-point estimation, which is very useful for the real life applications of those methods.

A key challenge for the insurance industry is to charge each customer an appropriate price for the risk they represent. Risk varies widely from customer to customer, and a deep understanding of different risk factors helps predict the likelihood and cost of insurance claims. The goal of this project is to see how well various statistical methods perform in predicting bodily injury liability Insurance claim payments based on the characteristics of the insured customer’s vehicles for this particular dataset from Allstate Insurance Company.We tried several statistical methods, including logistic regression, Tweedie’s compound gamma-Poisson model, principal component analysis (PCA), response averaging, and regression and decision trees. From all the models we tried, PCA combined with a with a Regression Tree produced the best results. This is somewhat surprising given the widespread use of the Tweedie model for insurance claim prediction problems.

Thesis (D.Sc.)--University of the Witwatersrand, 1963

Thesis advisor: Jeffrey H. Chuang / The field of lipidomics has rapidly progressed since its inception only a decade ago. Technological revolutions in mass spectrometry, chromatography, and computational biology now enables high-throughput high-accuracy quantification of the cellular lipidome. One significant improvement of these technologies is that lipids can now be identified and quantified as individual molecular species. Lipidomics provides an additional layer of information to genomics and proteomics and opens a new opportunity for furthering our understanding of cellular signaling networks and physiology, which have broad therapeutic values. As with other 'omics sciences, these new technologies are producing vast amounts of lipidomic data, which require sophisticated statistical and computational approaches for analysis and interpretation. However, computational tools for utilizing such data are sparse. The complexity of lipid metabolic systems and the fact that lipid enzymes remain poorly understood also present challenges to computational lipidomics. The focus of my dissertation has been the development of novel computational methods for systematic study of lipid metabolism in cellular function and human diseases using lipidomic data. In this dissertation, I first present a mathematical model describing cardiolipin molecular species distribution in steady state and its relationship with fatty acid chain compositions. Knowledge of this relationship facilitates determination of isomeric species for complex lipids, providing more detailed information beyond current limits of mass spectrometry technology. I also correlate lipid species profiles with diseases and predict potential therapeutics. Second, I present statistical studies of mechanisms influencing phosphatidylcholine and phosphatidylethanolamine molecular architectures, respectively. I describe a statistical approach to examine dependence of sn1 and sn2 acyl chain regulatory mechanisms. Third, I describe a novel network inference approach and illustrate a dynamic model of ethanolamine glycerophospholipid acyl chain remodeling. The model is the first that accurately and robustly describes lipid species changes in pulse-chase experiments. A key outcome is that the deacylation and reacylation rates of individual acyl chains can be determined, and the resulting rates explain the well-known prevalence of sn1 saturated chains and sn2 unsaturated chains. Lastly, I summarize and remark on future studies for lipidomics. / Thesis (PhD) — Boston College, 2012. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Biology.

In this thesis, we attempt to address some of these questions. First, we have devised a scheme to extract information of the plumes from simultaneous velocity and temperature measurements. Our method makes explicit use of the physical intuition that the velocity of the buoyant structures, e.g. plumes, should be related to the temperature fluctuation, in some apriori unknown manner as they are generated by buoyancy. Our scheme involves a decomposition of the local velocity measurement into two parts. The part that is correlated with some function of the temperature fluctuation measured at the same time is taken as the velocity of the plumes. Applying this scheme to measurements taken at the center and near the sidewall of the convection cell where the dominant buoyant structures are plumes, we have found the temperature dependence of the plume velocity at these two locations and understood our results from the equations of motion. Using these results of the temperature dependence of the plume velocity, we (i) conclude that heat is not mainly transported through the central region of the convection cell and (ii) obtain a relation between the scaling behavior of the plume velocity structure functions and the temperature structure functions that is different from what is implied by Bolgiano-Obukhov scaling. Then we have studied the possible effects of the large-scale mean circulation on the velocity and temperature statistics using simplified shell models of turbulent convection. We have introduced a large-scale mean flow into two shell models and found that its presence does not change the scaling behavior of velocity and temperature. / In turbulent thermal convection, velocity and temperature measurements taken at a point display complex fluctuations in time. On the other hand, visualization of the flow reveals recurring coherent structures. One prominent flow structure is a plume, which is generated from the thermal boundary layers by buoyancy. Another flow structure is a large-scale mean circulation that spans the entire convection cell. At least two strategies can be employed to study turbulent thermal convection or turbulent flows in general. One is to analyze and understand the fluctuations of the local measurements. The other is to characterize the coherent structures and study and understand their dynamics. These two approaches are not independent but provide complementary knowledge of the flows. Interesting questions hence include whether and how information about the ordered flow structures can be extracted from the fluctuating local measurements and how the presence of the ordered flow structures might affect the statistics of the fluctuations. / Guo, Hao = 热对流湍流中的统计特性与结构 / 郭昊. / "January 2007." / Source: Dissertation Abstracts International, Volume: 68-09, Section: B, page: 6036. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 62-66). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Title and abstract in English and Chinese. / School code: 1307. / Guo, Hao = Re dui liu tuan liu zhong de tong ji te xing yu jie gou / Guo Hao.

by Tong Pak Yee. / Parallel title in Chinese characters. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 12-16). / Acknowledgement --- p.i / List of Publications --- p.ii / Abstract --- p.iii / Chapter 1. --- Introduction / Chapter 1.1 --- Background --- p.1 / Chapter 1.2 --- Outline of the article --- p.5 / Chapter 1.2.1 --- Multifractal Scaling in Fractal Lattice --- p.6 / Chapter 1.2.2 --- Anomalous Multifractality in Percolation Model --- p.7 / Chapter 1.2.3 --- Anomalous Crossover Behavior in Two-Component Random Resistor Network --- p.8 / Chapter 1.2.4 --- Current Distribution in Two-Component Random Resistor Network --- p.10 / Chapter 1.2.5 --- Multif ractality in Wide Distribution Fractal Models --- p.11 / References --- p.12 / Chapter 2. --- Multifractal Analysis of Percolation Backbone and Fractal Lattices / Chapter 2.1 --- Multifractal Scaling in Fractal Lattice --- p.17 / Chapter 2.1.1 --- Multifractal Scaling in a Sierpinski Gasket --- p.18 / Chapter 2.1.2 --- Hierarchy of Critical Exponents on a Sierpinski Honeycomb --- p.38 / Chapter 2.2 --- Anomalous Multifractality in Percolation Model --- p.51 / Chapter 2.2.1 --- Anomalous Multifractality of Conductance Jumps in a Hierarchical Percolation Model --- p.52 / Chapter 2.3 --- Anomalous Crossover Behavior in Two-Component Random Resistor Network --- p.74 / Chapter 2.3.1 --- Anomalous Crossover Behaviors in the Two- Component Deterministic Percolation Model --- p.75 / Chapter 2.3.2 --- Minimum Current in the Two-Component Random Resistor Network --- p.90 / Chapter 2.4 --- Current Distribution in Two-Component Random Resistor Network --- p.105 / Chapter 2.4.1 --- Current Distribution in the Two-Component Hierarchical Percolation Model --- p.106 / Chapter 2.4.2 --- Current Distribution and Local Power Dissipation in the Two-Component Deterministic Percolation Model --- p.136 / Chapter 2.5 --- Multifractality in Wide Distribution Fractal Models --- p.174 / Chapter 2.5.1 --- Fractal Networks with a Wide Distribution of Conductivities --- p.175 / Chapter 2.5.2 --- Power Dissipation in an Exactly Solvable Wide Distribution Model --- p.193 / Chapter 3. --- Conclusion --- p.210

by Lee Siu-keung. / Parallel title in Chinese. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1992. / Includes bibliographical references (leaves 162-164). / Chapter Chapter 1 --- Introduction --- p.5 / Chapter Chapter 2 --- Path Integrals / Chapter 2.1 --- Path´ؤIntegral Approach to Quantum Mechanics --- p.8 / Chapter 2.2 --- Path´ؤIntegral Approach to Statistical Mechanics --- p.14 / Chapter 2.3 --- Variational Principle --- p.18 / Chapter 2.4 --- "Variational Method Proposed by Giachetti and Tognetti, and by Feynman and Kleinert" / Chapter 2.4.1 --- Effective Classical Partition Function --- p.24 / Chapter 2.4.2 --- Particle Distribution Function From Effective Classical Potential --- p.34 / Chapter Chapter 3 --- Systematic Perturbation Corrections to the Variational Approximation Proposed in Section2.4 / Chapter 3.1 --- Formalism / Chapter 3.1.1 --- Free Energy --- p.38 / Chapter 3.1.2 --- Particle Distribution Function --- p.49 / Chapter 3.2 --- Second Order Correction to Free Energy --- p.53 / Chapter 3.3 --- First Order Correction to Particle Distribution Function --- p.60 / Chapter Chapter 4 --- Examples and Results / Chapter 4.1 --- Quartic Anharmonic Oscillator / Chapter 4.1.1 --- "Free Energy, Internal Energy and Specific Heat" --- p.69 / Chapter 4.1.2 --- Particle Distribution Function --- p.87 / Chapter 4.2 --- Symmetric Double-well Potential / Chapter 4.2.1 --- "Free Energy, Internal Energy and Specific Heat" --- p.88 / Chapter 4.2.2 --- Particle Distribution Function --- p.106 / Chapter 4.3 --- Quartic-cubic Anharmonic Potential / Chapter 4.3.1 --- Free Energy --- p.108 / Chapter 4.3.2 --- Particle Distribution Function --- p.115 / Chapter Chapter 5 --- Application to the One-dimensional Ginzburg-Landau Model / Chapter 5.1 --- Introduction --- p.120 / Chapter 5.2 --- Exact Partition Function and Free Energy Per Unit Length --- p.123 / Chapter 5.3 --- Zeroth Order Approximation to Free Energy Per Unit Length --- p.126 / Chapter 5.4 --- Exact Specific Heat --- p.133 / Chapter 5.5 --- Zeroth Order Approximation to Specific Heat --- p.139 / Chapter Chapter 6 --- Conclusion --- p.141 / Chapter Appendix I --- Functional Calculus - Differentiation --- p.145 / Chapter Appendix II --- Evaluation of Feynman Propagator Δf(τ) --- p.147 / Chapter Appendix III --- Vanishing of the First Order Correction-βf1 --- p.150 / Chapter Appendix IV --- Numerical Method for the Energy Eigenvalues and Eigenfunctions of the One-dimensional Schroedinger Equation with ax2 + bx4 Potential --- p.153 / Chapter Appendix V --- Numerical Integrations with imaginary Ω --- p.158 / References --- p.162 / Figures --- p.165

by Vincent Hung Hin Yan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 76-77). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter §1.1 --- Classical approaches and their limitations --- p.1 / Chapter §1.2 --- New approach --- p.3 / Chapter Chapter 2 --- Two-dimensional Ordinal Square Tables --- p.5 / Chapter §2.1 --- Model --- p.5 / Chapter §2.2 --- Maximum likelihood estimator --- p.7 / Chapter §2.3 --- Optimization procedure --- p.8 / Chapter §2.4 --- Useful hypotheses --- p.9 / Chapter §2.5 --- Simulation study --- p.11 / Chapter §2.6 --- A real example --- p.18 / Chapter §2.7 --- Comparison of new and classical approaches --- p.22 / Chapter Chapter 3 --- Multi-dimensional Ordinal Tables --- p.25 / Chapter §3.1 --- Partition maximum likelihood estimator --- p.26 / Chapter §3.2 --- Optimization procedure --- p.28 / Chapter §3.3 --- Useful hypotheses --- p.37 / Chapter §3.4 --- Simulation study --- p.39 / Chapter Chapter 4 --- Conclusion --- p.45 / Tables --- p.48 / Appendix --- p.74 / References --- p.77

by Jian-Wei Chen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 84-86). / Chapter Chapter 1 --- Introduction / Chapter 1.1 --- Introduction --- p.1 / Chapter 1.2 --- Bayesian approach to single variable sampling plan for the exponential distribution --- p.3 / Chapter 1.3 --- Outline of the thesis --- p.7 / Chapter Chapter 2 --- Single Variable Sampling Plan With Type II Censoring / Chapter 2.1 --- Model --- p.10 / Chapter 2.2 --- Loss function and finite algorithm --- p.13 / Chapter 2.3 --- Numerical examples and sensitivity analysis --- p.17 / Chapter Chapter 3 --- Double Variable Sampling Plan With Type II Censoring / Chapter 3.1 --- Model --- p.25 / Chapter 3.2 --- Loss function and Bayes risk --- p.27 / Chapter 3.3 --- Discretization method and numerical analysis --- p.33 / Chapter Chapter 4 --- Bayesian Approach to Single Variable Sampling Plans for General Life Distribution with Type I Censoring / Chapter 4.1 --- Model --- p.42 / Chapter 4.2 --- The case of the Weibull distribution --- p.47 / Chapter 4.3 --- The case of the two-parameter exponential distribution --- p.49 / Chapter 4.4 --- The case of the gamma distribution --- p.52 / Chapter 4.5 --- Numerical examples and sensitivity analysis --- p.54 / Chapter Chapter 5 --- Discussions / Chapter 5.1 --- Comparison between Bayesian variable sampling plans and OC curve sampling plans --- p.63 / Chapter 5.2 --- Comparison between single and double sampling plans --- p.64 / Chapter 5.3 --- Comparison of both models --- p.66 / Chapter 5.4 --- Choice of parameters and coefficients --- p.66 / Appendix --- p.78 / References --- p.84

by Tsz-Kit Keung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaf 81). / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Testing Testable Hypotheses in Linear Models --- p.8 / Chapter 2.1 --- A General Theory --- p.9 / Chapter 2.2 --- The Method of Peixoto --- p.17 / Chapter 2.3 --- The Method of Chan and Li --- p.23 / Chapter Chapter 3 --- A New Method of Obtaining Equivalent Hypotheses --- p.32 / Chapter Chapter 4 --- Constrained Linear Models --- p.44 / Chapter 4.1 --- Hypothesis Testing in Constrained Linear Models --- p.44 / Chapter 4.2 --- Linear Models with Missing Observations --- p.50 / Chapter Chapter 5 --- Conclusions --- p.71 / Appendix --- p.74 / References --- p.81