published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

In recent years technical trading rules are widely known by more and more people, not only the academics many investors also learn to apply them in financial markets. One approach of constructing technical trading rules is to use technical indicators, such as moving average(MA) and filter rules. These trading rules are widely used possibly because the technical indicators are simple to compute and can be programmed easily. An alternative approach of constructing technical trading rules is to rely on some chart patterns. However, the patterns and signals detected by these rules are often made by the visual inspection through human eyes. As for as I know, there are no universally acceptable methods of constructing the chart patterns. In 2000, Prof. Andrew Lo and his colleagues are the first ones who define five pairs of chart patterns mathematically. They are Head-and-Shoulders(HS) & Inverted Headand- Shoulders(IHS), Broadening tops(BTOP) & bottoms(BBOT), Triangle tops(TTOP) & bottoms(TBOT), Rectangle tops(RTOP) & bottoms( RBOT) and Double tops(DTOP) & bottoms(DBOT). The basic formulation of a chart pattern consists of two steps: detection of (i) extreme points of a price series; and (ii) shape of the pattern. In Lo et al.(2000), the method of kernel smoothing was used to identify the extreme points. It was admitted by Lo et al. (2000) that the optimal bandwidth used in kernel method is not the best choice and the expert judgement is needed in detecting the bandwidth. In addition, their work considered chart pattern detection only but no buy/sell signal detection. It should be noted that it is possible to have a chart pattern formed without a signal detected, but in this case no transaction will be made. In this thesis, I propose a new class of technical trading rules which aims to resolve the above problems. More specifically, each chart pattern is parameterized by a set of parameters which governs the shape of the pattern, the entry and exit signals of trades. Then the optimal set of parameters can be determined by using genetic algorithms (GAs). The advantage of GA is that they can deal with a high-dimensional optimization problems no matter the parameters to be optimized are continuous or discrete. In addition, GA can also be convenient to use in the situation that the fitness function is not differentiable or has a multi-modal surface. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Traditional open interventions have been progressively replaced with minimally invasive techniques. Most notably, direct visual feedback is transitioned into indirect, image-based feedback, leading to the wide use of image-guided interventions (IGIs). One essential process of all IGIs is to align some 3D data with 2D images of patient through a procedure called 3D-2D registration during interventions to provide better guidance and richer information. When the 3D data is unavailable, a realistic 3D patient-speci_c model needs to be constructed from a few 2D images. The dominating methods that use only image intensity have narrow convergence range and are not robust to foreign objects presented in 2D images but not existed in 3D data. Feature-based methods partly addressed these problems, but most of them heavily rely on a set of \best" paired correspondences and requires clean image features. Moreover, the optimization procedures used in both kinds of methods are not e_cient. In this dissertation, two topics have been studied and novel algorithms proposed, namely, contour extraction from X-ray images and feature-based rigid/deformable 3D-2D registration. Inspired by biological and neuropsychological characteristics of primary visual cortex (V1), a contour detector is proposed for simultaneously extracting edges and lines in images. The synergy of V1 neurons is mimicked using phase congruency and tensor voting. Evaluations and comparisons showed that the proposed method outperformed several commonly used methods and the results are consistent with human perception. Moreover, the cumbersome \_ne-tuning" of parameter values is not always necessary in the proposed method. An extensible feature-based 3D-2D registration framework is proposed by rigorously formulating the registration as a probability density estimation problem and solving it via a generalized expectation maximization algorithm. It optimizes the transformation directly and treats correspondences as nuisance parameters. This is signi_cantly di_erent from almost all feature-based method in the literature that _rst single out a set of \best" correspondences and then estimate a transformation associated with it. This property makes the proposed algorithm not rely on paired correspondences and thus inherently robust to outliers. The framework can be adapted as a point-based method with the major advantages of 1) independency on paired correspondences, 2) accurate registration using a single image, and 3) robustness to the initialization and a large amount of outliers. Extended to a contour-based method, it di_ers from other contour-based methods mainly in that 1) it does not rely on correspondences and 2) it incorporates gradient information via a statistical model instead of a weighting function. Tuning into model-based deformable registration and surface reconstruction, our method solves the problem using the maximum penalized likelihood estimation. Unlike almost all other methods that handle the registration and deformation separately and optimized them sequentially, our method optimizes them simultaneously. The framework was evaluated in two example clinical applications and a simulation study for point-based, contour-based and surface reconstruction, respectively. Experiments showed its sub-degree and sub-millimeter registration accuracy and superiority to the state-of-the-art methods. It is expected that our algorithms, when thoroughly validated, can be used as valuable tools for image-guided interventions. / published_or_final_version / Orthopaedics and Traumatology / Doctoral / Doctor of Philosophy

Monitoring and detection of abrupt changes for multivariate processes are becoming increasingly important in modern manufacturing environments. Typical equipment may have multiple key variables to be measured continuously. Hotelling's 〖T 〗^2and CUSUM charts were widely applied to solve the problem of monitoring the mean vector of multivariate quality measurements. Besides, a new multivariate cumulative sum chart (MCUSUM) is introduced where the target shift mean is assumed to be a weighted sum of principal directions of the population covariance matrix. In practical problems, estimated parameters are needed and the properties of control charts differ from the case where the parameters are known in advance. In particular, it has been observed that the average run length (ARL), a performance indicator of the control charts, is larger when the estimated parameters are used. As a first contribution we provide a general and formal proof of the phenomenon. Also, to design an efficient 〖T 〗^2 or CUSUM chart with estimated parameters, a method to calculate or approximate the ARL function is necessarily needed. A commonly used approach consists in tabulating reference values using extensive Monte-Carlo simulation. By a different approach in thesis, an analytical approximation for the ARL function in univariate case is provided, especially in-control ARL function, which can help to directly set up control limits for different sample sizes of Phase I procedure instead of conducting complex simulation. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Genetic association study is a useful tool to identify the genetic component that is responsible for a disease. The phenomenon that a certain gene expresses in a parent-of-origin manner is referred to as genomic imprinting. When a gene is imprinted, the performance of the disease-association study will be affected. This thesis presents statistical testing methods developed specially for nuclear family data centering around the genetic association studies incorporating imprinting effects. For qualitative diseases with binary outcomes, a class of TDTI* type tests was proposed in a general two-stage framework, where the imprinting effects were examined prior to association testing. On quantitative trait loci, a class of Q-TDTI(c) type tests and another class of Q-MAX(c) type tests were proposed. The proposed testing methods flexibly accommodate families with missing parental genotype and with multiple siblings. The performance of all the methods was verified by simulation studies. It was found that the proposed methods improve the testing power for detecting association in the presence of imprinting. The class of TDTI* tests was applied to a rheumatoid arthritis study data. Also, the class of Q-TDTI(c) tests was applied to analyze the Framingham Heart Study data. The human microbiome is the collection of the microbiota, together with their genomes and their habitats throughout the human body. The human microbiome comprises an inalienable part of our genetic landscape and contributes to our metabolic features. Also, current studies have suggested the variety of human microbiome in human diseases. With the high-throughput DNA sequencing, the human microbiome composition can be characterized based on bacterial taxa relative abundance and the phylogenetic constraint. Such taxa data are often high-dimensional overdispersed and contain excessive number of zeros. Taking into account of these characteristics in taxa data, this thesis presents statistical methods to identify associations between covariate/outcome and the human microbiome composition. To assess environmental/biological covariate effect to microbiome composition, an additive logistic normal multinomial regression model was proposed and a group l1 penalized likelihood estimation method was further developed to facilitate selection of covariates and estimation of parameters. To identify microbiome components associated with biological/clinical outcomes, a Bayesian hierarchical regression model with spike and slab prior for variable selection was proposed and a Markov chain Monte Carlo algorithm that combines stochastic variable selection procedure and random walk metropolis-hasting steps was developed for model estimation. Both of the methods were illustrated using simulations as well as a real human gut microbiome dataset from The Penn Gut Microbiome Project. / published_or_final_version / Statistics and Actuarial Science / Doctoral / Doctor of Philosophy

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published_or_final_version / abstract / toc / Industrial and Manufacturing Systems Engineering / Master / Master of Philosophy

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