Diffusion tensor imaging (DTI) is a relatively new technology of magnetic resonance imaging, which enables us to observe the insight structure of the human body in vivo and non-invasively. It displays water molecule movement by a 3×3 diffusion tensor at each voxel. Tensor field processing, visualisation and tractography are all based on the diffusion tensors. The accuracy of estimating diffusion tensor is essential in DTI. This research focuses on exploring the potential improvements at the tensor estimation of DTI. We analyse the noise arising in the measurement of diffusion signals. We present robust methods, least median squares (LMS) and least trimmed squares (LTS) regressions, with forward search algorithm that reduce or eliminate outliers to the desired level. An investigation of the criterion to detect outliers is provided in theory and practice. We compare the results with the generalised non-robust models in simulation studies and applicants and also validated various regressions in terms of FA, MD and orientations. We show that the robust methods can handle the data with up to 50% corruption. The robust regressions have better estimations than generalised models in the presence of outliers. We also consider the multiple tensors problems. We review the recent techniques of multiple tensor problems. Then we provide a new model considering neighbours' information, the Bayesian single and double tensor models using neighbouring tensors as priors, which can identify the double tensors effectively. We design a framework to estimate the diffusion tensor field with detecting whether it is a single tensor model or multiple tensor model. An output of this framework is the Bayesian neighbour (BN) algorithm that improves the accuracy at the intersection of multiple fibres. We examine the dependence of the estimators on the FA and MD and angle between two principal diffusion orientations and the goodness of fit. The Bayesian models are applied to the real data with validation. We show that the double tensors model is more accurate on distinct fibre orientations, more anisotropic or similar mean diffusivity tensors. The final contribution of this research is in covariance tensor estimation. We define the median covariance matrix in terms of Euclidean and various non-Euclidean metrics taking its symmetric semi-positive definiteness into account. We compare with estimation methods, Euclidean, power Euclidean, square root Euclidean, log-Euclidean, Riemannian Euclidean and Procrustes median tensors. We provide an analysis of the different metric between different median covariance tensors. We also provide the weighting functions and define the weighted non-Euclidean covariance tensors. We finish with manifold-valued data applications that improve the illustration of DTI images in tensor field processing with defined non-weighted and weighted median tensors. The validation of non-Euclidean methods is studied in the tensor field processing. We show that the root square median estimator is preferable in general, which can effectively exclude outliers and clearly shows the important structures of the brain. The power Euclidean median estimator is recommended when producing FA map.

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

Tse Ka Ling Carol. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 72-76). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- The Factor Analysis Model --- p.1 / Chapter 1.2 --- Main Objectives --- p.2 / Chapter 1.2.1 --- Investigate the distribution of the estimated Factor Scores --- p.2 / Chapter 1.2.2 --- Propose an alternative method for getting the estimates of the LISREL model --- p.4 / Chapter 1.3 --- Summary --- p.4 / Chapter 2 --- Joint Bayesian Approach of the Factor Analysis Model --- p.6 / Chapter 2.1 --- Conditional Distribution --- p.7 / Chapter 2.1.1 --- Conditional distribution of Z given Y and θ --- p.7 / Chapter 2.1.2 --- Conditional distribution of θ given Y and Z --- p.7 / Chapter 2.2 --- Implementation of the Gibbs sampler for generating the random observations --- p.11 / Chapter 2.3 --- Bayesian Estimates and their Statistical Properties --- p.13 / Chapter 2.3.1 --- Estimates of unknown parameter --- p.13 / Chapter 2.3.2 --- Estimates of Factor Score --- p.14 / Chapter 3 --- Examine the distribution of the estimated factor scores --- p.15 / Chapter 3.1 --- The 1st Simulation Study --- p.15 / Chapter 3.2 --- The 2nd Simulation Study --- p.30 / Chapter 3.3 --- The 3rd Simulation Study --- p.31 / Chapter 4 --- An Alternative method for getting the parameter estimatesin the LISREL Model --- p.44 / Chapter 4.1 --- Full LISREL model --- p.44 / Chapter 4.2 --- Our proposed method --- p.46 / Chapter 4.3 --- Simulation Studies --- p.49 / Chapter 4.3.1 --- The 1st Simulation Study --- p.49 / Chapter 4.3.2 --- The 3rd Simulation Study --- p.50 / Chapter 4.4 --- Conclusion --- p.53 / Appendix --- p.56 / Bibliography --- p.72

在日常生活和科学研究中产生大量偏好数据，其反应一组被关注对象受偏好的程度。通常用排序数据或多元选择数据来记录观察结果。有时候关于两个对象的偏好没有明显强弱之分，导致排序产生节点，也就是所谓的删失排序。为了研究带有删失的排序数据，基于Thurstone的随机效用假设理论我们建立了一个对称贝叶斯probit模型。然而，参数识别是probit模型必须解决的问题，即确定一组潜在效用的位置和尺度。通常方法是选择其中一个对象为基，然后用其它对象的效用减去这个基的效用，最后我们关于这些效用差来建模。问题是，在用贝叶斯方法处理多元选择数据时，其预测结果对基的选择有敏感性，即选不同对象为基预测结果是不一样的。本文，我们虚构一个基，即一组对象偏好的平均。依靠这个基，我们为多元选择probit模型给出一个不依赖于对象标号的识别方法，即对称识别法。进一步，我们设计一种贝叶斯算法来估计这个模型。通过仿真研究和真实数据分析，我们发现这个贝叶斯probit模型被完全识别，而且消除通常识别法所存在的敏感性。接下来，我们把这个关于多元选择数据建立的probit模型推广到处理一般删失排序数据，即得到对称贝叶斯删失排序probit 模型。最后，我们用这个模型很好的分析了香港赌马数据。 / Vast amount of preference data arise from daily life or scientific research, where observations consist of preferences on a set of available objects. The observations are usually recorded by ranking data or multinomial data. Sometimes, there is not a clear preference between two objects, which will result in ranking data with ties, also called censored rank-ordered data. To study such kind of data, we develop a symmetric Bayesian probit model based on Thurstone's random utility (discriminal process) assumption. However, parameter identification is always an unavoidable problem for probit model, i.e., determining the location and scale of latent utilities. The standard identification method need to specify one of the utilities as a base, and then model the differences of the other utilities subtracted by the base. However, Bayesian predictions have been verified to be sensitive to specification of the base in the case of multinomial data. In this thesis, we set the average of the whole set of utilities as a base which is symmetric to any relabeling of objects. Based on this new base, we propose a symmetric identification approach to fully identify multinomial probit model. Furthermore, we design a Bayesian algorithm to fit that model. By simulation study and real data analysis, we find that this new probit model not only can be identifed well, but also remove sensitivities mentioned above. In what follows, we generalize this probit model to fit general censored rank-ordered data. Correspondingly, we get the symmetric Bayesian censored rank-ordered probit model. At last, we apply this model to analyze Hong Kong horse racing data successfully. / Detailed summary in vernacular field only. / Pan, Maolin. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 50-55). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Overview --- p.2 / Chapter 1.1.1 --- The Ranking Model --- p.2 / Chapter 1.1.2 --- Discrete Choice Model --- p.4 / Chapter 1.2 --- Methodology --- p.7 / Chapter 1.2.1 --- Data Augmentation --- p.8 / Chapter 1.2.2 --- Marginal Data Augmentation --- p.8 / Chapter 1.3 --- An Outline --- p.9 / Chapter 2 --- Bayesian Multinomial Probit Model Based On Symmetric I-denti cation --- p.11 / Chapter 2.1 --- Introduction --- p.11 / Chapter 2.2 --- The MNP Model --- p.14 / Chapter 2.3 --- Symmetric Identification and Bayesian Analysis --- p.17 / Chapter 2.3.1 --- Symmetric Identification --- p.18 / Chapter 2.3.2 --- Bayesian Analysis --- p.21 / Chapter 2.4 --- Case Studies --- p.25 / Chapter 2.4.1 --- Simulation Study --- p.25 / Chapter 2.4.2 --- Clothes Detergent Purchases Data --- p.27 / Chapter 2.5 --- Summary --- p.29 / Chapter 3 --- Symmetric Bayesian Censored Rank-Ordered Probit Model --- p.30 / Chapter 3.1 --- Introduction --- p.30 / Chapter 3.2 --- Ranking Model --- p.33 / Chapter 3.2.1 --- Ranking Data --- p.33 / Chapter 3.2.2 --- Censored Rank-Ordered Probit Model --- p.35 / Chapter 3.2.3 --- Symmetrically Identified CROP Model --- p.36 / Chapter 3.3 --- Bayesian Analysis on Symmetrically Identified CROP Model --- p.37 / Chapter 3.3.1 --- Model Estimation --- p.38 / Chapter 3.4 --- Application: Hong Kong Horse Racing --- p.41 / Chapter 3.5 --- Summary --- p.44 / Chapter 4 --- Conclusion and Further Studies --- p.45 / Chapter A --- Prior for covariance matrix with trace augmented restriction --- p.47 / Chapter B --- Derivation of sampling intervals --- p.49 / Bibliography --- p.50

The pharmaceutical industry is currently facing an industry wide problem of high attrition rates for new compounds and rising development costs. As a result of this, there is an emphasis on making the development process more ecient. By learning more about new compounds in the early stages of development, the aim is to stop ineective compounds earlier and improve dose selection for compounds that progress to phase III. One approach to this is to use adaptive designs. The focus of this thesis is on response adaptive designs within phase IIb dose-finding studies. We explore adapting the subject allocations based on accrued data, with the intention of focusing the allocation on the interesting parts of the curve and/or the best dose for phase III. In this thesis we have used simulation studies to assess the operational characteristics of a number of response adaptive designs. We found that there were consistent gains to be made by adapting when we were relatively cautious in our method of adaptation. That is, the adaptive method has the opportunity to alter the subject allocation when there is a clear signal in the data, but maintains roughly equal allocation when there is a lot of variability in the data. When we used adaptive designs that were geared to randomising subjects to a few doses, the results were more varied. In some cases the adaptation led to gains in efficacy whilst in others it was detrimental. One of the key aims of a phase IIb dose-finding study is to identify a dose to take forward into phase III. In the final chapter, we show that the way in which we choose the dose for phase III affects the expected gain, and so begin to consider how we can optimise the decision making process.

"Intelligent tutoring systems rely on student modeling to understand student behavior. The result of student modeling can provide assessment for student knowledge, estimation of student¡¯s current affective states (ie boredom, confusion, concentration, frustration, etc), prediction of student performance, and suggestion of the next tutoring steps. There are three focuses of this dissertation. The first focus is on better predicting student performance by adding more information, such as student identity and information about how many assistance students needed. The second focus is to analyze different performance and feature set for modeling student short-term knowledge and longer-term knowledge. The third focus is on improving the affect detectors by adding more features. In this dissertation I make contributions to the field of data mining as well as educational research. I demonstrate novel Bayesian networks for student modeling, and also compared them with each other. This work contributes to educational research by broadening the task of analyzing student knowledge to student knowledge retention, which is a much more important and interesting question for researchers to look at. Additionally, I showed a set of new useful features as well as how to effectively use these features in real models. For instance, in Chapter 5, I showed that the feature of the number of different days a students has worked on a skill is a more predictive feature for knowledge retention. These features themselves are not a contribution to data mining so much as they are to education research more broadly, which can used by other educational researchers or tutoring systems. "

This thesis documents work which is part of the ongoing effort by the Worcester Polytechnic Institute (WPI) Precision Personnel Locator (PPL) project, to track and locate first responders in urban/indoor settings. Specifically, the project intends to produce a system which can accurately determine the floor that a person is on, as well as where on the floor that person is, with sub-meter accuracy. The system must be portable, rugged, fast to set up, and require no pre-installed infrastructure. Several recent advances have enabled us to get closer to meeting these goals: The development of Transactional Array Reconciliation Tomography(TART) algorithm, and corresponding locator hardware, as well as the integration of barometric sensors, and a new antenna deployment scheme. To fully utilize these new capabilities, a Bayesian Fusion algorithm has been designed. The goal of this thesis is to present the necessary methods for incorporating diverse sources of information, in a constructive manner, to improve the performance of the PPL system. While the conceptual methods presented within are meant to be general, the experimental results will focus on the fusion of barometric height estimates and RF data. These information sources will be processed with our existing Singular Value Array Reconciliation Tomography (σART), and the new TART algorithm, using a Bayesian Fusion algorithm to more accurately estimate indoor locations.

"We analyze data on body mass index (BMI) in the third National Health and Nutrition Examination survey, predict finite population BMI stratified by different domains of race, sex and family income, and investigate what adjustment needed for nonresponse mechanism. We built two types of models to analyze the data. In the ignorable nonresponse models, each model is within the hierarchical Bayesian framework. For Model 1, BMI is only related to age. For Model 2, the linear regression is height on weight, and weight on age. The parameters, nonresponse and the nonsampled BMI values are generated from each model. We mainly use the composition method to obtain samples for Model 1, and Gibbs sampler to generate samples for Model 2. We also built two nonignorable nonresponse models corresponding to the ignorable nonresponse models. Our nonignorable nonresponse models have one important feature: the response indicators are not related to BMI and neither weight nor height, but we use the same parameters corresponding to the ignorable nonresponse models. We use sample important resampling (SIR) algorithm to generate parameters and nonresponse, nonsample values. Our results show that the ignorable nonresponse Model 2 (modeling height and weight) is more reliable than Model 1 (modeling BMI), since the predicted finite population mean BMI of Model 1 changes very little with age. The predicted finite population mean of BMI is affected by different domain of race, sex and family income. Our results also show that the nonignorable nonresponse models infer smaller standard deviation of regression coefficients and population BMI than in the ignorable nonresponse models. It is due to the fact that we are incorporating information from the response indicators, and there are no additional parameters. Therefore, the nonignorable nonresponse models allow wider inference."

"We analyze data (length, weight and location) from a study done by the Army Corps of Engineers along the Tennessee River basin in the summer of 1980. The purpose is to predict the probability that a hypothetical channel catfish at a location studied is toxic and contains 5 ppm or more DDT in its filet. We incorporate spatial information and treate it separetely from other covariates. Ultimately, we want to predict the probability that a catfish from the unobserved location is toxic. In a preliminary analysis, we examine the data for observed locations using frequentist logistic regression, Bayesian logistic regression, and Bayesian logistic regression with random effects. Later we develop a parsimonious extension of Bayesian logistic regression and the corresponding Gibbs sampler for that model to increase computational feasibility and reduce model parameters. Furthermore, we develop a Bayesian model to impute data for locations where catfish were not observed. A comparison is made between results obtained fitting the model to only observed data and data with missing values imputed. Lastly, a complete model is presented which imputes data for missing locations and calculates the probability that a catfish from the unobserved location is toxic at once. We conclude that length and weight of the fish have negligible effect on toxicity. Toxicity of these catfish are mostly explained by location and spatial effects. In particular, the probability that a catfish is toxic decreases as one moves further downstream from the source of pollution."

"This research introduces the structure and elements of the system used to predict the user's interested location. The combination of DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm and GMM (Gaussian Mixture Model) algorithm is used to find locations where the user usually visits. In addition, the testing result of applying other clustering algorithms such as Gaussian Mixture model, Density Based clustering algorithm and K-means clustering algorithm on actual data are also shown as comparison. With having the knowledge of locations where the user usually visits, Discrete Bayesian Network is generated from the user's time-sequence location data. Combining the Bayesian Network, the user's current location and the time when the user left the other locations, the user's interested location can be predicted."