This dissertation proposes a suite of novel Bayesian semiparametric estimators for a proportional hazard function associated with the gaptimes, or inter-arrival times, of a counting process in survival analysis. The Cox model is applied and extended in order to identify the subsequent effect of an event on future events in a system with renewal. The estimators may also be applied, without changes, to model the effect of a point treatment on subsequent events, as well as the effect of an event on subsequent events in neighboring subjects. These Bayesian semiparametric estimators are used to analyze the survival and reliability of the New York City electric grid. In particular, the phenomenon of "infant mortality," whereby electrical supply units are prone to immediate recurrence of failure, is flexibly quantified as a period of increased risk. In this setting, the Cox model removes the significant confounding effect of seasonality. Without this correction, infant mortality would be misestimated due to the exogenously increased failure rate during summer months and times of high demand. The structural assumptions of the Bayesian estimators allow the use and interpretation of sparse event data without the rigid constraints of standard parametric models used in reliability studies.

Documenting the extent of cellular diversity is a critical step in defining the functional organization of the nervous system. In this context, we sought to develop statistical methods capable of revealing underlying cellular diversity given incomplete data sampling - a common problem in biological systems, where complete descriptions of cellular characteristics are rarely available. We devised a sparse Bayesian framework that infers cell type diversity from partial or incomplete transcription factor expression data. This framework appropriately handles estimation uncertainty, can incorporate multiple cellular characteristics, and can be used to optimize experimental design. We applied this framework to characterize a cardinal inhibitory population in the spinal cord. Animals generate movement by engaging spinal circuits that direct precise sequences of muscle contraction, but the identity and organizational logic of local interneurons that lie at the core of these circuits remain unresolved. By using our Sparse Bayesian approach, we showed that V1 interneurons, a major inhibitory population that controls motor output, fractionate into diverse subsets on the basis of the expression of nineteen transcription factors. Transcriptionally defined subsets exhibit highly structured spatial distributions with mediolateral and dorsoventral positional biases. These distinctions in settling position are largely predictive of patterns of input from sensory and motor neurons, arguing that settling position is a determinant of inhibitory microcircuit organization. Finally, we extensively validated inferred cell types by direct experimental measurement and then, extend our Bayesian framework to full transcriptome technologies. Together, these findings provide insight into the diversity and organizational logic through which inhibitory microcircuits shape motor output.

This three-article dissertation aims to apply Bayesian data analysis to improve the methodologies that process effectiveness findings, cost information and subjective judgments with the purpose of providing clear, localized guidance for decision makers in educational resource allocation. The first article shows how to use a Bayesian hierarchical model to capture the uncertainty of the effectiveness-cost ratio. The uncertainty information produced by the model may inform the decision makers of the best- and worst-case scenarios of the program efficiency if it is replicated. The second article introduces Bayesian decision theory to address a subset of methodological barriers that hamper the influence of research on educational decision-making, including how to generalize or extrapolate effectiveness and cost information from the evaluation site(s) to a specific context, how to incorporate information from multiple sources, and how to aggregate multiple consequences of an intervention into one framework. The purpose of this article is to generate evidence of program comparison that applies to a specific school facing a decision problem by incorporating the decision-makers' subjective judgements and modeling their specific preference on multiple consequences. The third article proposes a randomized control trial to detect whether principals and practitioners update their beliefs on the effectiveness and cost of educational programs in the light of uncertainty information and localized evidence. Supplemented by a pilot qualitative study that guides decision makers to work on self-defined decision problems, the pilot testing of the experiment provides some evidence on the plausibility of using an experiment to identify the causal impact of research evidence on decision-making.

Sample surveys are often used to collect data for obtaining estimates of finite population quantities, such as disease prevalence. However, non-response and sampling frame under-coverage can cause the survey sample to differ from the target population in important ways. To reduce bias in the survey estimates that can arise from these differences, auxiliary information about the target population from sources including administrative files or census data can be used. Survey weighting is one approach commonly used to reduce bias. Although weighted estimates are relatively easy to obtain, they can be inefficient in the presence of highly dispersed weights. Model-based estimation in survey research offers advantages of improved efficiency in the presence of sparse data and highly variable weights. However, these models can be subject to model misspecification. In this dissertation, we propose Bayesian penalized spline regression models for survey inference about proportions in the entire population as well as in sub-populations. The proposed methods incorporate survey weights as covariates using a penalized spline to protect against model misspecification. We show by simulations that the proposed methods perform well, yielding efficient estimates of population proportion for binary survey data in the presence of highly dispersed weights and robust to model misspecification for survey outcomes. We illustrate the use of the proposed methods to estimate the prevalence of lifetime temper dysregulation disorder among National Guard service members overall and in sub-populations defined by gender and race using the Ohio Army National Guard Mental Health Initiative 2008-2009 survey data. We further extend the proposed framework to the setting where individual auxiliary data for the population are not available and utilize a Bayesian bootstrap approach to complete model-based estimation of current and undiagnosed depression in Hispanics/Latinos of different national backgrounds from the 2015 Washington Heights Community Survey.

Bayesian statistical procedures use probabilistic models and probability distributions to summarize data, estimate unknown quantities of interest, and predict future observations. The procedures borrow strength from other observations in the dataset by using prior distributions and/or hierarchical model specifications. The unique posterior sampling techniques can handle different issues, e.g., missing data, imputation, and extraction of parameters (and their functional forms) that would otherwise be difficult to address using conventional methods. In this dissertation, we propose Bayesian modeling strategies to address various challenges arising in the fields of neuroscience and medicine. Specifically, we propose a sparse Bayesian hierarchical Vector Autoregressive (VAR) model to map human brain connectivity using multi-subject multi-session functional magnetic resonance image (fMRI) data. We use the same model on patient diary databases, focusing on patient-level prediction of medical conditions using posterior predictive samples. We also propose a Bayesian model with an augmented Markov Chain Monte Carlo (MCMC) algorithm on repeat Electrical Stimulation Mappings (ESM) to evaluate the variability of localization in brain sites responsible for language function. We close by using Bayesian disproportionality analyses on spontaneous reporting system (SRS) databases for post-market drug safety surveillance, illustrating the caution required in real-world analysis and decision making.

A maioria dos textos na literatura de testes de hipóteses trata de critérios de otimalidade para um determinado problema de decisão. No entanto, existem, em menor quantidade, alguns textos sobre os problemas de se realizar testes de hipóteses simultâneos e sobre a concordância lógica de suas soluções ótimas. Algo que se espera de testes de hipóteses simultâneos e que, se uma hipótese H1 implica uma hipótese H0, então é desejável que a rejeição da hipótese H0 necessariamente implique na rejeição da hipótese H1, para uma mesma amostra observada. Essa propriedade é chamada aqui de monotonicidade. A fim de estudar essa propriedade sob um ponto de vista mais geral, neste trabalho é definida a nocão de classe de testes de hipóteses, que estende a funcão de teste para uma sigma-álgebra de possíveis hipóteses nulas, e introduzida uma definição de monotonicidade. Também é mostrado, por meio de alguns exemplos simples, que, para um nível de signicância fixado, a classe de testes Razão de Verossimilhanças Generalizada (RVG) não apresenta monotonicidade, ao contrário de testes formulados sob a perspectiva bayesiana, como o teste de Bayes baseado em probabilidades a posteriori, o teste de Lindley e o FBST. Porém, são verificadas, sob a teoria da decisão, quando possível, quais as condições suficientes para que uma classe de testes de hipóteses tenha monotonicidade. / Most of the texts in the literature of hypothesis testing deal with optimality criteria for a single decision problem. However, there are, to a lesser extent, texts on the problem of simultaneous hypothesis testing and the logical consistency of the optimal solutions of such procedures. For instance, the following property should be observed in simultaneous hypothesis testing: if a hypothesis H implies a hypothesis H0, then, on the basis of the same sample observation, the rejection of the hypothesis H0 necessarily should imply the rejection of the hypothesis H. Here, this property is called monotonicity. To investigate this property under a more general point of view, in this work, it is dened rst the notion of a class of hypothesis testing, which extends the test function to a sigma-eld of possible null hypotheses, and then the concept of monotonicity is introduced properly. It is also shown, through some simple examples, that for a xed signicance level, the class of Generalized Likelihood Ratio tests (GLR) does not meet monotonicity, as opposed to tests developed under the Bayesian perspective, such as Bayes tests based on posterior probabilities, Lindleys tests and Full Bayesian Signicance Tests (FBST). Finally, sucient conditions for a class of hypothesis testing to have monotonicity are determined, when possible, under a decision-theoretic approach.

An, Yujia. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 71-76). / Abstracts in English and Chinese. / Abstract --- p.ii / Acknowledgement --- p.iv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background --- p.1 / Chapter 1.1.1 --- Review on BFA --- p.2 / Chapter 1.1.2 --- Review on NFA --- p.3 / Chapter 1.1.3 --- Typical model selection criteria --- p.5 / Chapter 1.1.4 --- New model selection criterion and automatic model selection --- p.6 / Chapter 1.2 --- Our contributions --- p.7 / Chapter 1.3 --- Thesis outline --- p.8 / Chapter 2 --- Combination of B and BI architectures for BFA with automatic model selection --- p.10 / Chapter 2.1 --- Implementation of BFA using BYY harmony learning with au- tomatic model selection --- p.11 / Chapter 2.1.1 --- Basic issues of BFA --- p.11 / Chapter 2.1.2 --- B-architecture for BFA with automatic model selection . --- p.12 / Chapter 2.1.3 --- BI-architecture for BFA with automatic model selection . --- p.14 / Chapter 2.2 --- Local minima in B-architecture and BI-architecture --- p.16 / Chapter 2.2.1 --- Local minima in B-architecture --- p.16 / Chapter 2.2.2 --- One unstable result in BI-architecture --- p.21 / Chapter 2.3 --- Combination of B- and BI-architecture for BFA with automatic model selection --- p.23 / Chapter 2.3.1 --- Combine B-architecture and BI-architecture --- p.23 / Chapter 2.3.2 --- Limitations of BI-architecture --- p.24 / Chapter 2.4 --- Experiments --- p.25 / Chapter 2.4.1 --- Frequency of local minima occurring in B-architecture --- p.25 / Chapter 2.4.2 --- Performance comparison for several methods in B-architecture --- p.26 / Chapter 2.4.3 --- Comparison of local minima in B-architecture and BI- architecture --- p.26 / Chapter 2.4.4 --- Frequency of unstable cases occurring in BI-architecture --- p.27 / Chapter 2.4.5 --- Comparison of performance of three strategies --- p.27 / Chapter 2.4.6 --- Limitations of BI-architecture --- p.28 / Chapter 2.5 --- Summary --- p.29 / Chapter 3 --- A Comparative Investigation on Model Selection in Binary Factor Analysis --- p.31 / Chapter 3.1 --- Binary Factor Analysis and ML Learning --- p.32 / Chapter 3.2 --- Hidden Factors Number Determination --- p.33 / Chapter 3.2.1 --- Using Typical Model Selection Criteria --- p.33 / Chapter 3.2.2 --- Using BYY harmony Learning --- p.34 / Chapter 3.3 --- Empirical Comparative Studies --- p.36 / Chapter 3.3.1 --- Effects of Sample Size --- p.37 / Chapter 3.3.2 --- Effects of Data Dimension --- p.37 / Chapter 3.3.3 --- Effects of Noise Variance --- p.39 / Chapter 3.3.4 --- Effects of hidden factor number --- p.43 / Chapter 3.3.5 --- Computing Costs --- p.43 / Chapter 3.4 --- Summary --- p.46 / Chapter 4 --- A Comparative Investigation on Model Selection in Non-gaussian Factor Analysis --- p.47 / Chapter 4.1 --- Non-Gaussian Factor Analysis and ML Learning --- p.48 / Chapter 4.2 --- Hidden Factor Determination --- p.51 / Chapter 4.2.1 --- Using typical model selection criteria --- p.51 / Chapter 4.2.2 --- BYY harmony Learning --- p.52 / Chapter 4.3 --- Empirical Comparative Studies --- p.55 / Chapter 4.3.1 --- Effects of Sample Size on Model Selection Criteria --- p.56 / Chapter 4.3.2 --- Effects of Data Dimension on Model Selection Criteria --- p.60 / Chapter 4.3.3 --- Effects of Noise Variance on Model Selection Criteria --- p.64 / Chapter 4.3.4 --- Discussion on Computational Cost --- p.64 / Chapter 4.4 --- Summary --- p.68 / Chapter 5 --- Conclusions --- p.69 / Bibliography --- p.71

行为学、社会学、心理学和医药学方面，结构方程模型(SEMs) 是研究有关潜在变量最常用的模型。这篇论文的目的是研究基本和高级结构方程模型的贝叶斯诊断，本文研究的结构方程模型包括非线性纺构方程模型、变换结构方程模型、二层结构方程模型和混合结构方程模型。基于对数贝叶斯因子的一阶与二阶局部影响测度是本文进行贝贝叶斯诊断的基础。局部影响测度的计算和模型参数估计是利用了蒙特卡洛(MCMC) 和扩展数据的方法。对比传统的基于极大似然的诊断，本文提出的贝叶斯诊断方法不仅能检测异常点或者影响点，而且可以诊断模型假设和先验设定的敏感性。 这些是通过对数据、模型假设和先验设定进行不同的扰动获得的 本文用大量的模拟实验来说明所提出的贝叶斯诊断方法的作用。 本文基于不同类型的结构方程模型，应用所提出的贝叶斯诊断方法于一些实际数据。 / In the behavioral, social, psychological, and medical sciences, the most widely used models in assessing latent variables are structural equation models (SEMs). This thesis aims to develop Bayesian diagnostic procedures for basic and advanced SEMs such as nonlinear SEMs, transformation SEMs, two-level SEMs, and mixture SEMs. The first- and second-order local inference measures with the objective functions defined based on the logarithm of Bayes factor are proposed to perform the Bayesian diagnostics. Markov chain Monte Carlo (MCMC) methods, along with data augmentation, are developed to compute the local influence measures and to estimate unknown model parameters. Compared with conventional maximum likelihood-based diagnostic procedures, the proposed Bayesian diagnostic approach can not only detect outliers or influential points in the observed data, but also conduct model comparison and sensitivity analysis by perturbing the data, sampling distributions, and the prior distributions of model parameters via a variety of perturbations. The empirical performances of the proposed Bayesian diagnostic procedures are revealed through extensive simulation studies. Several real-life data sets are used to illustrate the application of our proposed methodology in the context of different SEMs. / Detailed summary in vernacular field only. / Chen, Ji. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 130-135). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Structural equation models --- p.1 / Chapter 1.2 --- Bayesian diagnostics --- p.3 / Chapter 1.2.1 --- The first and second order local influence measures --- p.5 / Chapter 1.2.2 --- A simple example --- p.9 / Chapter 2 --- Bayesian diagnostics of nonlinear SEMs --- p.15 / Chapter 2.1 --- Model description --- p.16 / Chapter 2.2 --- Bayesian estimation and local inference of nonlinear SEMs --- p.17 / Chapter 2.3 --- Simulation study --- p.24 / Chapter 2.3.1 --- Simulation study 1 --- p.24 / Chapter 2.3.2 --- Simulation study 2 --- p.25 / Chapter 2.3.3 --- Simulation study 3 --- p.27 / Chapter 2.4 --- Application: A study of kidney disease for type 2 diabetic patients --- p.29 / Chapter 3 --- Bayesian diagnostics of transformation SEMs --- p.40 / Chapter 3.1 --- Model description --- p.41 / Chapter 3.2 --- Bayesian estimation and local inference of the transformation SEMs --- p.44 / Chapter 3.3 --- Simulation study --- p.54 / Chapter 3.3.1 --- Simulation study 1 --- p.54 / Chapter 3.3.2 --- Simulation study 2 --- p.56 / Chapter 3.4 --- Application: A study on the risk factors of osteoporotic fracture in older people --- p.58 / Chapter 4 --- Bayesian diagnostics of two-level SEMs --- p.73 / Chapter 4.1 --- Model description --- p.74 / Chapter 4.2 --- Bayesian estimation and local inference of two-level SEMs --- p.75 / Chapter 4.3 --- Simulation study --- p.88 / Chapter 4.4 --- Application: A study of AIDS data --- p.91 / Chapter 5 --- Bayesian diagnostics of mixture SEMs --- p.106 / Chapter 5.1 --- Model description --- p.107 / Chapter 5.2 --- Bayesian estimation and local inference ofmixture SEMs --- p.108 / Chapter 5.3 --- Simulation study --- p.116 / Chapter 5.3.1 --- Simulation study 1 --- p.116 / Chapter 5.3.2 --- Simulation study 2 --- p.118 / Chapter 6 --- Conclusion --- p.126 / Bibliography --- p.130 / Chapter A --- Proof of Theorem 1.1 and 1.2 --- p.136 / Chapter B --- Full conditional distributions of the nonlinear SEM --- p.138 / Chapter C --- Full conditional distributions of the transformation SEM --- p.141 / Chapter D --- Full conditional distributions of the two-level SEM --- p.144 / Chapter E --- AIDS preventative intervention data --- p.150 / Chapter F --- Permutation sampler in the mixture SEM --- p.152 / Chapter G --- Full conditional distributions of the mixture SEM --- p.153

In medical, behavioral, and social-psychological sciences, latent variable models are useful in handling variables that cannot be directly measured by a single observed variable, but instead are assessed through a number of observed variables. Traditional latent variable models are usually based on parametric assumptions on both relations between outcome and explanatory latent variables, and error distributions. In this thesis, semiparametric models with Bayesian P-splines are developed to relax these rigid assumptions. / In the fourth part of the thesis, the methodology developed in the third part is further extended to a varying coefficient model with latent variables. Varying coefficient model is a class of flexible semiparametric models in which the effects of covariates are modeled dynamically by unspecified smooth functions. A transformation varying coefficient model can handle arbitrarily distributed dynamic data. A simulation study shows that our proposed method performs well in the analysis of this complex model. / In the last part of the thesis, we propose a finite mixture of varying coefficient models to analyze dynamic data with heterogeneity. A simulation study demonstrates that our proposed method can explore possible existence of different groups in a dynamic data, where in each group the dynamic influences of covariates on the response variables have different patterns. The proposed method is applied to a longitudinal study concerning the effectiveness of heroin treatment. Distinct patterns of heroin use and treatment effect in different patient groups are identified. / In the second part of the thesis, a latent variable model is proposed to relax the first assumption, in which unknown additive functions of latent variables in the structural equation are modeled by Bayesian P-splines. The estimation of nonparametric functions is based on powerful Markov chain Monte Carlo (MCMC) algorithm with block update scheme. A simulation study shows that the proposed method can handle much wider situation than traditional models. The proposed semiparametric latent variable model is applied to a study on osteoporosis prevention and control. Some interesting functional relations, which may be overlooked by traditional parametric latent variable models, are revealed. / In the third part of the thesis, a transformation model is developed to relax the second assumption, which usually assumes the normality of observed variables and random errors. In our proposed model, the nonnormal response variables are transformed to normal by unknown functions modeled with Bayesian P-splines. This semiparametric transformation model is shown to be applicable to a wide range of statistical analysis. The model is applied to a study on the intervention treatment of polydrug use in which the traditional model assumption is violated because many observed variables exhibit serious departure from normality. / Lu, Zhaohua. / Adviser: Xin-Yuan Song. / Source: Dissertation Abstracts International, Volume: 72-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 119-130). / 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 Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

Latent variable models (LVMS) are widely appreciated multivariate methods to explore variables that are related to the observed variables, and assessing the relationships among them. One of most widely used latent variable models is structural equation model (SEM). Based on more than a dozen standard packages for fitting SEMs, such as LISREL VIII (Jorskog and Sorbom, 1996), and EQS (Bentler, 2004), these models have been widely appreciated in behavioral, educational, medical, social, and psychological research. The statistical theories and methods in these packages are based on the normal distribution; hence, they are vulnerable to outliers and the non-normal assumption. As outliers and non-normal data set are commonly encountered in substantive research, this fundamental problem has received much attention in the field. However, almost all existing methods are developed via the covariance structure analysis approach that heavily depends on the asymptotical properties of the sample covariance matrices S. Hence, this approach cannot be applied to the more complex SEMs and/or SEMs with more complex data structure such as missing data, because under these more complicated situations S is complicated, and its asymptotical properties are not well known. The objectives of this thesis are to develop novel robust methods for analyzing complex SEMs and/or more data structures, including but not limited to nonlinear SEMs with missing data. Both maximum likelihood (ML) and Bayesian approaches for estimation, hypothesis testing and model comparison will be investigated. Efficient algorithm for computing the results for statistical inference will be developed through unitization and modification of the advanced tools in statistical computing, for example the Monte Carlo Expectation-Maximization algorithm, and the Markov Chains Monte Carlo methods. Asymptotical properties of some statistics are derived. Simulation studies and real examples are conducted to reveal the empirical performance of the Bayesian and ML approaches. The newly developed methodologies will be very useful for analyzing complex data in the substantive research. / Xia Yemao. / "October 2005." / Adviser: S. Y. Lee. / Source: Dissertation Abstracts International, Volume: 67-07, Section: B, page: 3883. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 105-114). / 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. / Abstract in English and Chinese. / School code: 1307.