The practice of evaluating situations with the Riverside Situational Q-Sort (RSQ:Wagerman & Funder, 2009) is relatively new. The present study aimed to investigate the theoretical framework supporting the RSQ with regards to the potential confounds of emotional state and the use of Likert-type ratings. Data were collected from a sample of Florida Atlantic University students (N = 206). Participants were primed for either a positive or negative mood state and asked to evaluate a situation with the RSQ in either the Q-Sort or Likert-type response format. Results suggested that response format has a significant influence on RSQ evaluations, but mood and the interaction between mood and response format do not. Exploratory analyses were conducted to determine the underlying mechanisms responsible. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

This thesis provides novel methodology for statistical analysis of paired high-dimensional genomic data, with the aimto identify gene interactions specific to each group of samples as well as the gene connections that change between the two classes of observations. An example of such groups can be patients under two medical conditions, in which the estimation of gene interaction networks is relevant to biologists as part of discerning gene regulatory mechanisms that control a disease process like, for instance, cancer. We construct these interaction networks fromdata by considering the non-zero structure of correlationmatrices, which measure linear dependence between random variables, and their inversematrices, which are commonly known as precision matrices and determine linear conditional dependence instead. In this regard, we study three statistical problems related to the testing, single estimation and joint estimation of (conditional) dependence structures. Firstly, we develop hypothesis testingmethods to assess the equality of two correlation matrices, and also two correlation sub-matrices, corresponding to two classes of samples, and hence the equality of the underlying gene interaction networks. We consider statistics based on the average of squares, maximum and sum of exceedances of sample correlations, which are suitable for both independent and paired observations. We derive the limiting distributions for the test statistics where possible and, for practical needs, we present a permuted samples based approach to find their corresponding non-parametric distributions. Cases where such hypothesis testing presents enough evidence against the null hypothesis of equality of two correlation matrices give rise to the problem of estimating two correlation (or precision) matrices. However, before that we address the statistical problem of estimating conditional dependence between random variables in a single class of samples when data are high-dimensional, which is the second topic of the thesis. We study the graphical lasso method which employs an L1 penalized likelihood expression to estimate the precision matrix and its underlying non-zero graph structure. The lasso penalization termis given by the L1 normof the precisionmatrix elements scaled by a regularization parameter, which determines the trade-off between sparsity of the graph and fit to the data, and its selection is our main focus of investigation. We propose several procedures to select the regularization parameter in the graphical lasso optimization problem that rely on network characteristics such as clustering or connectivity of the graph. Thirdly, we address the more general problem of estimating two precision matrices that are expected to be similar, when datasets are dependent, focusing on the particular case of paired observations. We propose a new method to estimate these precision matrices simultaneously, a weighted fused graphical lasso estimator. The analogous joint estimation method concerning two regression coefficient matrices, which we call weighted fused regression lasso, is also developed in this thesis under the same paired and high-dimensional setting. The two joint estimators maximize penalized marginal log likelihood functions, which encourage both sparsity and similarity in the estimated matrices, and that are solved using an alternating direction method of multipliers (ADMM) algorithm. Sparsity and similarity of thematrices are determined by two tuning parameters and we propose to choose them by controlling the corresponding average error rates related to the expected number of false positive edges in the estimated conditional dependence networks. These testing and estimation methods are implemented within the R package ldstatsHD, and are applied to a comprehensive range of simulated data sets as well as to high-dimensional real case studies of genomic data. We employ testing approaches with the purpose of discovering pathway lists of genes that present significantly different correlation matrices on healthy and unhealthy (e.g., tumor) samples. Besides, we use hypothesis testing problems on correlation sub-matrices to reduce the number of genes for estimation. The proposed joint estimation methods are then considered to find gene interactions that are common between medical conditions as well as interactions that vary in the presence of unhealthy tissues.

The United States health-care system is considered to be unsustainable due to its unbearably high cost. Many of the resources are spent on acute conditions rather than aiming at preventing them. Preventive medicine methods, therefore, are viewed as a potential remedy since they can help reduce the occurrence of acute health episodes. The work in this dissertation tackles two distinct problems related to the prevention of acute disease. Specifically, we consider: (1) early detection of incorrect or abnormal postures of the human body and (2) the prediction of hospitalization due to heart related diseases. The solution to the former problem could be used to prevent people from unexpected injuries or alert caregivers in the event of a fall. The latter study could possibly help improve health outcomes and save considerable costs due to preventable hospitalizations. For body posture detection, we place wireless sensor nodes on different parts of the human body and use the pairwise measurements of signal strength corresponding to all sensor transmitter/receiver pairs to estimate body posture. We develop a composite hypothesis testing approach which uses a Generalized Likelihood Test (GLT) as the decision rule. The GLT distinguishes between a set of probability density function (pdf) families constructed using a custom pdf interpolation technique. The GLT is compared with the simple Likelihood Test and Multiple Support Vector Machines. The measurements from the wireless sensor nodes are highly variable and these methods have different degrees of adaptability to this variability. Besides, these methods also handle multiple observations differently. Our analysis and experimental results suggest that GLT is more accurate and suitable for the problem. For hospitalization prediction, our objective is to explore the possibility of effectively predicting heart-related hospitalizations based on the available medical history of the patients. We extensively explored the ways of extracting information from patients' Electronic Health Records (EHRs) and organizing the information in a uniform way across all patients. We applied various machine learning algorithms including Support Vector Machines, AdaBoost with Trees, and Logistic Regression adapted to the problem at hand. We also developed a new classifier based on a variant of the likelihood ratio test. The new classifier has a classification performance competitive with those more complex alternatives, but has the additional advantage of producing results that are more interpretable. Following this direction of increasing interpretability, which is important in the medical setting, we designed a new method that discovers hidden clusters and, at the same time, makes decisions. This new method introduces an alternating clustering and classification approach with guaranteed convergence and explicit performance bounds. Experimental results with actual EHRs from the Boston Medical Center demonstrate prediction rate of 82% under 30% false alarm rate, which could lead to considerable savings when used in practice.

Typescript (photocopy). / Digitized by Kansas Correctional Industries

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.

A technique called gaussian temporal factor analysis (gaussian TFA) proposed by Xu in 2000 may be used to test the APT model under the mild assumption that the efficient market hypothesis (EMH) is violated. We are motivated to investigate statistical behaviors of the gaussian TFA model. / According to a recent survey by Cochrane (1999), the multi-factor APT model is gaining popularity and recognition over CAPM by the investment community. While empirical evidence shows that mutual funds can earn average returns not explained by the CAPM by following a variety of investment styles, this anomaly could be captured by APT which includes the single-factor CAPM as a special case. Yet, three aspects of APT still cannot be tested in practice. / First, a systematic testing package is proposed for testing gaussian TFA in six dimensions, including factor number, factor loadings, residuals correlations and autoregressive conditional heteroscedasticity (ARCH) effects, economic significance and factor independence, using financial data in Hong Kong. Particularly, a new hypothesis testing approach is proposed for statistically testing independence. / In the finance literature, an objective way to judge whether an asset pricing model is misspecified is by statistical tests. In the past, both the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT) have been the subjects of extensive tests. / Second, we investigate two extensions of the gaussian TFA model in view of ARCH in driving noise residuals. We test the extended models for ARCH as well as other aspects to ensure model specification adequacy. Furthermore, we find that ARCH effects are not quite significant driving noise residuals of the macroeconomic modulate independent state-space model. This may be due to long-term modelling of the market. / Third, we test gaussian TFA from the practical point of view in financial prediction and portfolio management. For prediction, we introduce the gaussian TFA alternative mixture experts (ME) approach for forecasting. For adaptive portfolio management, we derive the gaussian TFA adaptive algorithm for implementing the Sharpe-ratio based adaptive portfolio management under different scenarios. Empirical results reveal that APT-based portfolio management techniques are in general superior to return-based techniques. / by Kai-Chun Chiu. / "July, 2003." / Adviser: Lei Xu. / Source: Dissertation Abstracts International, Volume: 64-09, Section: B, page: 4451. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (p. 113-125). / 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 dissertations and theses, [200-] 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. / School code: 1307.

Este trabalho tem como objetivo o estudo de duas medidas de evidência, a saber: o p-valor e o s-valor. A estatística da razão de verossimilhanças é utilizada para o cálculo dessas duas medidas de evidência. De maneira informal, o p-valor é a probabilidade de ocorrer um evento extremo sob as condições impostas pela hipótese nula, enquanto que o s-valor é o maior nível de significância da região de confiança tal que o espaço paramétrico sob a hipótese nula e a região de confiança tenham ao menos um elemento em comum. Para ambas as medidas, quanto menor forem seus respectivos valores, maior é o grau de inconsistência entre os dados observados e a hipótese nula postulada. O estudo será restrito a hipóteses nulas simples e compostas, considerando independência e distribuição normal para os dados. Os resultados principais deste trabalho são: 1) obtenção de fórmulas analíticas para o p-valor, utilizando probabilidades condicionais, e para o s-valor; e 2) comparação entre o p-valor e o s-valor em diferentes cenários, a saber: variância conhecida e desconhecida, e hipóteses nulas simples e compostas. Para hipóteses nulas simples, o s-valor coincide com o p-valor, e quando as hipóteses nulas são compostas, a relação entre o p-valor e o s-valor são complexas. No caso da variância conhecida, se a hipótese nula for uma semi-reta o p-valor é majorado pelo s-valor, se a hipótese é um intervalo fechado a diferença entre as duas medidas de evidência diminui conforme o comprimento do intervalo da hipótese testada. No caso de variância desconhecida e hipóteses nulas compostas, o s-valor é majorado pelo p-valor para valores pequenos do s-valor, por exemplo, quando o s-valor é menor do que 0.05. / This work aims to study two measures of evidence, namely: the p-value and s-value. The likelihood ratio statistic is used to calculate these two evidence measures. Informally, the p-value is the probability of an extreme event under the conditions imposed by the null hypothesis, while the s-value is the greatest confidence level of the confidence region such that the parameter space under the null hypothesis and the confidence region have at least one element in common. For both measures, the smaller are the respective values, the greater is the degree of inconsistency between the observed values and the null hypothesis. In this study, we will consider simple and composite null hypotheses and it will be restricted to independently and normally distributed data. The main results are: 1) to obtain the analytical formulas for the p-value, by using conditional probabilities, and for the s-value, and 2) to compare the p-value and s-value under different scenarios, namely: known and unknown variance, and simple and composite null hypotheses. For simple null hypotheses, the s-value coincides with the p-value, and for composite null hypotheses, the p-value and the s-value relationships are complex. In the case of known variance, if the null hypothesis is a half-line the p-value is smaller than the s-value, if the null hypothesis is a closed interval the difference between the two measures of evidence decreases with the interval width specified in the null hypothesis. In the case of unknown variance and composite hypotheses, the s-value is smaller than the p-value when the value of the s-value is small.

The study seeks to determine the effect upon the Marascuilo Ú₀ statistic of violating the small sample assumption. The study employed a Monte Carlo simulation technique to vary the degree of sample size and unequal sample sizes within experiments to determine the effect of such conditions, Twenty-two simulations, with 1200 trials each, were used. The following conclusion appeared to be appropriate: The Marascuilo Ú₀ statistic should not be used with small sample sizes and it is recommended that the statistic be used only if sample sizes are larger than ten.

Optimization theories and algorithms are used to efficiently find optimal solutions under constraints. In the era of “Big Data”, the amount of data is skyrocketing,and this overwhelms conventional techniques used to solve large scale and distributed optimization problems. By taking advantage of structural information in data representations, this thesis offers convex and non-convex optimization solutions to various large scale optimization problems such as super-resolution, sparse signal processing,hypothesis testing, machine learning, and treatment planning for brachytherapy. Super-resolution: Super-resolution aims to recover a signal expressed as a sum of a few Dirac delta functions in the time domain from measurements in the frequency domain. The challenge is that the possible locations of the delta functions are in the continuous domain [0,1). To enhance recovery performance, we considered deterministic and probabilistic prior information for the locations of the delta functions and provided novel semidefinite programming formulations under the information. We also proposed block iterative reweighted methods to improve recovery performance without prior information. We further considered phaseless measurements, motivated by applications in optic microscopy and x-ray crystallography. By using the lifting method and introducing the squared atomic norm minimization, we can achieve super-resolution using only low frequency magnitude information. Finally, we proposed non-convex algorithms using structured matrix completion. Sparse signal processing: L1 minimization is well known for promoting sparse structures in recovered signals. The Null Space Condition (NSC) for L1 minimization is a necessary and sufficient condition on sensing matrices such that a sparse signal can be uniquely recovered via L1 minimization. However, verifying NSC is a non-convex problem and known to be NP-hard. We proposed enumeration-based polynomial-time algorithms to provide performance bounds on NSC, and efficient algorithms to verify NSC precisely by using the branch and bound method. Hypothesis testing: Recovering statistical structures of random variables is important in some applications such as cognitive radio. Our goal is distinguishing two different types of random variables among n>>1 random variables. Distinguishing them via experiments for each random variable one by one takes lots of time and efforts. Hence, we proposed hypothesis testing using mixed measurements to reduce sample complexity. We also designed efficient algorithms to solve large scale problems. Machine learning: When feature data are stored in a tree structured network having time delay in communication, quickly finding an optimal solution to the regularized loss minimization is challenging. In this scenario, we studied a communication-efficient stochastic dual coordinate ascent and its convergence analysis. Treatment planning: In the Rotating-Shield Brachytherapy (RSBT) for cancer treatment, there is a compelling need to quickly obtain optimal treatment plans to enable clinical usage. However, due to the degree of freedom in RSBT, finding optimal treatment planning is difficult. For this, we designed a first order dose optimization method based on the alternating direction method of multipliers, and reduced the execution time around 18 times compared to the previous research.

There is an increased emphasis on inquiry in national and Oregon state high school science standards. As hypothesis testing is a key component of these new standards, instructors need effective strategies to improve students' hypothesis testing skills. Recent research suggests that classroom exercises may prove useful. A general purpose classroom activity called the thought experiment is proposed. The effectiveness of 7 hours of instruction using this exercise was measured in an introductory biology course, using a quasi-experimental contrast group design. An instrument for measuring hypothesis testing skill is also proposed. Treatment (n=18) and control (n=10) sections drawn from preexisting high school classes were pre- and post-assessed using the proposed Multiple Choice Assessment of Deductive Reasoning. Both groups were also post-assessed by individually completing a written, short-answer format hypothesis testing exercise. Treatment section mean posttest scores on contextualized, multiple choice problem sets were significantly higher than those of the control section. Mean posttest scores did not significantly differ between sections on abstract deductive logic problems or the short answer format hypothesis testing exercise.