With new tests being developed and marketed, the comparison of the diagnostic accuracy of two continuous-scale diagnostic tests are of great importance. Comparing the partial areas under the receiver operating characteristic curves (pAUC) is an effective method to evaluate the accuracy of two diagnostic tests. In this thesis, we study the semi-parametric inference for the difference between two pAUCs. A normal approximation for the distribution of the difference between two pAUCs has been derived. The empirical likelihood ratio for the difference between two pAUCs is defined and its asymptotic distribution is shown to be a scaled chi-quare distribution. Bootstrap and empirical likelihood based inferential methods for the difference are proposed. We construct five confidence intervals for the difference between two pAUCs. Simulation studies are conducted to compare the finite sample performance of these intervals. We also use a real example as an application of our recommended intervals.

The correlation coefficient (CC) is a standard measure of the linear association between two random variables. The CC plays a significant role in many quantitative researches. In a bivariate normal distribution, there are many types of interval estimation for CC, such as z-transformation and maximum likelihood estimation based methods. However, when the underlying bivariate distribution is unknown, the construction of confidence intervals for the CC is still not well-developed. In this thesis, we discuss various interval estimation methods for the CC. We propose a generalized confidence interval and three empirical likelihood-based non-parametric intervals for the CC. We also conduct extensive simulation studies to compare the new intervals with existing intervals in terms of coverage probability and interval length. Finally, two real examples are used to demonstrate the application of the proposed methods.

The receiver operating characteristic (ROC) curve methodology is the statistical methodology for assessment of the accuracy of diagnostics tests or bio-markers. Currently most widely used statistical methods for the inferences of ROC curves are complete-data based parametric, semi-parametric or nonparametric methods. However, these methods cannot be used in diagnostic applications with missing data. In practical situations, missing diagnostic data occur more commonly due to various reasons such as medical tests being too expensive, too time consuming or too invasive. This dissertation aims to develop new nonparametric statistical methods for evaluating the accuracy of diagnostic tests or biomarkers in the presence of missing data. Specifically, novel nonparametric statistical methods will be developed with different types of missing data for (i) the inference of the area under the ROC curve (AUC, which is a summary index for the diagnostic accuracy of the test) and (ii) the joint inference of the sensitivity and the specificity of a continuous-scale diagnostic test. In this dissertation, we will provide a general framework that combines the empirical likelihood and general estimation equations with nuisance parameters for the joint inferences of sensitivity and specificity with missing diagnostic data. The proposed methods will have sound theoretical properties. The theoretical development is challenging because the proposed profile log-empirical likelihood ratio statistics are not the standard sum of independent random variables. The new methods have the power of likelihood based approaches and jackknife method in ROC studies. Therefore, they are expected to be more robust, more accurate and less computationally intensive than existing methods in the evaluation of competing diagnostic tests.

This thesis proposes a model reduction technique for nonlinear dynamical systems based upon combining Proper Orthogonal Decomposition (POD) and a new method, called the Discrete Empirical Interpolation Method (DEIM). The popular method of Galerkin projection with POD basis reduces dimension in the sense that far fewer variables are present, but the complexity of evaluating the nonlinear term generally remains that of the original problem. DEIM, a discrete variant of the approach from [11], is introduced and shown to effectively overcome this complexity issue. State space error estimates for POD-DEIM reduced systems are also derived. These [Special characters omitted.] error estimates reflect the POD approximation property through the decay of certain singular values and explain how the DEIM approximation error involving the nonlinear term comes into play. An application to the simulation of nonlinear miscible flow in a 2-D porous medium shows that the dynamics of a complex full-order system of dimension 15000 can be captured accurately by the POD-DEIM reduced system of dimension 40 with a factor of [Special characters omitted.] (1000) reduction in computational time.

The purpose of this thesis is to evaluate five different volatility forecasting models that are used to calculate financial market risk. The models are used on both daily exchange rates and high-frequency intraday data from four different series. The results show that time series models fitted to high-frequency intraday data together with a critical value taken from the empirical distribution displayed the best forecasts overall.

A formal specification language used during the requirements phase can reduce errors and rework, but formal specifications are regarded as expensive to maintain, discouraging their adoption. This work presents a single-subject experiment that explores the costs of modifying specifications written in two different languages: a tabular notation, Software Cost Reduction (SCR), and a state-of-the-practice notation, Real-time Unified Modeling Language (UML). The study records the person-hours required to write each specification, the number of defects made during each specification effort, and the amount of time repairing these defects. Two different problems are specified&mdash;a Bidirectional Formatter (BDF), and a Bicycle Computer (BC)&mdash;to balance a learning effect from specifying the same problem twice with different specification languages. During the experiment, an updated feature for each problem is sent to the subject and each specification is modified to reflect the changes. <br /><br /> The results show that the cost to modify a specification are highly dependent on both the problem and the language used. There is no evidence that a tabular notation is easier to modify than a state-of-the-practice notation. <br /><br /> A side-effect of the experiment indicates there is a strong learning effect, independent of the language: in the BDF problem, the second time specifying the problem required more time, but resulted in a better-quality specification than the first time; in the BC problem, the second time specifying the problem required less time and resulted in the same quality specification as the first time. <br /><br /> This work demonstrates also that single-subject experiments can add important information to the growing body of empirical data about the use of formal requirements specifications in software development.

The complexity of many failure mechanisms and variations in component manufacture often make standard probability distributions inadequate for reliability modeling. Finite mixture distributions provide the necessary flexibility for modeling such complex phenomena but add considerable difficulty to the inference. This difficulty is overcome by drawing an analogy to neural networks. With appropropriate modifications, a neural network can represent a finite mixture CDF or PDF exactly. Training with Bayesian Regularization gives an efficient empirical Bayesian inference of the failure time distribution. Training also yields an effective number of parameters from which the number of components in the mixture can be estimated. Credible sets for functions of the model parameters can be estimated using a simple closed-form expression. Complete, censored, and inpection samples can be considered by appropriate choice of the likelihood function. In this work, architectures for Exponential, Weibull, Normal, and Log-Normal mixture networks have been derived. The capabilities of mixture networks have been demonstrated for complete, censored, and inspection samples from Weibull and Log-Normal mixtures. Furthermore, mixture networks' ability to model arbitrary failure distributions has been demonstrated. A sensitivity analysis has been performed to determine how mixture network estimator errors are affected my mixture component spacing and sample size. It is shown that mixture network estimators are asymptotically unbiased and that errors decay with sample size at least as well as with MLE.

The intraseasonal Oscillation (ISO) is a very strong and coherent mode of variability observed in the Earths climate. Rainfall variability in the intraseasonal timescale is particularly strong in the Tropics and it directly interacts with the South Asian monsoon during boreal summer and with the Australian monsoon during winter. A detailed analysis of the horizontal and vertical structure of the ISO during both summer and winter is presented in this work considering the coupled ocean-atmosphere system. In addition, the role of the intraseasonal variability of the Southeast Asian monsoon is studied in detail. From the applications point of view, the intraseasonal time scale is arguably the most important period of variability. However, extended forecasting of intraseasonal activity has proven to be a difficult task for the state of the art numerical models. In order to improve the forecasts of the ISO activity over the Southeast Asian monsoon region, a physically based empirical scheme was designed. The scheme uses wavelet banding to separate the predictand and predictors into physically significant bands where linear regression followed by recombination of the bands is used to generate the forecast. Results of the empirical scheme suggest that isolating the evolution of the intraseasonal signal from higher frequency variability and noise improve the skill of the prediction. The hypothesis is that a similar phenomenon occurs in numerical models: The strong intraseasonal signal is eroded by high frequency errors due to the model parameterizations, especially in convection. To evaluate the hypothesis, a coupled ocean-atmosphere model was run in ensemble mode for 30 day periods initialized daily for 20 days before to 20 days after major intraseasonal oscillations, allowing the examination of the skill of the model relative to the phase of the oscillation. The results, which confirm the previous hypothesis, represent well the observations for about 7 days after which the magnitude of the errors is greater than the signal itself. An integration scheme was developed for the coupled ocean-atmosphere general circulation model in order to mimic the philosophy of the empirical scheme and use for 30-day forecasts. The propagation features associated to ISO activity are improved.

The main topic of this research is the simulation of internal wave interaction by a two-dimensional numerical model developed by Lynett & Liu (2002) of Cornell University, then modified by Cheng et al. (2005). The governing equation includes two-dimensional momentum and continuity equation. The model uses constant upper and lower layer densities; hence, these factors as well as the upper layer thickness. Should be determined before the simulation. This study discusses the interface depth and the density according to the buoyancy frequency distribution, the EOF, and the eigen-value based on the measured density profile. Besides, a method based on the two-layer KdV equation and the KdV of continuously-stratified fluid. By minimize the difference of linear celeriy, nonlinear and dispersion terms, the upper layer thicknes can also be determined. However, the interface will be much deeper than the depth of max temperature drop in the KdV method if the total water depth is bigger than 500 meters. Thus, the idealization buoyancy frequency formula proposed by Vlasenko et al. (2005) or Xie et al. (2010) are used to modify the buoyancy frequency. The internal wave in the Luzon Strait and the South China Sea are famous and deserves detailed study. We use the KdV method to find the parameters in the two fluid model to speed up the simulation of internal wave phenomena found in the satellite image.

In this thesis we use pulse shaping system to generate pulse train. Using empirical mode decomposition(EMD) and short-time Fourier transform(STFT) to analyze the signal of terahertz radiation. we use pulse shaping system to modulate the amplitude and phase of light which provide for pulse train generation. Compare with other method, first, our method will improve the stability of time delay control. Second this method is easier to control the time delay and number of pulse in the pulse train. In the past, people find the occur time of high frequency by observed the time domain of terahertz radiation directly, but if the occur time near the time of the peak power of terahertz radiation, we can¡¦t find out the occur time of high frequency. Using STFT can find out the relationship between intensity and time, but if the modes in signal have different width of frequency STFT have to use different time window to get the best frequency resolution and time resolution. However the time window with different width will have different frequency resolution, and the relationship between intensity and time will change with different frequency resolution, therefore using different frequency resolution will get different result, so we need a new signal analysis method. To solve this problem we use EMD to decompose different mode in the signal of terahertz radiation into different intrinsic mode function(IMF), and analyze the signal of terahertz by STFT to find the occur time of high frequency of terahertz radiation. Because the modes are separated in to different IMF, we can use STFT with the same time window. We expect this method applied to narrow-band frequency-tunable THz wave generation will be better.