Thesis (M.S. in Aeronautical Engineering)--Naval Postgraduate School, September 1995. / Thesis advisor(s): Daniel J. Collins, Rocjard M. Howard. Includes bibliographical references (p. 83-84).

Thesis (M.S. in Electrical Engineering)--Naval Postgraduate School, September 2003. / Thesis advisor(s): Charles W. Therrien, Roberto Cristi. Includes bibliographical references (p. 45). Also available online.

The Multidimensional Generalized Graded Unfolding Model (MGGUM) is a proximity-based, noncompensatory item response theory (IRT) model with applications in the context of attitude, personality, and preference measurement. Model development used fully Bayesian Markov Chain Monte Carlo (MCMC) parameter estimation (Roberts, Jun, Thompson, & Shim, 2009a; Roberts & Shim, 2010). Challenges can arise while estimating MGGUM parameters using MCMC where the meaning of dimensions may switch during the estimation process and difficulties in obtaining informative starting values may lead to increased identification of local maxima. Furthermore, researchers must contend with lengthy computer processing time. It has been shown alternative estimation methods perform just as well as, if not better than, MCMC in the unidimensional Generalized Graded Unfolding Model (GGUM; Roberts & Thompson, 2011) with marginal maximum a posteriori (MMAP) item parameter estimation paired with expected a posteriori (EAP) person parameter estimation being a viable alternative. This work implements MMAP/EAP parameter estimation in the multidimensional model. Additionally, item location initial values are derived from detrended correspondence analysis (DCA) based on previous implementation of correspondence analysis in the GGUM (Polak, 2011). A parameter recovery demonstrates the accuracy of two-dimensional MGGUM MMAP/EAP parameter estimates and a comparative analysis of MMAP/EAP and MCMC demonstrates equal accuracy, yet much improved efficiency of the former method. Analysis of real attitude measurement data also provides an illustrative application of the model.

published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Efficient and comprehensive forecasting of information is of great importance to traffic management. Three types of forecasting methods based on irregularly spaced data—for situations when traffic detectors cannot be installed to generate regularly spaced data on all roads—are studied in this thesis, namely, the single segment forecasting method, multi-segment forecasting method and model-based forecasting method. The proposed models were tested using Global Positioning System (GPS) data from 400 Hong Kong taxis collected within a 2-kilometer section on Princess Margaret Road and Hong Chong Road, approaching the Cross Harbour Tunnel. The speed limit for the road is 70 km/h. It has flyovers and ramps, with a small number of merges and diverges. There is no signalized intersection along this road section. A total of 14 weeks of data were collected, in which the first 12 weeks of data were used to calibrate the models and the last two weeks of data were used for validation. The single-segment forecasting method for irregularly spaced data uses a neural network to aggregate the predicted speeds from the naive method, simple exponential smoothing method and Holt’s method, with explicit consideration of acceleration information. The proposed method shows a great improvement in accuracy compared with using the individual forecasting method separately. The acceleration information, which is viewed as an indicator of the phase-transition effect, is considered to be the main contribution to the improvement. The multi-segment forecasting method aggregates not only the information from the current forecasting segment, but also from adjacent segments. It adopts the same sub-methods as the single-segment forecasting method. The forecasting results from adjacent segments help to describe the phase-transition effect, so that the forecasting results from the multi-segment forecasting method are more accurate than those that are obtained from the single segment forecasting method. For one-second forecasting length, the correlation coefficient between the forecasts from the multi-segment forecasting method and observations is 0.9435, which implies a good consistency between the forecasts and observations. While the first two methods are based on pure data fitting techniques, the third method is based on traffic models and is called the model-based forecasting method. Although the accuracy of the one-second forecasting length of the model-based method lies between those of the single-segment and multi-segment forecasting methods, its accuracy outperforms the other two for longer forecasting steps, which offers a higher potential for practical applications. / published_or_final_version / Civil Engineering / Master / Master of Philosophy

In statistical inference, one is often interested in estimating the distribution of a root, which is a function of the data and the parameters only. Knowledge of the distribution of a root is useful for inference problems such as hypothesis testing and the construction of a confidence set. Shrinkage-type estimators have become popular in statistical inference due to their smaller mean squared errors. In this thesis, the performance of different bootstrap methods is investigated for estimating the distributions of roots which are constructed based on shrinkage estimators. Focus is on two shrinkage estimation problems, namely the James-Stein estimation and the model selection problem in simple linear regression. A hybrid bootstrap procedure and a bootstrap test method are proposed to estimate the distributions of the roots of interest. In the two shrinkage problems, the asymptotic errors of the traditional n-out-of-n bootstrap, m-out-of-n bootstrap and the proposed methods are derived under a moving parameter framework. The problem of the lack of uniform consistency of the n-out-of-n and the m-out-of-n bootstraps is exposed. It is shown that the proposed methods have better overall performance, in the sense that they yield improved convergence rates over almost the whole range of possible values of the underlying parameters. Simulation studies are carried out to illustrate the theoretical findings. / published_or_final_version / Statistics and Actuarial Science / Master / Master of Philosophy

Parameter estimation plays a key role in many signal processing applications. Traditional parameter estimation relies on centralized method which requires gathering of all information dispersed over the network in a central processing unit. As the scale of network increases, centralized estimation is not preferred since it requires not only the knowledge of network topology but also heavy communications from peripheral nodes to central processing unit. Besides, computation at the control center cannot scale indefinitely with the network size. Therefore, distributed estimation which involves only local computation at each node and limited information exchanges between immediate neighbouring nodes is needed. In this thesis, for local observations in the form of a pairwise linear model corrupted by Gaussian noise, belief propagation (BP) algorithm is investigated to perform distributed estimation. It involves only iterative updating of the estimates with local message exchange between immediate neighboring nodes. Since convergence has always been the biggest concern when using BP, we establish the convergence properties of asynchronous vector form Gaussian BP under the pairwise model. It is shown analytically that under mild condition, the asynchronous BP algorithm converges to the optimal estimates with estimation mean square error (MSE) at each node approaching the centralized Bayesian Cram´er-Rao bound (BCRB) regardless of the network topology. The proposed framework encompasses both classes of synchronous and asynchronous algorithms for distributed estimation and is robust to random link failures. Two challenging parameter estimation problems in large-scale networks, i.e., network-wide distributed carrier frequency offsets (CFOs) estimation, and global clock synchronization in sensor network, are studied based on BP. The proposed algorithms do not require any centralized information processing nor knowledge of the global network topology and are scalable with the network size. Simulation results further verify the established theoretical analyses: the proposed algorithms always converge to the optimal estimates regardless of network topology. Simulations also demonstrate the MSE at each node approaches the corresponding centralized CRB within a few iterations of message exchange. Furthermore, distributed estimation is studied for the linear model with unknown coefficients. Such problem itself is challenging even for centralized estimation as the nonlinear property of the observation model. One problem following this model is the power state estimation with unknown sampling phase error. In this thesis, distributed estimation scheme is proposed based on variational inference with parallel update schedule and limited message exchange between neighboring areas, and the convergence is guaranteed. Simulation results show that after convergence the proposed algorithm performs very close to that of the ideal case which assumes perfect synchronization, and centralized information processing. / published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Stochastic programming facilitates decision making under uncertainty. It is usually impractical or impossible to find the optimal solution to a stochastic problem, and approximations are required. Sampling-based approximations are simple and attractive, but the standard point estimate of optimization and the Monte Carlo approximation. We provide a method to reduce this bias, and hence provide a better, i.e., tighter, confidence interval on the optimal value and on a candidate solution's optimality gap. Our method requires less restrictive assumptions on the structure of the bias than previously-available estimators. Our estimators adapt to problem-specific properties, and we provide a family of estimators, which allows flexibility in choosing the level of aggressiveness for bias reduction. We establish desirable statistical properties of our estimators and empirically compare them with known techniques on test problems from the literature.

published_or_final_version / abstract / toc / Statistics and Actuarial Science / Master / Master of Philosophy

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