Optimal experimental designs for generalized linear models have received increasing attention in recent years. Yet, most of the current research focuses on binary data models especially the one-variable first-order logistic regression model. This research extends this topic to count data models. The primary goal of this research is to develop efficient and robust experimental designs for the Poisson regression model in toxicity studies. D-optimal designs for both the one-toxicant second-order model and the two-toxicant interaction model are developed and their dependence upon the model parameters is investigated. Application of the D-optimal designs is very limited due to the fact that these optimal designs, in terms of ED levels, depend upon the unknown parameters. Thus, some practical designs like equally spaced designs and conditional D-optimal designs, which, in terms of ED levels, are independent of the parameters, are studied. It turns out that these practical designs are quite efficient when the design space is restricted. Designs found in terms of ED levels like D-optimal designs are not robust to parameters misspecification. To deal with this problem, sequential designs are proposed for Poisson regression models. Both fully sequential designs and two-stage designs are studied and they are found to be efficient and robust to parameter misspecification. For experiments that involve two or more toxicants, restrictions on the survival proportion lead to restricted design regions dependent on the unknown parameters. It is found that sequential designs perform very well under such restrictions. In most of this research, the log link is assumed to be the true link function for the model. However, in some applications, more than one link functions fit the data very well. To help identify the link function that generates the data, experimental designs for discrimination between two competing link functions are investigated. T-optimal designs for discrimination between the log link and other link functions such as the square root link and the identity link are developed. To relax the dependence of T-optimal designs on the model truth, sequential designs are studied, which are found to converge to T-optimal designs for large experiments. / Ph. D.

The proliferation of renewables, electric vehicles, and power electronic devices calls for innovative approaches to learn, optimize, and plan the power system. The uncertain and volatile nature of the integrated components necessitates using swift and probabilistic solutions. Gaussian process regression is a machine learning paradigm that provides closed-form predictions with quantified uncertainties. The key property of Gaussian processes is the natural ability to integrate the sensitivity of the labels with respect to features, yielding improved accuracy. This dissertation tailors Gaussian process regression for three applications in power systems. First, a physics-informed approach is introduced to infer the grid dynamics using synchrophasor data with minimal network information. The suggested method is useful for a wide range of applications, including prediction, extrapolation, and anomaly detection. Further, the proposed framework accommodates heterogeneous noisy measurements with missing entries. Second, a learn-to-optimize scheme is presented using Gaussian process regression that predicts the optimal power flow minimizers given grid conditions. The main contribution is leveraging sensitivities to expedite learning and achieve data efficiency without compromising computational efficiency. Third, Bayesian optimization is applied to solve a bi-level minimization used for strategic investment in electricity markets. This method relies on modeling the cost of the outer problem as a Gaussian process and is applicable to non-convex and hard-to-evaluate objective functions. The designed algorithm shows significant improvement in speed while attaining a lower cost than existing methods. / Doctor of Philosophy / The proliferation of renewables, electric vehicles, and power electronic devices calls for innovative approaches to learn, optimize, and plan the power system. The uncertain and volatile nature of the integrated components necessitates using swift and probabilistic solutions. This dissertation focuses on three practically important problems stemming from the power system modernization. First, a novel approach is proposed that improves power system monitoring, which is the first and necessary step for the stable operation of the network. The suggested method applies to a wide range of applications and is adaptable to use heterogeneous and noisy measurements with missing entries. The second problem focuses on predicting the minimizers of an optimization task. Moreover, a computationally efficient framework is put forth to expedite this process. The third part of this dissertation identifies investment portfolios for electricity markets that yield maximum revenue and minimum cost.

In typical normal theory regression, the assumption of homogeneity of variances is often not appropriate. Instead of treating the variances as a nuisance and transforming away the heterogeneity, the structure of the variances may be of interest and it is desirable to model the variances. Aitkin (1987) proposes a parametric dual model in which a log linear dependence of the variances on a set of explanatory variables is assumed. Aitkin's parametric approach is an iterative one providing estimates for the parameters in the mean and variance models through joint maximum likelihood. Estimation of the mean and variance parameters are interrelatedas the responses in the variance model are the squared residuals from the fit to the means model. When one or both of the models (the mean or variance model) are misspecified, parametric dual modeling can lead to faulty inferences. An alternative to parametric dual modeling is to let the data completely determine the form of the true underlying mean and variance functions (nonparametric dual modeling). However, nonparametric techniques often result in estimates which are characterized by high variability and they ignore important knowledge that the user may have regarding the process. Mays and Birch (1996) have demonstrated an effective semiparametric method in the one regressor, single-model regression setting which is a "hybrid" of parametric and nonparametric fits. Using their techniques, we develop a dual modeling approach which is robust to misspecification in either or both of the two models. Examples will be presented to illustrate the new technique, termed here as Dual Model Robust Regression. / Ph. D.

This dissertation is concerned with the evaluation of a robust modification of existing methodology within the classical inference framework. This results in an F-test based on the robust weights used in arriving at the M or Bounded-Influence estimates. These estimates are known to be robust to outliers and highly influential points, respectively. The first part of this evaluation involves a Monte Carlo power study, under violations of the classical assumptions, of this F-test based on robust weights and several other proposed robust tests. It is shown in simulation studies that, under certain conditions, the F-test based on robust weights is a much more powerful test than the classical F -test, and compares favorably to all other proposals studied. The second part involves the development of the influence curve (IC) for the F-test based on robust weights and one empirical approximation to the IC, the Sample Influence Curve (SIC). It is shown for two sample data sets that the SIC demonstrates the resistance to unusual points of the F-test based on robust weights. / Ph. D.

This study seeks to investigate weather-related flight delay trends at 13 United States airports. Flight delay data were collected from 2004-2019 and normalized by airport operations data. Using Support Vector Regression (SVR), visual trends were identified. Further analysis was conducted by comparing all four meteorological seasons through computing 95% bootstrap confidence intervals on their means. Finally, precipitation and snowfall data were correlated with normalized delays to investigate how they are related. This study found that the season with the highest normalized delay values is heavily dependent upon location. Most airports saw a decrease in the SVR line at some point since 2004, but have since leveled off. It was also discovered that while precipitation trends are not changing drastically, delay variability has decreased at many airports in the last 10 years, which may be indicative of more effective mitigation strategies.

M.S.

The prediction of future engine states are useful for performance evaluation and anomaly detection of jet turbines. While a variety of modeling approaches exist, many are not capable of efficiently utilizing the vast quantities of data from test experimentation in a manner that is not opaque to the operator or observer. The literature describes several approaches to interpretable modeling on various types of systems in different domains for applications such as Remaining Useful Life estimation and accident prognosis, but do not perform prediction on measured state quantities or performance. Additionally, of modeling studies that focus on jet turbines, the data is synthetic instead of experimental. In this thesis, we utilize an attention-based neural network, the Temporal Fusion Transformer, on experimental data for prediction, allowing for interpretability and insight into model dynamics. We describe a series of experiments on different configurations of the model architecture and show that through the incorporation of physical information into the system, the models produce better forecasts and confidence qualities on all outputs, with robustness to some level of failure and noise in inputs. For the TFT, we include control inputs as future covariates and evaluate modifications to the loss function to include the physics of key performance parameters of the gas turbine as residual form equations, finding that it increases model accuracy and the usefulness of interpretability results, even when model size is reduced. These key performance parameters were derived from and introduced into the dataset, with a comparison of performance on the full dataset and a reduced dataset showing increased performance on the smaller dataset. Additionally, these interpretable models are able to provide more useful insight into system dynamics, allowing for vision into time horizon attention and model-discovered variable importance. While there is further exploration in the extent of robustness and accuracy of physics-informed attention networks, we expect this approach to lead to models with reduced training time, higher accuracy, increased user confidence in prediction, and more interpretable models which will allow for future incorporation into anomaly detection algorithms or the study of dynamic systems. / Master of Science / The prediction of future engine states are useful for performance evaluation and anomaly detection of jet turbines. While a variety of modeling approaches exist, many are not capable of efficiently utilizing the vast quantities of data from test experimentation in a manner that is not opaque to the operator or observer. The literature describes several approaches to interpretable modeling on various types of systems in different domains for applications such as Remaining Useful Life estimation and accident prognosis, but do not perform prediction on measured state quantities or performance. Additionally, of modeling studies that focus on jet turbines, the data is synthetic instead of experimental. In this thesis, we utilize an attention-based neural network on experimental data for prediction, allowing for interpretability and insight into model dynamics. We describe a series of experiments on different configurations of the model architecture and show that through the incorporation of physical information into the system, the models produce better forecasts and confidence qualities. Additionally, models with interpretability are able to provide more useful insight into system dynamics. We expect this approach to lead to models with reduced training time, higher accuracy, increased user confidence in prediction, and more interpretable models which will allow for future incorporation into anomaly detection algorithms or study of dynamic systems.

The linear calibration problem, frequently referred to as inverse regression or the discrimination problem can be stated briefly as the problem of estimating the independent variable x in a regression situation for a measured value of the dependent variable y. The literature on this problem deals primarily with the Classical method where the Classical estimator is obtained by expressing the linear model as y_i = α + βx_i + ε_i , obtaining the least squares estimator for y for a given value of x and inverting the relationship. A second estimator for calibration, the Inverse estimator, is obtained by expressing the linear model as x_i = γ + δy_i + ε’_i and using the resulting least squares estimator to estimate x. The experimental design problem for the Inverse estimator is explored first in this dissertation using the criterion of minimizing the average or integrated mean squared error, and the resulting optimal and near optimal designs are then compared with those for the Classical estimator which were recently derived by Ott and Nycrs. Optimal designs are developed for a linear approximation when the true model is linear and when it is quadratic. In both cases, the optimal designs depend on unknown model parameters and are not realistically useable. However, designs are shown to exist which are near optimal and do not depend on the unknown model parameters. For the linear approximation to the quadratic model, these near optimal designs depend on N, the number of observations used to estimate the model parameters, and specific designs are developed and set forth in tables for N = 5(1)20(2)30(5)50. The cost of misclassifying a quadratic model as linear is discussed from a design point of view as well as the cost of protecting against a possible quadratic effect, The costs are expressed in terms of the percent deviation from the average mean squared error that would be obtained if the model were classified correctly, The derived designs for the Inverse estimator are compared with the recently derived designs for the Classical estimator using as a measure of comparison the ratio of minimum average mean squared errors obtained by using the optimal design for both estimators. Further comparisons are also made between optimal designs for the Classical estimator and the derived near optimal designs for the Inverse estimator using the ratio of the corresponding average mean squared errors as a measure of comparison. Parallels are drawn between forward regression (estimating, the dependent variable for a given value of the independent variable) and inverse regression using both the Classical and Inverse methods. / Ph. D.

This study analyzes the wage and non-wage factors underlying non-metropolitan-to-metropolitan commuting decisions of households in five non-metropolitan counties in Northern Virginia. The potential fiscal and planning implications of these decisions are also discussed. Chapter one contains a description of the study area, problem statement and objectives. Chapter two reviews related literature on commuting, housing and job location, as well as rent and wage gradients. Chapter three provides a theoretical framework for analyzing household commuting decisions. Chapter four presents descriptive statistics, and introduces a switching regression system of equations to simultaneously estimate factors influencing commuting decisions and earnings in non-metropolitan and metropolitan labor markets. Chapter five reports the regression results, and simulates wage gaps and the distance of the metropolitan labor market draw for different groups of workers. Chapter six discusses potential fiscal implications of commuting and potential policies to manage growth in commuting. The empirical result shows that the major incentive for workers to commute is a large age gap between metropolitan and non-metropolitan labor market areas. Household responsibilities, housing preference and ability to find local jobs represent non-wage factors underlying commuting decisions. Two study findings suggest that the local fiscal implications of non-metropolitan-to-metropolitan commuting households may be limited. First, commuting households are found to have fewer school-aged children, and require less local expenditures on education. Second, commuting households are more likely to be homeowners, have more rooms in their homes, and provide a larger tax base. / Master of Science

Master of Science