The aim of this project is to find a statistical method that describes survival and outcome of a prototype drilling tool from several references and determine how many references are needed for a statistically secure result. The project also answers which variables that affects the outcome. 60 drilling bits of two different types were studied and the variables that are investigated are penetration rate, rotation speed, rotation torque, flush flow, feed force and accumulated depth. Hypothesis test is used for determining how a prototype drills compared to the references and linear regression is used to determine how the references drills. Only accumulated depth affects the survival time with a correlation of 77.7% that was improved to 89.6 % by removing big time gaps that was not of interest for the result. The accuracy of the linear regression for 30 drill bits of one type for max depth related to survival time was 80.3 %. A minimum of 20 prototypes must be tested before determining the outcome of the prototypes in comparison to the references.

The ABC algorithm is a Bayesian method which simulates samples from the posterior distribution. In this thesis, the method is applied on both synthetic and observed data of a regression model. Under normal error distribution a conjugate prior and the likelihood function are used in the algorithm. Additionally, a bootstrap method is implemented in a modified algorithm to provide an alternative method, without requiring normal error distribution. The results of both methods are thereafter presented and compared with the analytic posterior under a conjugate prior, to evaluate their performances. Lastly, advantages and possible issues are discussed.

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In today’s world, where air pollution has become a ubiquitous problem, city air is normally monitored. Such monitoring can produce large amounts of data, and this enables the development of statistical and machine learning techniques for modeling and forecasting air quality. However, the complex nature of air pollution makes such data a challenge to fully utilize. To this end, machine learning methods, especially deep neural networks, have in recent years emerged as a promising technology for more accurate predictions of air pollution levels, and the research problem in this work is; To capture and model the complex dynamics of air pollution with machine learning methods, with an emphasis on deep neural networks. Connected to the research problem is the research question; How can machine learning, in particular deep neural networks, be used to forecast air pollution levels and pollution peaks? An emphasis is put on pollution peaks, as these are the episodes when existing forecasting models tend to give the largest prediction errors. In this work, historical data from air monitoring sensors were utilized to train several neural network architectures, as well as a more straightforward multiple linear regression model, for forecasting background levels of nitrogen dioxide in the center of Stockholm. Several evaluation metrics showed that the neural network models outperformed the multiple linear regression model, however, none of the models had the desired structure of the forecast errors, and all models failed to successfully capture sudden pollution peaks. Nevertheless, the results point to an advantage for the more complex neural network models, and further advances in the field of machine learning, together with higher resolution data, have the potential to improve air quality forecasts even more and cross conventional forecasting limits.

Automated scoring of essays has been a research topic for some time in computational linguistics studies. Only recently have the particular challenges of automatic holistic scoring of ESL essays with their high grammatical, spelling and other error rates been a topic of research. This thesis evaluates the effectiveness of using statistical measures of linguistic maturity to predict holistic scores for ESL essays using several techniques. Selected linguistic attributes include parts of speech, part-of-speech patterns, vocabulary density, and sentence and essay lengths. Using customized algorithms based on multivariable regression analysis as well as memory-based machine learning, holistic scores were predicted on test essays within ±1.0 of the scoring level of human judges' scores successfully an average of 90% of the time. This level of prediction is an improvement over a 66% prediction level attained in a previous study using customized algorithms.

The research in this dissertation is divided between three different approaches for predicting the shear strength of reinforcement masonry shear walls. Each approach provides increasing accuracy and precision in predicting the shear strength of masonry walls. The three approaches were developed or validated using data from 353 wall tests that have been conducted over the past half century. The data were collected, scrutinized, and synthesized using principles of meta-analysis. Predictions made with current Masonry Standards Joint Committee (MSJC) shear strength equation are unconservative and show a higher degree of variation for partially-grouted walls. The first approach modifies the existing MSJC equation to account for the differences in nominal strength and uncertainty between fully- and partially-grouted walls. The second approach develops a new shear strength equation developed to perform equally well for both fully- and partially-grouted walls to replace and improve upon the current MSJC equation. The third approach develops a methodology for creating strut-and-tie models to analyze or design masonry shear walls. It was discovered that strut-and-tie modeling theory provides the best description of masonry shear wall strength and performance. The masonry strength itself provides the greatest contribution to the overall shear capacity of the wall and can be represented as diagonal compression struts traveling from the top of the wall to the compression toe. The shear strength of masonry wall is inversely related to the shear span ratio of the wall. Axial load contributes to shear strength, but to a lesser degree than what has been previously believed. The prevailing theory about the contribution of horizontal shear reinforcement was shown to not be correct and the contribution is much smaller than was originally assumed by researchers. Horizontal shear reinforcement principally acts by resisting diagonal tensile forces in the masonry and by helping to redistribute stresses in a cracked masonry panel. Vertical reinforcement was shown to have an effect on shear strength by precluding overturning of the masonry panel and by providing vertical anchorages to the diagonal struts.

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Today increasing amounts of data are available for analysis purposes and often times for resource allocation. One method for analysis is linear regression which utilizes the least squares estimation technique to estimate a model's parameters. This research investigated, from a user's perspective, the ability of linear regression to estimate the parameters' confidence intervals at the usual 95% level for medium sized data sets. A controlled environment using simulation with known data characteristics (clean data, bias and or multicollinearity present) was used to show underlying problems exist with confidence intervals not including the true parameter (even though the variable was selected). The Elder/Pregibon rule was used for variable selection. A comparison of the bootstrap Percentile and BCa confidence interval was made as well as an investigation of adjustments to the usual 95% confidence intervals based on the Bonferroni and Scheffe multiple comparison principles. The results show that linear regression has problems in capturing the true parameters in the confidence intervals for the sample sizes considered, the bootstrap intervals perform no better than linear regression, and the Scheffe method is too wide for any application considered. The Bonferroni adjustment is recommended for larger sample sizes and when the t-value for a selected variable is about 3.35 or higher. For smaller sample sizes all methods show problems with type II errors resulting from confidence intervals being too wide.

This dissertation develops a comprehensive statistical learning framework that is robust to (distributional) perturbations in the data using Distributionally Robust Optimization (DRO) under the Wasserstein metric. The learning problems that are studied include: (i) Distributionally Robust Linear Regression (DRLR), which estimates a robustified linear regression plane by minimizing the worst-case expected absolute loss over a probabilistic ambiguity set characterized by the Wasserstein metric; (ii) Groupwise Wasserstein Grouped LASSO (GWGL), which aims at inducing sparsity at a group level when there exists a predefined grouping structure for the predictors, through defining a specially structured Wasserstein metric for DRO; (iii) Optimal decision making using DRLR informed K-Nearest Neighbors (K-NN) estimation, which selects among a set of actions the optimal one through predicting the outcome under each action using K-NN with a distance metric weighted by the DRLR solution; and (iv) Distributionally Robust Multivariate Learning, which solves a DRO problem with a multi-dimensional response/label vector, as in Multivariate Linear Regression (MLR) and Multiclass Logistic Regression (MLG), generalizing the univariate response model addressed in DRLR. A tractable DRO relaxation for each problem is being derived, establishing a connection between robustness and regularization, and obtaining upper bounds on the prediction and estimation errors of the solution. The accuracy and robustness of the estimator is verified through a series of synthetic and real data experiments. The experiments with real data are all associated with various health informatics applications, an application area which motivated the work in this dissertation. In addition to estimation (regression and classification), this dissertation also considers outlier detection applications.

Knowledge of construction duration is pertinent to a number of project planning functions prior to detailed design development. Funding, financing, and resource allocation decisions take place early in project design development and are significantly influenced by the construction duration. Currently, there is not an understanding of the project factors having a statistically significant relationship with highway construction duration. Other industry sectors have successfully used statistical regression analysis to identify and model the project parameters related to construction duration. While the need is seen for such work in highway construction, there are very few studies which attempt to identify duration-influential parameters and their relationship with the highway construction duration. This research identifies the project factors, known early in design development, which influence highway construction duration. The factors identified are specific to their respective project types and are those factors which demonstrate a statistically-significant relationship with construction duration. This work also quantifies the relationship between the duration-influential factors and highway construction duration. The quantity, magnitude, and sign of the factor coefficient yields evidence regarding the importance of the project factor to highway construction duration. Finally, the research incorporates the duration-influential project factors and their relationship with highway construction duration into mathematical models which assist in the prediction of construction duration. Full and condensed models are presented for Full-Depth Section and Highway Improvement project types. This research uses statistical regression analysis to identify, quantify, and model these early-known, duration-influential project factors. The results of this research contribute to the body of knowledge of the sponsoring organization (Virginia Department of Transportation), the highway construction industry, and the general construction industry at large. / Ph. D.