Performance and Robustness Analysis of Co-Prime and Nested Sampling

Coprime and nested sampling are well known deterministic sampling techniques that operate at rates significantly lower than the Nyquist rate, and yet allow perfect reconstruction of the spectra of wide sense stationary signals. However, theoretical guarantees for these samplers assume ideal conditions such as synchronous sampling, and ability to perfectly compute statistical expectations. This thesis studies the performance of coprime and nested samplers in spatial and temporal domains, when these assumptions are violated. In spatial domain, the robustness of these samplers is studied by considering arrays with perturbed sensor locations (with unknown perturbations). Simplified expressions for the Fisher Information matrix for perturbed coprime and nested arrays are derived, which explicitly highlight the role of co-array. It is shown that even in presence of perturbations, it is possible to resolve $O(M^2)$ under appropriate conditions on the size of the grid. The assumption of small perturbations leads to a novel ``bi-affine" model in terms of source powers and perturbations. The redundancies in the co-array are then exploited to eliminate the nuisance perturbation variable, and reduce the bi-affine problem to a linear underdetermined (sparse) problem in source powers. This thesis also studies the robustness of coprime sampling to finite number of samples and sampling jitter, by analyzing their effects on the quality of the estimated autocorrelation sequence. A variety of bounds on the error introduced by such non ideal sampling schemes are computed by considering a statistical model for the perturbation. They indicate that coprime sampling leads to stable estimation of the autocorrelation sequence, in presence of small perturbations. Under appropriate assumptions on the distribution of WSS signals, sharp bounds on the estimation error are established which indicate that the error decays exponentially with the number of samples. The theoretical claims are supported by extensive numerical experiments.

Statistical Analysis of Text Summarization Evaluation

This dissertation applies statistical methods to the evaluation of automatic summarization using data from the Text Analysis Conferences in 2008-2011. Several aspects of the evaluation framework itself are studied, including the statistical testing used to determine significant differences, the assessors, and the design of the experiment. In addition, a family of evaluation metrics is developed to predict the score an automatically generated summary would receive from a human judge and its results are demonstrated at the Text Analysis Conference. Finally, variations on the evaluation framework are studied and their relative merits considered. An over-arching theme of this dissertation is the application of standard statistical methods to data that does not conform to the usual testing assumptions.

SEEKING CULTURAL FAIRNESS IN A MEASURE OF RELATIONAL REASONING

Relational reasoning, or the ability to identify meaningful patterns within any stream of information, is a fundamental cognitive ability associated with academic success across a variety of domains of learning and levels of schooling. However, the measurement of this construct has been historically problematic. For example, while the construct is typically described as multidimensional—including the identification of multiple types of higher-order patterns—it is most often measured in terms of a single type of pattern: analogy. For that reason, the Test of Relational Reasoning (TORR) was conceived and developed to include three other types of patterns that appear to be meaningful in the educational context: anomaly, antinomy, and antithesis. Moreover, as a way to focus on fluid relational reasoning ability, the TORR was developed to include, except for the directions, entirely visuo-spatial stimuli, which were designed to be as novel as possible for the participant. By focusing on fluid intellectual processing, the TORR was also developed to be fairly administered to undergraduate students—regardless of the particular gender, language, and ethnic groups they belong to. However, although some psychometric investigations of the TORR have been conducted, its actual fairness across those demographic groups has yet to be empirically demonstrated. Therefore, a systematic investigation of differential-item-functioning (DIF) across demographic groups on TORR items was conducted. A large (N = 1,379) sample, representative of the University of Maryland on key demographic variables, was collected, and the resulting data was analyzed using a multi-group, multidimensional item-response theory model comparison procedure. Using this procedure, no significant DIF was found on any of the TORR items across any of the demographic groups of interest. This null finding is interpreted as evidence of the cultural-fairness of the TORR, and potential test-development choices that may have contributed to that cultural-fairness are discussed. For example, the choice to make the TORR an untimed measure, to use novel stimuli, and to avoid stereotype threat in test administration, may have contributed to its cultural-fairness. Future steps for psychometric research on the TORR, and substantive research utilizing the TORR, are also presented and discussed.

Assessment and Life-Cycle Analysis of Recycled Materials for Sustainable Highway

Recycled materials replacing part of virgin materials in highway applications has shown great benefits to the society and environment. Beneficial use of recycled materials can save landfill places, sparse natural resources, and energy consumed in milling and hauling virgin materials. Low price of recycled materials is favorable to cost-saving in pavement projects. Considering the availability of recycled materials in the State of Maryland (MD), four abundant recycled materials, recycled concrete aggregate (RCA), recycled asphalt pavement (RAP), foundry sand (FS), and dredged materials (DM), were studied. A survey was conducted to collect the information of current usage of the four recycled materials in States’ Department of Transportation (DOTs). Based on literature review, mechanical and environmental properties, recommendations, and suggested test standards were investigated separately for the four recycled materials in different applications. Constrains in using these materials were further studied in order to provide recommendations for the development of related MD specifications. To measure social and environmental benefits from using recycled materials, life-cycle assessment was carried out with life-cycle analysis (LCA) program, PaLATE, and green highway rating system, BEST-in-Highway. The survey results indicated the wide use of RAP and RCA in hot mix asphalt (HMA) and graded aggregate base (GAB) respectively, while FS and DM are less used in field. Environmental concerns are less, but the possibly low quality and some adverse mechanical characteristics may hinder the widely use of these recycled materials. Technical documents and current specifications provided by State DOTs are good references to the usage of these materials in MD. Literature review showed consistent results with the survey. Studies from experimental research or site tests showed satisfactory performance of these materials in highway applications, when the substitution rate, gradation, temperature, moisture, or usage of additives, etc. meet some requirements. The results from LCA revealed significant cost savings in using recycled materials. Energy and water consumption, gas emission, and hazardous waste generation generally showed reductions to some degree. Use of new recycled technologies will contribute to more sustainable highways.