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Cluster analysis identifies homogeneous groups that are relevant within a population. In model-based clustering, group membership is estimated using a parametric finite mixture model, commonly the mathematically tractable Gaussian mixture model. One-way clustering methods can be restrictive in cases where there are suspected relationships between the variables in each component, leading to the idea of biclustering, which refers to clustering both observations and variables simultaneously. When the relationships between the variables are known, biclustering becomes one-way supervised. To this end, this thesis focuses on a novel one-way supervised biclustering family based on the Gaussian mixture model. In cases where biclustering may be overestimating the number of components in the data, a model averaging technique utilizing Occam's window is applied to produce better clustering results. Automatic outlier detection is introduced into the biclustering family using mixtures of contaminated Gaussian mixture models. Algorithms for model-fitting and parameter estimation are presented for the techniques described in this thesis, and simulation and real data studies are used to assess their performance. / Thesis / Doctor of Philosophy (PhD)

Despite valiant effort by astronomers, the mass of the Milky Way (MW) Galaxy is poorly constrained, with estimates varying by a factor of two. A range of techniques have been developed and different types of data have been used to estimate the MW’s mass. One of the most promising and popular techniques is to use the velocity and position information of satellite objects orbiting the Galaxy to infer the gravitational potential, and thus the total mass. Using these satellites, or Galactic tracers, presents a number of challenges: 1) much of the tracer velocity data are incomplete (i.e. only line-of-sight velocities have been measured), 2) our position in the Galaxy complicates how we quantify measurement uncertainties of mass estimates, and 3) the amount of available tracer data at large distances, where the dark matter halo dominates, is small. The latter challenge will improve with current and upcoming observational programs such as Gaia and the Large Synoptic Survey Telescope (LSST), but to properly prepare for these data sets we must overcome the former two. In this thesis work, we have created a hierarchical Bayesian framework to estimate the Galactic mass profile. The method includes incomplete and complete data simultaneously, and incorporates measurement uncertainties through a measurement model. The physical model relies on a distribution function for the tracers that allows the tracer and dark matter to have different spatial density profiles. When the hierarchical Bayesian model is confronted with the kinematic data from satellites, a posterior distribution is acquired and used to infer the mass and mass profile of the Galaxy. This thesis walks through the incremental steps that led to the development of the hierarchical Bayesian method, and presents MW mass estimates when the method is applied to the MW’s globular cluster population. Our best estimate of the MW’s virial mass is 0.87 (0.67, 1.09) x 10^(12) solar masses. We also present preliminary results from a blind test on hydrodynamical, cosmological computer-simulated MW-type galaxies from the McMaster Unbiased Galaxy Simulations. These results suggest our method may be able to reliably recover the virial mass of the Galaxy. / Thesis / Doctor of Philosophy (PhD)

Advocates of privatizing education suggest that traditional public schools are not adequately preparing students for college, career readiness, and global citizenship (Lobosco, 2019; Schneider and Berkshire, 2020; Tienken and Mullen, 2016). Charter school supporters believe charter school students perform better than public school children on state standardized tests (Lubienski and Lubienski, 2014). Advocates for traditional public schools promote the idea that there are no significant differences between public and charter schools in academic achievement (Chen, 2020b; Fischler, 2021). This study compares public and charter elementary school students in terms of their reading and math assessment scores, both as measured by the Virginia Standard of Learning (SOL) for the 2018-2019 school year. Data were collected and analyzed on 642 students enrolled in three of Virginia's elementary charter schools and three traditional public schools in Loudoun County and Richmond City. SOL assessment data for the public and charter schools were compared for the overall student population per grade level to determine if there is a significant difference for the 2018-2019 school year. A two-way ANOVA was utilized in this study. Results indicated no significant differences in the reading mean SOL assessment scores between traditional public elementary and public charter school students: F (1, 636) = .119, p = .730. Additionally, results showed no significant interaction between school type and grade level between traditional public elementary and public charter schools: F (2, 636) = 1.076, p = .342. However, findings revealed a significant difference in the reading SOL assessment scores between grade levels of traditional public elementary schools and public charter schools: F (2, 636) = 4.473, p = .012. Furthermore, results from the math analysis indicated no statistical differences in math SOL scores between traditional public elementary schools and public charter schools: F (1, 636) = .000, p = .997. Also, findings indicated no significant difference in the math SOL scores between the grade levels of traditional public elementary and public charter schools: F (2, 636) = .520, p = .595. / Doctor of Education / Advocates of privatizing education suggest that traditional public "brick-and-mortar" schools are not adequately preparing students for college, career readiness, and global citizenship (Lobosco, 2019; Tienken and Mullen, 2016; Schneider and Berkshire, 2020). Charter school supporters believe charter school students perform better than public school children on state standardized tests (Lubienski and Lubienski, 2014). Advocates for traditional public schools promote the idea that there are no significant differences between public and charter schools in academic achievement (Chen, 2020b; Fischler, 2021). This study compares public and charter elementary school students in terms of their reading and math assessment scores, both as measured by the Virginia Standard of Learning (SOL) for the 2018-2019 school year. Data were collected and analyzed on 642 students enrolled in three of Virginia's elementary charter schools and three traditional public schools in Loudoun County and Richmond City. SOL assessment data for the public and charter schools were compared for the overall student population per grade level to determine if there is a significant difference for the 2018-2019 school year. This study did not reveal any significant differences in reading and math SOL scores between traditional elementary public schools and public elementary charter schools. However, findings in this study revealed significant differences in reading SOL scores on average among grade levels. Conversely, findings did not reveal any differences in math SOL assessment scores on average between grade levels of traditional public elementary school and public elementary charter school students.

The subject of this thesis was the verification and the implementation of a multiple retransmission technique for the one-way asynchronous communication channel of the Interactive Video Data Service (IVDS) system. The commercial application of the IVDS project made reliability of the retransmission technique important. Verification of the reliability of the technique was done using a simulator written in the C programming language. The results of the IVDS simulator were compared to the existing statistical model of the transmission channel. Following a favorable comparison of the statistical model and simulator results, a prototype of the control section for the IVDS Consumer Control Unit (CCU) was designed and constructed. This was an important step towards the completion of the IVDS system. The CCU design defined protocols for message format and error detection and also helped to establish an IVDS test-bed system. / Master of Science