Score Test Derivations and Implementations for Bivariate Probability Mass and Density Functions with an Application to Copula Functions

This dissertation is comprised and grounded in statistical theory with an application to solving real world problems. In particular, the development and implementation of multiple score tests under a variety of scenarios are derived, applied, and interpreted. In chapter 2, I propose a score test for independence of the marginals based on Lakshminarayana’s bivariate Poisson distribution. Each marginal distribution of the bivariate model is a univariate Poisson distribution, and the parameters of the bivariate distribution can be estimated using maximum likelihood methods. The simulation study shows that the score test maintains size close to the nominal level. To assess the efficiency of the derived score test, the estimated significance levels and powers of the likelihood ratio and Wald tests are compared. A relevant data set is used to illustrate the application of the bivariate Poisson model and the proposed score test for independence. In chapter 3, two score tests are proposed: one for testing independence based on Sankaran and Nair’s bivariate Pareto distribution and one for testing whether Sankaran and Nair’s parameterization reduces to the more popular bivariate Pareto distribution introduced by Lindley–Singpurwalla. The marginal distributions of both bivariate parameterizations are univariate Pareto II distributions, and the parameters of the bivariate distribution are estimated using numerical methods. The simulation studies show that both score tests maintain a significance level close to the nominal size. To check the efficiency of the derived score tests, the estimated significance levels and powers of the likelihood ratio and Wald tests are also compared. One real world data set is used to illustrate the application of both score tests. In chapter 4, an increasingly popular approach to model the dependence between random variables via the use of copula functions is explored. A score test for testing independence of response variables is proposed for the specific case where the marginal distributions are known to be Poisson. The simulation study shows the test keeps the significance level close to the nominal one. Similarly, the estimated significance levels and powers of the likelihood ratio and Wald tests are also compared to show our test is numerically stable. A real world data set is used to demonstrate the application of the test

Metacognition of First Year Occupational Therapy Students: A Comparison of Entry-Level Degrees

The purpose of this study was to compare the metacognitive awareness among first year students in entry-level occupational therapy programs. The study investigated the similarities and differences in awareness of cognition and strategies used to regulate cognition in occupational therapy assistant (OTA), Master of Occupational Therapy (MOT), and Occupational Therapy Doctorate (OTD) programs to inform teaching practices for the different educational demands and expected outcomes of each program. Thirty occupational therapy students (11 OTA, 10 MOT, and 9 OTD) completed the Metacognitive Awareness Inventory (MAI) during their first semester of occupational therapy courses at two universities. Overall, the results indicated the student reported use of metacognitive strategies was more similar than dissimilar among the three entry-level programs. Additionally, MAI responses were not predictive of course grades. Instructors can design educational experiences to tap into the metacognition of the student, promoting effective and efficient learning to meet the high educational standards required for our profession. Students who are effective and efficient learners will be more prepared to meet the demands of a complex healthcare environment in their respective practitioner roles

Patterns of Land Use Change, Land Governance, and the Supply of Ecosystem Services in a Multifunctional Landscape: A Case Study from Upstate SC, USA

Urban expansion and development continue to increase globally, threatening rural multifunctional landscapes that provide a diversity of direct and indirect ecological benefits. However, not all landscapes are equally impacted, thus making conservation planning more difficult. We used 8 years of land use and land cover to understand this change in Greenville Co. SC, a region experiencing rapid expansion of development into rural landscapes. Regression models helped explain the relationships between development predictor variables and rural response variables. To explore where these changes were occurring, we determined which size categories of land parcels were the most developed and how this is changing over time. Developed open space was revealed to significantly impact rural character, pasture, and evergreen forest most frequently. It was also found to be most prevalent in the smallest parcels. Determining relationships between development, rural character, and multifunctionality will aid in potential solutions for the conservation of multifunctional landscapes

Using Metacognitive Training with Kinesiology Students

As future healthcare practitioners, kinesiology students must become expert learners who choose strategies resulting in deep and durable learning. Metacognitive instruction goes beyond the use of study skills as it focuses on student reflection and evaluation of their learning success, and ultimately establishes effective learning skills, a requirement for professional practice. To examine if an intervention in a kinesiology course affected metacognitive awareness and use of metacognitive strategies, a quasi-experimental research design utilized a convenience sample of 89 upper division undergraduate occupational therapy students and master’s level athletic training students enrolled in kinesiology courses. Using an online survey including the Metacognitive Awareness Inventory (Schraw & Dennison, 1994) and three Likert scale questions about perception of study skills, pre-test and post-test data were collected over three years, and 6-month follow-up data were collected during the final two years of the study. The intervention included information about metacognition and key study tips, five learning activities, and teaching techniques to promote metacognition. Treating the pre-test group as the reference group, the results showed that the post-test and 6-month follow-up test groups were significant predictors of students’ scores on the Metacognitive Awareness Inventory, indicating an improved and sustained metacognitive awareness after completing the course. The intervention was found to have a positive association with scores of planning, information management, comprehension monitoring, and evaluation. These results indicate the value of metacognition instruction. Considering that not all students come equipped with metacognitive skills, instruction in this area could be beneficial to students

Magnetic field near the central region of the Galaxy: Rotation measure of extragalactic sources

To determine the properties of the Faraday screen and the magnetic field near the central region of the Galaxy, we measured the Faraday rotation measure (RM) towards 60 background extragalactic source components through the -6 deg < l <6 deg, -2 deg < b < 2 deg region of the Galaxy using the 4.8 and 8.5 GHz bands of the ATCA and VLA. Here we use the measured RMs to estimate the systematic and the random components of the magnetic fields. The measured RMs are found to be mostly positive for the sample sources in the region. This is consistent with either a large scale bisymmetric spiral magnetic fields in the Galaxy or with fields oriented along the central bar of the Galaxy. The outer scale of the RM fluctuation is found to be about 40 pc, which is much larger than the observed RM size scales towards the non-thermal filaments (NTFs). The RM structure function is well-fitted with a power law index of 0.7 +/- 0.1 at length scales of 0.3 to 100 pc. If Gaussian random processes in the ISM are valid, the power law index is consistent with a two dimensional Kolmogorov turbulence. If there is indeed a strong magnetic field within 1 degree (radius 150 pc) from the GC, the strength of the random field in the region is estimated to be 20 microGauss. Given the highly turbulent magnetoionic ISM in this region, the strength of the systematic component of the magnetic fields would most likely be close to that of the random component. This suggests that the earlier estimated milliGauss magnetic field near the NTFs is localised and does not pervade the central 300 pc of the Galaxy.Comment: 9 pages, 6 figures, accepted for publication in A&

Testing the viability of measuring intraocular pressure using soundwaves from a smartphone

Abstract Early detection of increasing values of intraocular pressure (IOP) due to glaucoma can prevent severe ocular diseases and ultimately, prevent loss of vision. Currently, the need for an accurate, mobile measurement of IOP that shows no correlation to central corneal thickness is unmet within the modern healthcare practices. There is a potential to utilize soundwaves as a mobile measurement method and therefore, the relationship between IOP and the reflection coefficient of sound waves is investigated. Simulations are conducted using COMSOL Multiphysics to provide theoretical confirmation of the worthiness of the experiment. An experiment is conducted to further investigate the relationship between the internal pressure of an object and its acoustic reflection coefficient. The experiment exploits the use of hydrostatic pressure to determine internal pressure, and the reflection coefficient is measured and analyzed. An initial experiment is conducted to identify the resonant frequency of the object and the optimal frequency for maximizing reflection. The experiment shows comprehensively that there is a relationship between the internal pressure of an object and its acoustic reflection coefficient, providing a confirmation of the theory that would allow mobile measurements of IOP to be conducted with the use of a smart phone

Multiwavelength VLBI observations of Sagittarius A*

The compact radio source Sgr\,A*, associated with the super massive black hole at the center of the Galaxy, has been studied with VLBA observations at 3 frequencies (22, 43, 86\,GHz) performed on 10 consecutive days in May 2007. The total VLBI flux density of Sgr\,A* varies from day to day. The variability is correlated at the 3 observing frequencies with higher variability amplitudes appearing at the higher frequencies. For the modulation indices, we find 8.4\,% at 22\,GHz, 9.3\,% at 43\,GHz, and 15.5\,% at 86\,GHz. The radio spectrum is inverted between 22 and 86\,GHz, suggesting inhomogeneous synchrotron self-absorption with a turnover frequency at or above 86\,GHz. The radio spectral index correlates with the flux density, which is harder (more inverted spectrum) when the source is brighter. The average source size does not appear to be variable over the 10-day observing interval. However, we see a tendency for the sizes of the minor axis to increase with increasing total flux, whereas the major axis remains constant. Towards higher frequencies, the position angle of the elliptical Gaussian increases, indicative of intrinsic structure, which begins to dominate the scatter broadening. At cm-wavelength, the source size varies with wavelength as $\lambda^{2.12\pm0.12}$, which is interpreted as the result of interstellar scatter broadening. After removal of this scatter broadening, the intrinsic source size varies as $\lambda^{1.4 ... 1.5}$. The VLBI closure phases at 22, 43, and 86\,GHz are zero within a few degrees, indicating a symmetric or point-like source structure. In the context of an expanding plasmon model, we obtain an upper limit of the expansion velocity of about 0.1\,c from the non-variable VLBI structure. This agrees with the velocity range derived from the radiation transport modeling of the flares from the radio to NIR wavelengths.}Comment: 14pages, 14 Figures, Accepted for publication in A&

GCRT J1742-3001: A New Radio Transient Towards the Galactic Center

We report the detection of a new transient radio source, GCRT J1742-3001, located ~1 degree from the Galactic center. The source was detected ten times from late 2006 to 2007 May in our 235 MHz transient monitoring program with the Giant Metrewave Radio Telescope (GMRT). The radio emission brightened in about one month, reaching a peak observed flux density of ~100 mJy on 2007 January 28, and decaying to ~50 mJy by 2007 May when our last monitoring observation was made. Two additional faint, isolated 235 MHz detections were made in mid-2006, also with the GMRT. GCRT J1742-3001 is unresolved at each epoch, with typical resolutions of ~20 arcsec x 10 arcsec. No polarization information is available from the observations. Based on nondetections in observations obtained simultaneously at 610 MHz, we deduce that the spectrum of GCRT J1742-3001 is very steep, with a spectral index less than about -2. Follow-up radio observations in 2007 September at 330 MHz and 1.4 GHz, and in 2008 February at 235 MHz yielded no detections. No X-ray counterpart is detected in a serendipitous observation obtained with the X-ray telescope aboard the Swift satellite during the peak of the radio emission in early 2007. We consider the possibilities that GCRT J1742-3001 is either a new member of an existing class of radio transients, or is representative of a new class having no associated X-ray emission.Comment: 19 pages, 3 figures, submitted to Ap

Extragalactic sources towards the central region of the Galaxy

We have observed a sample of 64 small diameter sources towards the central -6 degree < l< 6 degree, -2 degree < b < 2 degree of the Galaxy with the aim of studying the Faraday rotation measure near the Galactic Centre (GC) region. All the sources were observed at 6 and 3.6 cm wavelengths using the ATCA and the VLA. Fifty nine of these sources are inferred to be extragalactic. The observations presented here constitute the first systematic study of the radio polarisation properties of the background sources towards this direction and increases the number of known extragalactic radio sources in this part of the sky by almost an order of magnitude. Based on the morphology, spectral indices and lack of polarised emission, we identify four Galactic HII regions in the sample.Comment: 24 pages, 67 figures, published earlier in MNRA

VLBI observations of weak sources using fast frequency switching

We have developed a new phase referencing technique for high frequency VLBI observations. In conventional phase referencing, one interleaves short scans on a nearby phase calibrator between the target source observations. In fast frequency switching described here, one observes the target source continuously while switching rapidly between the target frequency and a lower reference frequency. We demonstrate that the technique allows phase calibration almost reaching the thermal noise limit and present the first detection of the AGN in the FR I radio galaxy NGC 4261 at 86 GHz. Although point-like, this is the weakest source ever detected with VLBI at this frequency.Comment: Accepted by A&A, 14 pages, 12 figures, needs aa.cls, aas_macros.sty and amsmath.sty, replaced due reformattin