Effects of management on native and exotic plant communities in Pictured Rocks National Lakeshore in the Upper Peninsula of Michigan

Ecological disturbances may be caused by a range of biotic and abiotic factors. Among these are disturbances that result from human activities such as the introduction of exotic plants and land management activities. This dissertation addresses both of these types of disturbance in ecosystems in the Upper Peninsula of Michigan. Invasive plants are a significant cause of disturbance at Pictured Rocks Natural Lakeshore. Management of invasive plants is dependent on understanding what areas are at risk of being invaded, what the consequences of an invasion are on native plant communities and how effective different tools are for managing the invasive species. A series of risk models are described that predict three stages of invasion (introduction, establishment and spread) for eight invasive plant species at Pictured Rocks National Lakeshore. These models are specific to this location and include species for which models have not previously been produced. The models were tested by collecting point data throughout the park to demonstrate their effectiveness for future detection of invasive plants in the park. Work to describe the impacts and management of invasive plants focused on spotted knapweed in the sensitive Grand Sable Dunes area of Pictured Rocks National Lakeshore. Impacts of spotted knapweed were assessed by comparing vegetation communities in areas with varying amounts of spotted knapweed. This work showed significant increases in species diversity in areas invaded by knapweed, apparently as a result of the presence of a number of non-dune species that have become established in spotted knapweed invaded areas. An experiment was carried out to compare annual spot application of two herbicides, Milestone® and Transline® to target spotted knapweed. This included an assessment of impacts of this type of treatment on non-target species. There was no difference in the effectiveness of the two herbicides, and both significantly reduced the density of spotted knapweed during the course of the study. Areas treated with herbicide developed a higher percent cover of grasses during the study, and suffered limited negative impacts on some sensitive dune species such as beach pea and dune stitchwort, and on some other non-dune species such as hawkweed. The use of these herbicides to reduce the density of spotted knapweed appears to be feasible over large scales.

Detection of complex point targets with distributed assets in a MIMO radar system

The report explores the problem of detecting complex point target models in a MIMO radar system. A complex point target is a mathematical and statistical model for a radar target that is not resolved in space, but exhibits varying complex reflectivity across the different bistatic view angles. The complex reflectivity can be modeled as a complex stochastic process whose index set is the set of all the bistatic view angles, and the parameters of the stochastic process follow from an analysis of a target model comprising a number of ideal point scatterers randomly located within some radius of the targets center of mass. The proposed complex point targets may be applicable to statistical inference in multistatic or MIMO radar system. Six different target models are summarized here – three 2-dimensional (Gaussian, Uniform Square, and Uniform Circle) and three 3-dimensional (Gaussian, Uniform Cube, and Uniform Sphere). They are assumed to have different distributions on the location of the point scatterers within the target. We develop data models for the received signals from such targets in the MIMO radar system with distributed assets and partially correlated signals, and consider the resulting detection problem which reduces to the familiar Gauss-Gauss detection problem. We illustrate that the target parameter and transmit signal have an influence on the detector performance through target extent and the SNR respectively. A series of the receiver operator characteristic (ROC) curves are generated to notice the impact on the detector for varying SNR. Kullback–Leibler (KL) divergence is applied to obtain the approximate mean difference between density functions the scatterers assume inside the target models to show the change in the performance of the detector with target extent of the point scatterers.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.