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.

Characterization of legacy organic carbon in a culturally eutrophic lake : the role of the historic carbon deposition in the time course and extent of lake recovery

The time course of lake recovery after a reduction in external loading of nutrients is often controlled by conditions in the sediment. Remediation of eutrophication is hindered by the presence of legacy organic carbon deposits, that exert a demand on the terminal electron acceptors of the lake and contribute to problems such as internal nutrient recycling, absence of sediment macrofauna, and flux of toxic metal species into the water column. Being able to quantify the timing of a lake’s response requires determination of the magnitude and lability, i.e., the susceptibility to biodegradation, of the organic carbon within the legacy deposit. This characterization is problematic for organic carbon in sediments because of the presence of different fractions of carbon, which vary from highly labile to refractory. The lability of carbon under varied conditions was tested with a bioassay approach. It was found that the majority of the organic material found in the sediments is conditionally-labile, where mineralization potential is dependent on prevailing conditions. High labilities were noted under oxygenated conditions and a favorable temperature of 30 °C. Lability decreased when oxygen was removed, and was further reduced when the temperature was dropped to the hypolimnetic average of 8° C . These results indicate that reversible preservation mechanisms exist in the sediment, and are able to protect otherwise labile material from being mineralized under in situ conditions. The concept of an active sediment layer, a region in the sediments in which diagenetic reactions occur (with nothing occurring below it), was examined through three lines of evidence. Initially, porewater profiles of oxygen, nitrate, sulfate/total sulfide, ETSA (Electron Transport System Activity- the activity of oxygen, nitrate, iron/manganese, and sulfate), and methane were considered. It was found through examination of the porewater profiles that the edge of diagenesis occurred around 15-20 cm. Secondly, historical and contemporary TOC profiles were compared to find the point at which the profiles were coincident, indicating the depth at which no change has occurred over the (13 year) interval between core collections. This analysis suggested that no diagenesis has occurred in Onondaga Lake sediment below a depth of 15 cm. Finally, the time to 99% mineralization, the t99, was viewed by using a literature estimate of the kinetic rate constant for diagenesis. A t99 of 34 years, or approximately 30 cm of sediment depth, resulted for the slowly decaying carbon fraction. Based on these three lines of evidence , an active sediment layer of 15-20 cm is proposed for Onondaga Lake, corresponding to a time since deposition of 15-20 years. While a large legacy deposit of conditionally-labile organic material remains in the sediments of Onondaga Lake, it becomes clear that preservation, mechanisms that act to shield labile organic carbon from being degraded, protects this material from being mineralized and exerting a demand on the terminal electron acceptors of the lake. This has major implications for management of the lake, as it defines the time course of lake recovery following a reduction in nutrient loading.

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.

SYSTEM DYNAMICS MODELING AS A QUANTITATIVE-QUALITATIVE FRAMEWORK FOR SUSTAINABLE WATER RESOURCES MANAGEMENT: INSIGHTS FOR WATER QUALITY POLICY IN THE GREAT LAKES REGION

Early water resources modeling efforts were aimed mostly at representing hydrologic processes, but the need for interdisciplinary studies has led to increasing complexity and integration of environmental, social, and economic functions. The gradual shift from merely employing engineering-based simulation models to applying more holistic frameworks is an indicator of promising changes in the traditional paradigm for the application of water resources models, supporting more sustainable management decisions. This dissertation contributes to application of a quantitative-qualitative framework for sustainable water resources management using system dynamics simulation, as well as environmental systems analysis techniques to provide insights for water quality management in the Great Lakes basin. The traditional linear thinking paradigm lacks the mental and organizational framework for sustainable development trajectories, and may lead to quick-fix solutions that fail to address key drivers of water resources problems. To facilitate holistic analysis of water resources systems, systems thinking seeks to understand interactions among the subsystems. System dynamics provides a suitable framework for operationalizing systems thinking and its application to water resources problems by offering useful qualitative tools such as causal loop diagrams (CLD), stock-and-flow diagrams (SFD), and system archetypes. The approach provides a high-level quantitative-qualitative modeling framework for "big-picture" understanding of water resources systems, stakeholder participation, policy analysis, and strategic decision making. While quantitative modeling using extensive computer simulations and optimization is still very important and needed for policy screening, qualitative system dynamics models can improve understanding of general trends and the root causes of problems, and thus promote sustainable water resources decision making. Within the system dynamics framework, a growth and underinvestment (G&U) system archetype governing Lake Allegan's eutrophication problem was hypothesized to explain the system's problematic behavior and identify policy leverage points for mitigation. A system dynamics simulation model was developed to characterize the lake's recovery from its hypereutrophic state and assess a number of proposed total maximum daily load (TMDL) reduction policies, including phosphorus load reductions from point sources (PS) and non-point sources (NPS). It was shown that, for a TMDL plan to be effective, it should be considered a component of a continuous sustainability process, which considers the functionality of dynamic feedback relationships between socio-economic growth, land use change, and environmental conditions. Furthermore, a high-level simulation-optimization framework was developed to guide watershed scale BMP implementation in the Kalamazoo watershed. Agricultural BMPs should be given priority in the watershed in order to facilitate cost-efficient attainment of the Lake Allegan's TP concentration target. However, without adequate support policies, agricultural BMP implementation may adversely affect the agricultural producers. Results from a case study of the Maumee River basin show that coordinated BMP implementation across upstream and downstream watersheds can significantly improve cost efficiency of TP load abatement.

The study of agricultural non-point source pollution control policy system

As the agricultural non-point source pollution(ANPSP) has become the most significant threat for water environmental deterioration and lake eutrophication in China, more and more scientists and technologists are focusing on the control countermeasure and pollution mechanism of agricultural non-point source pollution. The unreasonable rural production structure and limited scientific management measures are the main reasons for acute ANSPS problems in China. At present, the problem for pollution control is a lack of specific regulations, which affects the government's management efficiency. According to these characteristics and problems, this paper puts forward some corresponding policies. The status of the agricultural non-point source pollution of China is analyzed, and ANSPS prevention and control model is provided based on governance policy, environmental legislation, technical system and subsidy policy. At last, the case analysis of Qiandao Lake is given, and an economic policy is adopted based on its situation.