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.

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.