The objectives of this research are to propose a Bayesian model for spatial time series analysis to apply the proposed model to forecast a monthly rubber yield in Southern provinces of Thailand and to compare the performance of the proposed model with the classical Holt-Winters Additive Exponential smoothing. The proposed model is a linear mixed model (LMM) with spatial effects which follow a conditional autoregressive model (CAR). Dummy variables are used for seasonal effects. A Bayesian method is used for parameter estimation. The estimated monthly yields are used for the monthly rubber yield forecasting. The dependent variables are the rubber yield in each month of each province. The data are secondary data at a provincial level. The factors considered are spatial effects heterogeneity effects and seasonal effects. The results show that the factors influencing on the amount of rubber yields are spatial heterogeneity and seasonal effects. The proposed model is proper and forecast accurately. Using the mean absolute error (MAE) the proposed model has a better performance compared to the classical Holt-Winters Additive Exponential smoothing in both model fitting and model validating. The proposed model should be the first consideration for spatial time series forecasting.

The objectives of this research are: to study the characteristics of students in the Faculty of Engineering at Rajamangala University of Technology Pra Nakorn North Bangkok Campus that influence to the risk of withdrawal from Calculus 2 for Engineers; to predict the risk of withdrawal from Calculus 2 for Engineers; and to use the results of the study for planning and solving the problems of withdrawal from Calculus 2 for Engineers. The sample is 226 students in the Faculty of Engineering at Rajamangala University of Technology who enrolled the Calculus 2 for engineers in the second semester of the academic year 2009. The data are from the questionnaire. The factors considered are grad point average the number of enrollments for the Calculus 1 for engineers Calculus 1 for Engineers grade the number of courses that emphasize on calculation that were enrolled in the second semester of the academic year 2009 the sacrifices of students for the Calculus 2 for Engineers course and the need to withdraw from Calculus 2 for Engineers course before other courses. The logistic regression model in which the parameters are estimated by using Bayesian methods is used for analyzing the data. The study shows that the factors that influence to the risk of withdrawal from the Calculus 2 for Engineers are grade point average Calculus 1 for Engineers grade the number of courses that emphasize on calculation that were enrolled in the second semester of the academic year 2009 and the sacrifices of students for the Calculus 2 for Engineers and the need to withdraw from Calculus 2 for Engineers before other courses. The factor that does not influence to the risk of withdrawal from the Calculus 2 for Engineers is the number of enrollments for the Calculus 1 for Engineers.

This research aims to apply the principle of stochastic process for modeling. The parameters are estimated using Bayesian methods. The monthly average real price of paddy rice 15% and yield of paddy rice in Thailand were studied. The price and the yield of paddy rice which are time series data consisting of four components autocorrelation an exponential cumulative distribution function for trend outliers and two different types of seasons: the dummy seasons and Fourier function seasons. Writing algorithms programming in OpenBUGS and evaluating the performance of models from simulation programming in R were conducted. After that Bayesian methods with dummy seasons and Fourier function season were compared using RMSE MSE and MAE as the criteria. The results show that the Bayesian model with an exponential cumulative distribution function for trend and dummy seasons give the lowest RMSE MSE and MAE for both model fitting and model validating.

The objectives of this research are to estimate the morbidity rate of Dengue Hemorrhagic fever in each province of Thailand and to construct the map of the Dengue Hemorrhagic fever. A Bayesian model is used for the data analysis. The data are mathematical spatial correlated in the form of the conditional autoregressive model (CAR). The secondary data were collected at a provincial level. They were the number of Dengue Hemorrhagic fever patients rainfall and average temperature. The research found that the rainfall (RR = 1.0026) and the average temperature (RR = 1.2681) had influence on the morbidity of Dengue Hemorrhagic fever. The season during July to September had more influence on the morbidity of Dengue Hemorrhagic fever than during the other seasons. The top 5 highest morbidity rates per 100000 population were Chiangmai in October (1288.00) July (1096.00) September (804.30) Surin in October (772.30) and Nakhon Si Thammarat in August (666.20). The disease map constructed for showing the distribution of the disease is easy to understand and useful for public health.