การเปรียบเทียบวิธีการคัดเลือกสมการถดถอยที่ดีที่สุดเชิงเบส์เมื่อใช้การแจกแจงก่อนแบบคู่สังยุคปกติ - จิตติมา ผสมญาติ (จุฬาลงกรณ์มหาวิทยาลัย, 2003)
The objective of this research is to compare the Bayesian selection methods for best regression equation with conjugate normal prior distribution. The three Bayesian selection methods for best regression equation in this comparison composed of Bayesian Model Averaging method using Markov Chain Monte Carlo model composition via Simultaneous Variable and Transformation Selection (BMA[subscript SVT]), Optimal Predictive Model Selection (OPM) and Stepwise Regression method (SR). The average of mean square error (AMSE) and the ratio of different average mean square error (RDAMSE) were used as the criteria in this project. The details of the data were represented as follows. In this study, the distribution of random errors are normal distribution with mean equal to 0 and standard deviation equal to 0.25 0.50 and 2.50, respectively. The sizes of the samples are varied, which composed of 15, 30, 50 and 100 samples. The numbers of independent variables in regression model are 3, 5, 8, 10, 12, and 15. The Bayesian hyperparameters (sigma[subscript beta]/tau,c) for BMA[subscript SVT] and OPM are (1,5) (1,10) (10,100) and (10,500), respectively. Using the Monte Carlo simulation technique with 500 repetitions for each case generated all data. The analyzed results of data were demonstrated as follow. The comparisons of the AMSE from three methods ranging from minimum to maximum were BMA[subscript SVT], OPM and SR for all cases. The OPM gave AMSE slightly higher than BMA[subscript SVT] especially when the Bayesian hyperparameters (sigma[subscript beta]/tau,c) had low values. The SR gave AMSE clearly different from BMA[subscript SVT] and OPM in all cases. The factors that affected AMSE of all methods are sample size, the standard deviation of random errors and the number of independent variables. The AMSE of all method were proportionate to the standard deviation of random errors and the number of independent variables although they were inversely proportionate to sample size. Furthermore, the AMSE of two methods under Bayesian Approach, BMA[subscript SVT] and OPM were proportionate to the Bayesian hyperparameters (sigma[subscript beta]/tau,c) and whereas the AMSE of SR was constant because we did not consider the Bayesian hyperparameters (sigma[subscript beta]/tau,c).