การทดสอบความเป็นอิสระแบบเบส์สำหรับการแจกแจงพหุนาม โดยใช้การแจกแจงก่อนที่เป็นอิสระต่อกัน / นริศรา วิเชียรเจริญ = Bayesian test of independence for multinomial distribution using independence prior / Narisara Wichiencharoen
To study the test of independence for bivariate incontingency table using Bayesian approach. The computation of Bayesian statistic does not only depends on the collected data but also depends on prior distribution. Prior distribution in this research is in the form of dirichlet distribution and concentrated about independence surface. In addition, the research will compare two classes of test statistics for testing independence between two variables. The statistics in the first class are Pearson's chi-square test statistic and likelihood ratio test statistic and the statistic in the second class is Bayes factors. The variables are in two-way contingency table and have multinomail distribution. For this research, Monte Carlo technique is used by repeating 1,000 times for each case. The results of this research can be summarized as follow: 1. The ability to control probability of type I error. All of 11 test statistics can control probability of type I error in all cases when significance levels are 0.01 and 0.05 2. Power of the test. Power of the test statistics vary according to the sample size, the strength of the relationship between the variables and significance levels. Classic statistics tend to have higer power of the test than Bayes factors in the cases that the sample size is small or the relationship of the variables is weak because the computation of Bayes factors has included the hyperparameter K which reflects the strength of one's prior belief about the independence so that the null hypothesis rejection of Bayes factors are fewer than the null hypothesis rejection of classic statistics. In case that the sample size is large or the relationship of the variable is strong, the power of the test of classic statistics are equal the power of the test of the Bayes factors. Thus, the selection of test statistic depends on one's prior belief about the data. User with no prior belief about the data would better manipulate classic statistic. On the other hand, user with prior belief about independence would find it more compelling to engage Bayes factor using independence prior.
