方差未知且不等时均数差别Bayes分析的MonteCarlo方法

Bayesian Analysis for the Difference of Means of Two lndependent Normal Populations with Unequal Variances:A Monte Carlo Sampling Approach

目的 解决方差未知且不等时总体均值差别的推断问题。方法 根据Bayes理论构造两总体均数差值的后验分布Behrens Fisher分布 ,用MonteCarlo模拟方法产生Behrens Fisher的频数分布进行统计推断。结果 模拟样本足够大时 ,获得Behrens Fisher的精确分布、均数差值的置信区间及假设检验结果。结论 与其他Behrens Fisher分布的近似方法结果相同 ,但本方法不依赖t分布和其他任何界值表 ,并同时给出置信区间。

Objective To solve the problem of statistical inference for the difference of means when the populations' variances are unknown and not assumed equal.Methods Performing a Bayesian analysis by Monte Carlo sampling technique to get Behrens Fisher frequency distribution.Results Summary statistics such as the difference of means and 95% credible interval are presented,also a hypotheses test is performed.Conclusion The results are accordance with classical results,but the advantage is no any more critical values such as t distribution are needed and to present credible interval directly.