对Johnson (2004)提出的Bayes${\chi }^2$-检验进行了两种修正, 一种修正是基于后验期望和后验分位数,另一种修正是基于后验预测 $p$-值的概念修正的检验不仅大大减小了计算的复杂度, 而且从模拟结果来看,在功效上有明显的改进和提高.

In this paper, we present two classes of modifications to the Bayesian 2 test proposed by Johnson (2004). One methois based on the posterior mean
and posterior quantiles, the other is based on the concept of the posterior predictive p-value. The new tests are not only easy to compute, but also have some better performances in the power.