基于后验预测分布的贝叶斯模型评价及其在霍乱传染数据中的应用*
Bayesian model checking based on posterior predictive distribution and application to cholera data

目的：探讨基于后验预测分布的贝叶斯模型评价方法。 方法：采用贝叶斯ZIP模型和Possion模型分析霍乱传染数据，通过后验预测分布评价2个模型的拟合优度。结果：如果以数据中0的家庭数为差别检验统计量，则Poisson模型和ZIP模型的后验预测P值分别为0.038和0.503。如果以χ2为差别检验统计量，则Poisson模型和ZIP模型的后验预测P值分为0.005和0.476。结论：ZIP模型对霍乱传染数据拟合良好，而Possion模型拟合不足。
Aim: To explore methods for the Bayesian model checking based on the posterior predictive distribution. Methods: The Bayesian zero？？inflated Poisson (ZIP) and Possion models were employed to fit the cholera data, and the posterior predictive distribution was applied for model checking. Results: The posterior predictive P values were respectively 0.038 and 0.503 for the Poisson and ZIP models if the proportion of zero in the data was used as the discrepancy test quantity, and they were respectively 0.005 and 0.476 for the Poisson and ZIP models if χ2 was used as the discrepancy test quantity. Conclusion: The results suggest that the ZIP model could appropriately handle the presence of too many zeros in the cholera data, but Poisson model fails