论文标题
后平均信息标准
Posterior Averaging Information Criterion
论文作者
论文摘要
我们从预测的角度提出了一种新的模型选择方法，即后平均信息标准，用于贝叶斯模型评估。理论基础建立在Kullback-Leibler差异上，以量化所提出的候选模型与基础真实模型之间的相似性。从贝叶斯的角度来看，我们的方法在预测未来的独立观察方面评估了整个后验分布的候选模型。在不假设候选模型中包含真正的分布的情况下，新标准是通过纠正对数似然的后均值偏差来与其预期的对数似然性的。它通常可以应用于具有非信息性先验的贝叶斯模型。在正常和二项式设置中的模拟都表明了体面的小样本性能。
We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the similarity between the proposed candidate model and the underlying true model. From a Bayesian perspective, our method evaluates the candidate models over the entire posterior distribution in terms of predicting a future independent observation. Without assuming that the true distribution is contained in the candidate models, the new criterion is developed by correcting the asymptotic bias of the posterior mean of the log-likelihood against its expected log-likelihood. It can be generally applied even for Bayesian models with degenerate non-informative prior. The simulation in both normal and binomial settings demonstrates decent small sample performance.
