A theoretical approach to Bayesian statistical inference by a special shrinkage prior distribution

对于平衡的ANOVA设置，我们提出了一种新的闭合形式的贝叶斯因子，它不需要积分表示，但它是基于完全贝叶斯方法的，对于两种渐近情况(该因子的级数或每级的重复次数都是无穷的)，具有合理的模型选择一致性。在一种特殊的先验选择下，对边际密度的精确解析计算使这样的贝叶斯因子成为可能。与现有的贝叶斯因子相比，我们的贝叶斯因子最大的优点是它的良好的闭合形式。由于许多基于完全贝叶斯方法的贝叶斯因子在表示中涉及积分，在实际应用中必须使用拉普拉斯近似。然而，对于哪种类型的拉普拉斯近似更合适的问题，在某些情况下，答案是模糊的。另一方面，我们的贝叶斯因子不需要考虑，并且具有合理的模型选择一致性

For the balanced ANOVA setup, we propose a new closed form Bayes factor without integral representation, which is however based on fully Bayes method, with reasonable model selection consistency for two asymptotic situations (either number of levels of the factor or number of replication in each level goes to infinity). Exact analytical calculation of the marginal density under a special choice of the priors enables such a Bayes factor. The most advantage of our Bayes factor over existing Bayes factors is its excellent closed form. Since many Bayes factors based on fully Bayes method involve the integral in the representation, they have to apply the Laplace approximation in practice. However, the answer to the question which type of the Laplace approximation is more appropriate, is obscure for some cases. On the other hand, our Bayes factor does not require thought and has a reasonable model selection consistency