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

对于平衡方差分析设置，我们提出了一个新的封闭形式的贝叶斯因子没有积分表示，这是完全贝叶斯方法的基础上，合理的模型选择的一致性为两个渐近的情况下（无论是因子的水平数或在每个水平的重复数趋于无穷大）。精确的分析计算的边缘密度下的先验的特殊选择，使这样的贝叶斯因子。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具有良好的封闭形式。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，因此在实际应用中必须采用拉普拉斯近似。然而，在某些情况下，哪种类型的拉普拉斯近似更合适的问题的答案是模糊的。另一方面，我们的贝叶斯因子不需要思考，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