BAYESIAN REGRESSION ANALYSIS WITH SCALE MIXTURES OF NORMALS
研究了在正态尺度混合分布下线性回归模型的贝叶斯分析，探讨了后验分布的存在性及后验矩的存在条件，并给出了有限混合正态、Pearson VII等分布下的完整刻画，推荐使用吉布斯抽样进行数值实现。
This paper considers a Bayesian analysis of the linear regression model under independent sampling from general scale mixtures of normals. Using a common reference prior, we investigate the validity of Bayesian inference and the existence of posterior moments of the regression and scale parameters. We find that whereas existence of the posterior distribution does not depend on the choice of the design matrix or the mixing distribution, both of them can crucially intervene in the existence of posterior moments. We identify some useful characteristics that allow for an easy verification of the existence of a wide range of moments. In addition, we provide full characterizations under sampling from finite mixtures of normals, Pearson VII, or certain modulated normal distributions. For empirical applications, a numerical implementation based on the Gibbs sampler is recommended.