We develop a robust Bayesian analysis based on heavy-tailed modeling. It is common to impose a Student-$t$ distribution to eliminate the influence of outliers. We apply it to large-scale studies in Bayesian inference, and provide diagnoses for detecting outliers using the posterior predictive $p$-value ($ppp$). In addition, we propose an adaptive method to decide the level of the posterior FDR. We suggest an adaptive method to determine it using an estimated ratio of true null genes using Storey's $q$-value method. Our methods are demonstrated on gene expression data for colorectal cancer.

翻译：我们提出一种基于重尾分布的鲁棒贝叶斯分析方法。通常采用学生-$t$分布来消除异常值的影响。我们将此方法应用于大规模贝叶斯推断研究，并利用后验预测$p$值（$ppp$）提供异常值检测诊断。此外，我们提出一种自适应方法来确定后验FDR的水平。我们建议使用Storey的$q$值方法，通过估计真实零假设基因的比例来自适应地确定该水平。我们的方法在结直肠癌基因表达数据上得到了验证。