We consider the general problem of Bayesian binary regression and we introduce a new class of distributions, the Perturbed Unified Skew Normal (pSUN), which generalizes the SUN class. We show that the new class is conjugate to any binary regression model, provided that the link function may be expressed as a scale mixture of Gaussian densities. We discuss in detail the popular logit case, and we show that, when a logistic regression model is combined with a Gaussian prior, posterior summaries such as cumulants and normalizing constant, can be easily obtained, opening the way to straightforward variable selection procedures. For more general priors, the proposed methodology is based on a straightforward Gibbs sampler algorithm. We also claim that, in the p > n case, it shows better performances both in terms of mixing and accuracy, compared to the existing methods. We illustrate the performance of the proposal through a simulation study and two real datasets, one covering the standard case with n >> p and the other related to the p >> n situation.

翻译：我们考虑了巴伊西亚二进制回归的一般问题,我们引入了一个新的分布类别,即普接统一Skew常态(pSUN),该类别对 SUN 类进行概括化。我们表明,新类别与任何二进制回归模式是共通的,条件是链接函数可以作为高斯密度的尺度混合表示。我们详细讨论流行的登录案例,我们显示,当后勤回归模式与先前的Gausian 合并时,可以很容易地获得堆积物和常态等事后总结,为直接的变量选择程序开辟道路。对于更一般而言,拟议的方法以直截了当的Gibbs采样器算法为基础。我们还声称,在p > n 的情况下,与现有方法相比,在混合和准确性两方面都表现得更好。我们通过模拟研究和两个真实数据集来说明该提案的绩效,一个是覆盖n+p,另一个是覆盖标准案例。