论文标题
统一偏度分布家族的扩展以及对贝叶斯二进制回归的应用
An Extension of the Unified Skew-Normal Family of Distributions and Application to Bayesian Binary Regression
论文作者
论文摘要
我们考虑贝叶斯二进制回归模型，并引入了新的分布，即扰动的统一偏度正常（PSUN，此后），后者概括了统一的偏度正常（Sun）类。我们表明，新类是与任何二进制回归模型共轭的，前提是链接函数可以表示为高斯CDF的比例混合物。我们详细讨论了流行的logit案例，我们表明，当逻辑回归模型与高斯先验结合使用时，可以通过使用重要性采样方法来轻松获得后验摘要，例如累积和正常定义常数，从而为直接的变量选择程序开辟了道路。对于更一般的先验分布，提出的方法基于简单的Gibbs采样器算法。我们还声称，与现有方法相比，在P> n情况下，我们的建议在混合和准确性方面提出了更好的性能。
We consider the Bayesian binary regression model and we introduce a new class of distributions, the Perturbed Unified Skew-Normal (pSUN, henceforth), which generalizes the Unified Skew-Normal (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 CDFs. 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 constants can easily be obtained through the use of an importance sampling approach, opening the way to straightforward variable selection procedures. For more general prior distributions, the proposed methodology is based on a simple Gibbs sampler algorithm. We also claim that, in the p>n case, our proposal presents better performances - both in terms of mixing and accuracy - compared to the existing methods.
