In this paper, we develop a Bayesian hierarchical model and associated computation strategy for simultaneously conducting parameter estimation and variable selection in binary quantile regression. We specify customary asymmetric Laplace distribution on the error term and assign quantile-dependent priors on the regression coefficients and a binary vector to identify the model configuration. Thanks to the normal-exponential mixture representation of the asymmetric Laplace distribution, we proceed to develop a novel three-stage computational scheme starting with an expectation–maximization algorithm and then the Gibbs sampler followed by an importance re-weighting step to draw nearly independent Markov chain Monte Carlo samples from the full posterior distributions of the unknown parameters. Simulation studies are conducted to compare the performance of the proposed Bayesian method with that of several existing ones in the literature. Finally, two real-data applications are provided for illustrative purposes.

中文翻译：

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二元分位数回归中变量选择和估计的新贝叶斯方法

在本文中，我们开发了贝叶斯层次模型和相关的计算策略，用于在二元分位数回归中同时进行参数估计和变量选择。我们在误差项上指定惯用的非对称拉普拉斯分布，并在回归系数和二元向量上分配依赖于分位数的先验以识别模型配置。由于非对称拉普拉斯分布的正态指数混合表示，我们继续开发一种新颖的三阶段计算方案，从期望最大化算法开始，然后是吉布斯采样器，然后是重要性重新加权步骤以绘制几乎独立的马尔可夫链蒙特卡罗样本来自未知参数的完整后验分布。进行了仿真研究，以将所提出的贝叶斯方法的性能与文献中几种现有方法的性能进行比较。最后，为了说明目的，提供了两个真实数据应用程序。