We propose a Bayesian elastic net that uses empirical likelihood and develop an efficient tuning of Hamiltonian Monte Carlo for posterior sampling. The proposed model relaxes the assumptions on the identity of the error distribution, performs well when the variables are highly correlated, and enables more straightforward inference by providing posterior distributions of the regression coefficients. The Hamiltonian Monte Carlo method implemented in Bayesian empirical likelihood overcomes the challenges that the posterior distribution lacks a closed analytic form and its domain is nonconvex. We develop the leapfrog parameter tuning algorithm for Bayesian empirical likelihood. We also show that the posterior distributions of the regression coefficients are asymptotically normal. Simulation studies and real data analysis demonstrate the advantages of the proposed method in prediction accuracy.
翻译:我们建议建立贝叶斯弹性网,使用经验可能性,并开发汉密尔顿·蒙特卡洛有效调试用于后方取样。拟议模型将放松误差分布的假设,在变量高度关联时运行良好,通过提供回归系数的后方分布,可以更直接地推断。在贝叶斯州实施的汉密尔顿·蒙特卡洛实验可能性方法克服了后方分布缺乏封闭式分析形式且其域域不相容的挑战。我们为巴伊斯州的经验可能性开发了跳蛙参数调算法。我们还表明,回归系数的后方分布是平时的正常。模拟研究和真实数据分析显示了拟议方法在预测准确性方面的优势。