In recent times empirical likelihood has been widely applied under Bayesian framework. Markov chain Monte Carlo (MCMC) methods are frequently employed to sample from the posterior distribution of the parameters of interest. However, complex, especially non-convex nature of the likelihood support erects enormous hindrances in choosing an appropriate MCMC algorithm. Such difficulties have restricted the use of Bayesian empirical likelihood (BayesEL) based methods in many applications. In this article, we propose a two-step Metropolis Hastings algorithm to sample from the BayesEL posteriors. Our proposal is specified hierarchically, where the estimating equations determining the empirical likelihood are used to propose values of a set of parameters depending on the proposed values of the remaining parameters. Furthermore, we discuss Bayesian model selection using empirical likelihood and extend our two-step Metropolis Hastings algorithm to a reversible jump Markov chain Monte Carlo procedure to sample from the resulting posterior. Finally, several applications of our proposed methods are presented.
翻译:近些年来,在巴伊西亚框架下广泛应用了经验可能性。Markov链链Monte Carlo(MCMC)方法经常用于从利益参数的事后分布样本中取样。然而,复杂,特别是可能性支持的非混凝土性质,在选择适当的MCMC算法时设置了巨大的障碍。这些困难限制了在许多应用中采用巴伊西亚经验可能性(Bayese EL)方法。在文章中,我们建议从BayesEL后层取样采用两步大都会黑斯廷斯算法。我们的提议按等级分明。我们的提议是用估计公式确定经验可能性,根据其余参数的拟议值提出一套参数的数值。此外,我们讨论巴伊西亚模式的选择,利用经验可能性,并将我们两步的Metopolis Hastings算法扩大到可逆跳跃马尔科夫链蒙特卡洛程序。最后,介绍了我们拟议方法的若干应用。