Hamiltonian Monte Carlo Sampling in Bayesian Empirical Likelihood Computation
针对贝叶斯经验似然估计，提出一种高效的哈密顿蒙特卡洛抽样方法，利用对数经验似然函数的梯度性质，克服传统MCMC在非凸边界上的困难，适用于混合效应模型、广义线性模型等。
Summary We consider Bayesian empirical likelihood estimation and develop an efficient Hamiltonian Monte Carlo method for sampling from the posterior distribution of the parameters of interest. The method proposed uses hitherto unknown properties of the gradient of the underlying log-empirical-likelihood function. We use results from convex analysis to show that these properties hold under minimal assumptions on the parameter space, prior density and the functions used in the estimating equations determining the empirical likelihood. Our method employs a finite number of estimating equations and observations but produces valid semiparametric inference for a large class of statistical models including mixed effects models, generalized linear models and hierarchical Bayes models. We overcome major challenges posed by complex, non-convex boundaries of the support routinely observed for empirical likelihood which prevent efficient implementation of traditional Markov chain Monte Carlo methods like random-walk Metropolis–Hastings sampling etc. with or without parallel tempering. A simulation study confirms that our method converges quickly and draws samples from the posterior support efficiently. We further illustrate its utility through an analysis of a discrete data set in small area estimation.