论文标题
ELHMC：贝叶斯经验可能性的汉密尔顿蒙特卡洛采样的R包装
elhmc: An R Package for Hamiltonian Monte Carlo Sampling in Bayesian Empirical Likelihood
论文作者
论文摘要
在本文中，我们描述了使用汉密尔顿蒙特卡洛方法从基于经验可能性的后验取样的{\ tt r}包。最近，基于经验可能性的方法已用于近期许多感兴趣问题的贝叶斯建模。该半参数过程可以轻松地将非参数分布估计器的灵活性与参数模型的可解释性结合在一起。该模型是通过估计基于方程的约束来指定的。从贝叶斯的经验可能性（贝耶斯）中提取推断是具有挑战性的。可能性是数值计算的，因此不存在后部的闭合表达。此外，对于任何有限尺寸的样本，可能性的支持是非凸，这阻碍了许多马尔可夫链蒙特卡洛（MCMC）程序的快速混合。最近已经表明，使用对数经验可能性的梯度的特性，可以设计有效的汉密尔顿蒙特卡洛（HMC）算法来从贝内斯尔后验样品。 该软件包要求用户仅指定估计方程，先验及其各自的梯度。从参数后部绘制的MCMC样本，并获得了用户所需的各种细节。
In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems of interest in recent times. This semiparametric procedure can easily combine the flexibility of a non-parametric distribution estimator together with the interpretability of a parametric model. The model is specified by estimating equations-based constraints. Drawing an inference from a Bayesian empirical likelihood (BayesEL) posterior is challenging. The likelihood is computed numerically, so no closed expression of the posterior exists. Moreover, for any sample of finite size, the support of the likelihood is non-convex, which hinders the fast mixing of many Markov Chain Monte Carlo (MCMC) procedures. It has been recently shown that using the properties of the gradient of log empirical likelihood, one can devise an efficient Hamiltonian Monte Carlo (HMC) algorithm to sample from a BayesEL posterior. The package requires the user to specify only the estimating equations, the prior, and their respective gradients. An MCMC sample drawn from the BayesEL posterior of the parameters, with various details required by the user is obtained.
