elhmc: An R Package for Hamiltonian Monte Carlo Sampling in Bayesian Empirical Likelihood

TL;DR

This paper introduces an R package that implements Hamiltonian Monte Carlo sampling for Bayesian empirical likelihood models, enabling efficient inference in complex semiparametric Bayesian problems.

Contribution

The paper presents a novel R package that facilitates HMC sampling for Bayesian empirical likelihood, addressing challenges of non-convex support and numerical likelihood computation.

Findings

Efficient HMC sampling from BayesEL posterior demonstrated.

Package simplifies Bayesian inference with empirical likelihood constraints.

Provides detailed MCMC diagnostics and user-friendly interface.

Abstract

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.