Journal of the Royal Statistical Society: Series B (Statistical Methodology)

Hamiltonian Monte Carlo sampling in Bayesian empirical likelihood computation

Journal Article

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.

Related Topics

Related Publications

Related Content

Site Footer

Address:

This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on StatisticsViews.com are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and StatisticsViews.com express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.