Bayesian penalized empirical likelihood and Markov Chain Monte Carlo sampling

TL;DR

This paper introduces Bayesian Penalized Empirical Likelihood (BPEL), a flexible framework combining penalization and MCMC sampling to improve empirical likelihood methods' efficiency and adaptability in statistical inference.

Contribution

The paper proposes a novel BPEL framework that regularizes Lagrange multipliers and employs MCMC sampling, enhancing empirical likelihood's flexibility and computational efficiency.

Findings

BPEL reduces problem dimensionality through penalization.

MCMC sampling converges rapidly to global optima.

BPEL improves inference in complex models.

Abstract

In this study, we introduce a novel methodological framework called Bayesian Penalized Empirical Likelihood (BPEL), designed to address the computational challenges inherent in empirical likelihood (EL) approaches. Our approach has two primary objectives: (i) to enhance the inherent flexibility of EL in accommodating diverse model conditions, and (ii) to facilitate the use of well-established Markov Chain Monte Carlo (MCMC) sampling schemes as a convenient alternative to the complex optimization typically required for statistical inference using EL. To achieve the first objective, we propose a penalized approach that regularizes the Lagrange multipliers, significantly reducing the dimensionality of the problem while accommodating a comprehensive set of model conditions. For the second objective, our study designs and thoroughly investigates two popular sampling schemes within the BPEL context. We demonstrate that the BPEL framework is highly flexible and efficient, enhancing the adaptability and practicality of EL methods. Our study highlights the practical advantages of using sampling techniques over traditional optimization methods for EL problems, showing rapid convergence to the global optima of posterior distributions and ensuring the effective resolution of complex statistical inference challenges.