Hamiltonian Monte Carlo Approaches to Bayesian Empirical Likelihood in Longitudinal Data Analysis

Music City Center 

There is a rich and growing body of research focusing on the development of empirical likelihood (EL) estimation and inference methods. Unlike traditional likelihood-based methods, EL techniques rely on a set of unbiased estimating equations (EE) that summarize the parametric constraints of the model, offering greater flexibility in handling complex data, while solving restricted optimization by using Lagrange Multipliers. In recent years, significant progress has been made leveraging the EL approach for longitudinal data analysis and its adaptation to the Bayesian paradigm. In this work, we combine both ideas. Standard Markov chain Monte Carlo (MCMC) procedures within the Bayesian EL (BEL) framework are particularly challenging due to the nonparametric nature of the EL and the restrictions imposed by EE, presenting several limitations that affect their efficiency, mainly dealing with dependent data. Alternatively, by imposing a simple correlation structure often useful in such studies, we develop a method that jointly estimates regression and correlation parameters via the Hamiltonian Monte Carlo (HMC) algorithm that can efficiently sample from the BEL-based posterior distribution

nonparametric estimation


Lagrange multipliers

Bayesian estimation

correlated data 

Section on Nonparametric Statistics