Abstract

In this work, we introduce Bayesian Empirical Likelihood for Longitudinal Analysis (BELLA), a Bayesian semiparametric framework for analyzing longitudinal data while accounting for within-subject dependence. The proposed approach combines the distributional flexibility of empirical likelihood with the computational capabilities of Hamiltonian Monte Carlo (HMC), enabling joint Bayesian inference on regression coefficients, correlation parameters, and residual variance through a set of unbiased estimating equations. A key feature of our methodology is the incorporation of HMC for posterior sampling. Drawing on principles from classical mechanics, HMC exploits gradient information to generate informed parameter proposals, allowing more efficient exploration of complex posterior distributions. This integration, however, introduces computational challenges, particularly those associated with constrained optimization in empirical likelihood and the tuning of HMC parameters. Within this framework, dependence is modeled through an AR(1) correlation structure. To assess the performance of BELLA, we conduct three simulation studies investigating the effects of sample size, number of time points, correlation strength, heavy-tailed distributions, and misspecification of the correlation structure on estimation accuracy and convergence. We further illustrate the practical applicability of the proposed method through an analysis of longitudinal CD4 cell counts in patients with HIV. The results suggest that BELLA provides a flexible and robust framework for longitudinal data analysis, combining the advantages of empirical likelihood without requiring a fully specified parametric distribution, the computational efficiency of HMC, and the incorporation of prior information and posterior uncertainty quantification afforded by Bayesian inference. These findings highlight the potential of integrating empirical likelihood and HMC for semiparametric Bayesian modeling of dependent data and open avenues for further methodological developments.
This is joint work with Dr. Asuman Türkmen and Dr. Fernanda Schumacher (OSU)