A more efficient Gibbs sampler estimation using steady-state simulation: applications to public health studies

Abstract

Markov chain Monte Carlo methods, in particular, the Gibbs sampler, are widely used algorithms both in application and theoretical works in the classical and Bayesian paradigms. However, these algorithms are often computer intensive. Samawi et al. [Steady-state ranked Gibbs sampler. J. Stat. Comput. Simul. 2012;82(8), 1223–1238. doi:10.1080/00949655.2011.575378] demonstrate through theory and simulation that the dependent steady-state Gibbs sampler is more efficient and accurate in model parameter estimation than the original Gibbs sampler. This paper proposes the independent steady-state Gibbs sampler (ISSGS) approach to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in multidimensional problems.

Keywords:

• Markov chain Monte Carlo (MCMC) methods
• Gibbs sampler
• dependent steady-state Gibbs sampler (DSSGS)
• ranked set sampling
• independent steady-state Gibbs sampler (ISSGS)
• steady-state ranked simulated sampling

Acknowledgements

We would like to thank the referees and the associate editor for their valuable comments which improved the manuscript.