A More Efficient Gibbs Sampler Estimation Using Steady State Simulation: Applications to Public Health Studies

Markov Chain Monte Carlo (MCMC) methods, in particular, the Gibbs sampler, are widely used algorithms both in application and theoretical work in the classical and Bayesian paradigms. However, these algorithms are often computer intensive. Samawi et al. (2011) demonstrates through theory and simulation that the Dependent Steady State Gibbs Sampler (DSSGS) is more efficient and accurate in model parameter estimation than the original Gibbs sampler. This paper proposes the Independent Steady State Gibbs Sampling (ISSGS) approach to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and substantially improves the performance and convergence of the Gibbs sampler in multidimensional problems. This results in a significant reduction in computing time that is required to attain a certain level of accuracy in parameter estimation. ISSGS is used to estimate model parameters of simulated data and public health data, i.e. coronary heart disease (CHD) data, autism data, and lung cancer data