Steady-state ranked Gibbs sampler

Gibbs sampler as a computer-intensive algorithm is an important statistical tool both in application and in theoretical work. This algorithm, in many cases, is time-consuming; this paper extends the concept of using the steady-state ranked simulated sampling approach, utilized in Monte Carlo methods by Samawi [On the approximation of multiple integrals using steady state ranked simulated sampling, 2010, submitted for publication], to improve the well-known Gibbs sampling algorithm. It is demonstrated that this approach provides unbiased estimators, in the case of estimating the means and the distribution function, and substantially improves the performance of the Gibbs sampling algorithm and convergence, which results in a significant reduction in the costs and time required to attain a certain level of accuracy. Similar to Casella and George [Explaining the Gibbs sampler, Am. Statist. 46(3) (1992), pp. 167-174], we provide some analytical properties in simple cases and compare the performance of our method using the same illustrations.