Improving the Efficiency of the Monte-Carlo Methods Using Ranked Simulated Approach

This chapter explores the concept of using ranked simulated sampling approach (RSIS) to improve the well-known Monte-Carlo methods, introduced by Samawi (1999), and extended to steady-state ranked simulated sampling (SRSIS) by Al-Saleh and Samawi (2000). Both simulation sampling approaches are then extended to multivariate ranked simulated sampling (MVRSIS) and multivariate steady-state ranked simulated sampling approach (MVSRSIS) by Samawi and Al-Saleh (2007) and Samawi and Vogel (2013). These approaches have been demonstrated as providing unbiased estimators and improving the performance of some of the Monte-Carlo methods of single and multiple integrals approximation. Additionally, the MVSRSIS approach has been shown to improve the performance and efficiency of Gibbs sampling (Samawi et al. 2012). Samawi and colleagues showed that their approach resulted in a large savings in cost and time needed to attain a specified level of accuracy.