The multilevel regression and post-stratification approach (MRP) has been used to estimate public health data for small areas in recent years, yet how to accurately assess the variability in model fitting and prediction with less computational intensity is still a major challenge. We used the MRP approach with 2013 Florida Behavioral Risk Factor Surveillance System data to generate both state- and county-level estimates for chronic obstructive pulmonary disease, arthritis, current smoking, and binge drinking among adults aged ?18 years. We then used Bayesian via Markov Chain Monte Carlo, parametric bootstrapping, non-parametric bootstrapping, and Monte Carlo simulation approaches, respectively, to estimate the predicted standard errors (SEs) of those estimates. We found that the distribution of SEs for both state- and county-level estimates of each health-related outcome using non-parametric bootstrapping and Monte Carlo simulation was very close to that using the Bayesian approach. Compared with the others, Monte Carlo simulation was most computationally efficient.