Efficient and accurate methods of estimating the sensitivity of seismic hazard calculations to statistical uncertainties in models and parameters are demonstrated. These models require knowledge of the earthquake magnitude and distance that contribute most to the probability of exceedence of a chosen acceleration level; the methods estimate sensitivities using point-source seismic-hazard approximations for which closed-form solutions are available. An additional result is that the use of Bayesian estimates for seismicity and ground motion parameters in the hazard analysis produces unbiased Bayesian estimates of the seismic ground motion hazard, due to the almost linear relationship between ground motion amplitudes at a given probability level, and parameter uncertainties. Application of these methods to the San Francisco, California, Bay area indicates a coefficient of variation (cov) of the 500-yr acceleration of about 0.4 at sites close to major faults, and a cov of about 0.2 at sites 50 km to the east of the major east bay faults. These cov's result from statistical uncertainty in the depth of energy release, the activity rate and Richter b value for each fault, and the mean acceleration-attenuation relationship. A similar analysis in the central Mississippi Valley area indicates a cov in 500-yr acceleration of 0.4 near the major faults, with a value of about 0.3 at distances greater than 50 km. The sources of statistical uncertainty in this region are the depth of energy release as well as its location, the activity rate and Richter b value for each fault, and the mean acceleration-attenuation function.