World Meteorological Organization (WMO) regression models for precipitation gauge bias developed by Goodison et al. (1998) were optimized using the very fast simulated annealing algorithm. The regression model uncertainties were estimated by use of a Bayesian stochastic inversion (BSI) algorithm. Legates and Willmott's (1990) precipitation correction factors database (applicable to average monthly conditions) were used to constrain model parameters. Daily wind speed, air temperature, and precipitation from the North American Land Data Assimilation System (NLDAS) were used as input for the WMO regression models in the United States. The results show that the optimal regression model is reasonably bounded by the WMO Alter-shielded and unshielded models for both rain and snow. The optimized regression model, aside from reproducing reasonably well the Legates-Willmott average monthly adjustment factors, also describes daily and interannual variation of precipitation correction factors. The relations among model parameters and model uncertainties, including regression parameter uncertainty and input data uncertainty, are examined. The results show strong relations between regression model uncertainties and uncertain NLDAS wind speed. Uncertainty of NLDAS data has little effect on optimization of the WMO regression model. However, it has significant effects on uncertainty of the regression model parameters and the precipitation correction factors.