We describe and evaluate a novel method to blend two observed cloud fraction (CF) datasets through Bayesian posterior estimation. The research reported here is a feasibility study designed to explore the method. In this proof-of-concept study, we illustrate the approach using specific observational datasets from the U. S. Department of Energy Atmospheric Radiation Measurement (ARM) Programs Southern Great Plains (SGP) site in the central United States, but the method is quite general and is readily applicable to other datasets. The total sky image (TSI) camera observations are used to determine the prior distribution. A regression model and the active remote sensing of clouds (ARSCL) radar/lidar observations are used to determine the likelihood function. The posterior estimate is a probability density function (pdf) of the CF whose mean is taken to be the optimal blend of the two observations. Our results have demonstrated that a Bayesian approach yields a pdf of CF rather than a single CF value and is feasible to blend both TSI and ARSCL data with some form of bias correction. To further understand cloud and precipitation processes, we have also made a statistical analysis of the data of liquid water path (LWP) and precipitable water vapor (PWV) at the SGP site as well as the site of Tropical Warm Pool - International Cloud Experiment (TWP-ICE). Our results unsurprisingly demonstrate that between LWP and PWV when one increases, the other decreases; and when both have a sufficiently long period of no activity, there is a hike in increase for both within the next couple of days. We have also shown how these properties and relationships vary in seasons.