A random renormalization group technique is reviewed, and a related set of Bayesian scaling techniques are presented. The techniques are employed to study the motion of drifters in Lake Michigan on a time scale ranging from 30 min to 5 days and in the Gulf of Mexico on a time scale ranging from 8 h to 85 days. The scaling laws generalize the standard power law scalings. One of the advantages of the Bayesian approach is that scaling laws can be determined even with a paucity of data with the caveat that less data produce greater uncertainty in the scaling laws.