What you are describing is the maximum entropy principle. Assume the minimal information known about the process, such as a mean, and then use the probability distributions that arise from maximum entropy. This approach is studiously avoided by lots of people. For example, it is not mentioned in Curry’s paper even though that is the basis of properly applying uncertainty propagation, starting from the large spread in CO2 residence times. Most of these writers are neophytes when it comes to doing stochastic phenomenon properly.
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