I have ave a small model running under R. This is basically running various power-law relations on a variable (in this case water level in a river) changing spatially and through time. I'd like to include some kind of error propagation to this.
My first intention was to use a kind of monte carlo routine and run the model many times by changing the power law parameters. These power laws were obtained by fitting data points under R. I thus have std error associated to them: alpha (ąda) * WaterHight ^ beta (ądb). Is it statistically correct to sample alpha and beta for each run by picking them from a normal distribution centered on alpha (resp. beta) with a standard deviation of da (resp. db) and to perform my statistics (mean and standard deviation of the model result) on the model output?
It seems to me that da and db are correlated in some way and by doing what I intended to, I would overestimate the final error of my model...
My statistical skills are rather weak, is there a way people usually deal with this kind of problems?