I have 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 (?da) * WaterHight ^ beta (?db). 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 standrad edviation 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 entended 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? Thanks -- View this message in context: http://r.789695.n4.nabble.com/Uncertainty-propagation-tp2713499p2713499.html Sent from the R help mailing list archive at Nabble.com.
Maayt <m.lupker <at> hotmail.com> writes: [snip]> 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 (?da) * WaterHight ^ beta (?db). 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 standrad edviation 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 > entended to, I would overestimate the final error of my model...How have you fitted the models? Many of the fitting procedures in R give you access not just to the standard errors of the parameters, but also to their correlations/ covariances. If you have this information, you can sample the pairs of parameters from an appropriate multivariate normal distribution. Typically you could do something like ... params <- MASS::mvrnorm(1000,mu=coef(modelfit),Sigma=vcov(modelfit)) predictions <- apply(params,1,predictfun)
Thanks a lot for the help, I linearized my power relations en fitted them with a linear rlm() function. When I re-sample my pairs from a bivariate normal distribution for my power law what transformation do I need to apply a transformation to my covariance (vcov) matrix to get back from my linearized regression to my power law "space". Thanks -- View this message in context: http://r.789695.n4.nabble.com/Uncertainty-propagation-tp2713499p2714549.html Sent from the R help mailing list archive at Nabble.com.