like the a priori assumption that the noise/variability obeys an assumed statistical distribution, pulled out of a hat?? Then there is the Bayesian approach where several bad approximations can be used to tease out the error bars. then there are human subject-- i dont understand how assigning 1 number to a person can ever be valid.

i've been working on a brain mapping project [far from my comfort zone] and biomed people on the collaboration cant answer questions like "How many sig digits are accurate in an MRI?" I'd hope someone can answer the question.

In the sort of cases I understand [as a non-statistician], accuracy of the data is known [how many digits does the apparatus report accurately] and tracked thru the inference process- a very classical approach due I think to von Neumann and Goldstine. In CFD typically one calculates the perturbations where the rate of error growth is greatest [a known problem in linear algebra] and perturbations for the ensemble include that set. (a good description is in Eugenia Kalnay's book ... data assimlation and predictability--which has the best dedication of ay boo I've ever seen.]

Bill