Physical Chem: Unqualified Use of Statistical Based Error Estimates?
Seeking opinions on the unqualified employment of statistical models parameter based error estimates, especially in physical sciences.
In particular, consider the question of employing Stein's related suggested confidence interval for precision (see http://statweb.stanford.edu/~ckirby/charles/Siegmund_Stein.p...) as generally appropriate in say a generalized regression model scenario (which
covers a range of models in practice).
My opinion is that the answer is contextual at best!
When working in say the physical sciences, and there is very little possibility for the near future of a model misspecification error (due to say the
likelihood of new variables entering, major changes in operating conditions, etc), then using regression theory expected parameter error estimates as
a function of the sample size, may actually be helpful.
In effect, the above regression theory can be verified, assuming all underlying model assumptions are valid, in a spreadsheet simulation exercise with
known parameter values and specified random error distribution (I do generally recommend this exercise as it can highlight areas of leverage impacting
results).
Otherwise, say in a different context of econometric modeling, for example, with changing macroeconomic dynamics, even assuming continuing model
appropriateness is probably likely a leap, so increasing sampling efforts may not produce the intended results (like a statistic based reduction in a
parameter's observed sampling error).
I suspect that even the physical sciences (as in Physical Chemistry) may not be always immuned either. For example, recently looked at a paper on the
electro-oxidation of the sulfate ion as a path to persulfate. There was a curious mention of a significant factor arising from surface chemistry
surrounding the apparent aging of an electrode's surface. To quote from the abstract of the referenced paper (link address: https://www.sciencedirect.com/science/article/pii/S001346861...):
"The RDE [rotating disk electrode] experiments indicated that rates of persulfate generation were strongly dependent of the condition of the electrode
surface, and that aged electrode surfaces favored water oxidation over direct SO42− and HSO4− oxidation."
As such, even pure physical science-based model of persulfate yield with time in an electrolysis setting apparently could be the subject to an
unexpected aging factor, which serves as a precautionary example for those working on their thesis.
[Edited on 21-9-2020 by AJKOER]
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