SystematicErrorsFactsAndFictions

https://arxiv.org/abs/hep-ex/0207026

[BROKEN LINK: UncertiantyOnUncertianty]

• Interesting. Great commentary on errors on errors: Conclusions! dont go there.
• Statistics provides tools to identify a mistake, but not to use it. Statistics does not and cannot tell us what to do next. What we do next has to be based on experience and common sense, but statistics does not prescribe it.

• Once a bias is known, it can be corrected for. If the bias is unknown and unsuspected then one can by definition do nothing about it.

  What if you are just estimating a bias by some VR ?

• The quoted result is R(a0), and the error due to the uncertainty in a is \simga_a R' which is the difference in R (divided by 2)

  =>sigma_R = 0.5 * (R(a0 + sigma_a) - R(a0 - sigma_a) )

• If you have a large number of such corrections for parameters a,b,c…z then this approach may be arguable. But not if it’s unique. You will never get it past the referee: you investigate an uncertainty and as a result you reduce the systematic error, on the grounds that you might have increased it (or, perhaps, that in many parallel universes you increased it?)

  No, at this point statistical sophistication has clearly gone too far for plain common sense. We therefore recommend Argument 3: that this error on error correction should not be done as there is no sensible way of doing it. It can be left out of the reckoning if small, and if large then more work is needed to make it small.

• Thou shalt not add uncertainties on uncertainties in quadrature.