# Separating instrument error and process error

If I have a series of measurements without any calibration data for an instrument, are there statistical techniques to recover how much error (variance) is attributable to the instrument and how much is error intrinsic to the process under observation?

• If there's any information you've got regarding the instrument or any expected model for the data, some separation can be made. Commented Nov 7, 2017 at 16:45
• @Spätzle - otherwise, it's hopeless? Commented Nov 7, 2017 at 17:03
• IMHO If you've got no clue, we can't do anything. But if you know anything - even a basic relation these samples should comply, maybe $y=ax$ or any other form of $y=f(x)$ - there's a lot to be done. Commented Nov 7, 2017 at 17:14
• Thanks! I'm thinking that in some cases, the "instrument" might be a component of a measurement chain, where you can't really calibrate. Commented Nov 7, 2017 at 20:23

Here's an example: I tell you that two random numbers, $a$ and $b$, sum to 7, and ask you what your guess is for $a$ and $b$. You have no idea: the support for the answers is the entire real line! The probability you guess the correct answer is $0$. However, if I tell you that $a$ and $b$ come from two fair dice, then you have some prior information to work with. Your guesses are likely far more accurate.