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Thread: combination of uncertainties

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    combination of uncertainties




    I try to measure a specific quantity in a target. I assume there are mainly 2 sources of uncertainties, let's call them sigma 1 and sigma 2. I want to know the contribution in the uncertainty due to sigma 2.
    I already have a some knowledge about sigma 1 (sigma 1 is known) and since I made multiple measurements on the target, I have the experimental variance s.

    Is it correct to say that, since s = s1+s2, then s2 = sqrt(s-s1) and is a good estimate of sigma 2?

    If yes, what to do when the contribution from sigma 2 is very small, which leads me sometimes with a s2 being negative...

    Kinda lost, would really appreciate any help

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    Re: combination of uncertainties

    hi,
    this is a bit more complicated and the estimate will depend in the model you have. Do you have a simple additive midel (like Y=X1+X2)?

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    Re: combination of uncertainties

    Yes i have Y=X1+X2, and expected value of both X1 and X2 is 0.


    Basically, the second contribution to the uncertainty is due to an specific effect I want to quantify. Since i know the first contribution to the uncertainty analytically, and since I can calculate the experimental variance, I'm trying to say : "See, the experimental variance is bigger than just s1, so it is reasonnable to think that it is because of that specific effect, and its contribution to the total uncertainty (at least its best estimate ) is s2 = sqrt(s-s1). "

    Eventually, if i can estimate the risk of being wrong, that would be even better.

    Does this seems okay?
    Last edited by Tweepee; 05-10-2017 at 02:40 PM.

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    Re: combination of uncertainties


    This problem is very like that of estimating Variance Components from an anova table. In Variance Components, if a particular variance is estimated to be less than zero, it is simply put to zero.
    You can probably get a bootstrap confidence interval for s2 if you have set of experimental data.

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