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Error Calculus

  1. Oct 4, 2012 #1
    1. The problem statement, all variables and given/known data
    Given is a set of measurements with their respective errors for example an energy spectrum. In gnuplot one is to fit a function [itex] f(x;\{p_i\})[/itex] depending on a variable x and on fit parameters [itex] p_i[/itex]. When the fit is done one gets values for the [itex]p_i[/itex] with errors and a correlation matrix with values [itex] c_{ij}[/itex]. Now one has to calculate a value [itex]v(\{\text{some of the }p_i\})[/itex] that depends on some of the the [itex]p_i[/itex] and find its error [itex]\Delta p_i[/itex].


    2. Relevant equations
    How will a calculate the error e? Do i have to take correlations into account? Can i do it the way i attemp it in my solution attempt.


    3. The attempt at a solution
    [itex]e^2=\sum_{i}\left(\frac{\partial v}{\partial p_i}\cdot \Delta p_i\right)^2+\sum_{ij}\frac{\partial v}{\partial p_i}\frac{\partial v}{\partial p_j}c_{ij}\Delta p_i \Delta p_j[/itex]

    If this is right what happens if one of the [itex]c_{ij}[/itex] is negative?
     
    Last edited: Oct 4, 2012
  2. jcsd
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