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A Integrate data plot, combine errors including correlation

  1. Jun 16, 2016 #1
    Hello

    I have a set of data points, with errors (X1 , Y1 +- deltaY1) , (X2 , Y2 +-deltaY2) etc
    I have the covariance matrix for these bins

    I want to integrate this set of data points: SUM_i ( Y_i * X_binWidth_i )

    How do I combine the errors, taking into consideretation the covariance matrix?
    So I end up with a single value and a single error?

    If anyone can explain or point me in the direction of some text about this that would be very helpful thanks
     
  2. jcsd
  3. Jun 16, 2016 #2
    So for two numbers that are correlated, if I wanted to add them I would do
    y1 with error delta1, y2 with error delta2

    B = y1 + y2

    And the thing i want is detalB = (delta1)^2 + (delta2)^2 + 2 cov[ y1, y2 ]

    But what do I do when I am trying to add more than two numbers that are all correlated.. i.e. integrate a set of correlated data points.
     
  4. Jun 16, 2016 #3

    mathman

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    Gold Member

    Basically the same thing: sum of all squares and twice the sum of all covariances gives the variance of the sum.
     
  5. Jun 19, 2016 #4

    chiro

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    Science Advisor

    Hey venus_in_furs.

    General co-variance formulas can be done using matrix techniques with the co-variance term.

    There is a vCv^t formulation where C is the co-variance matrix and v represents the scalar component of the random variable.

    It mimics the variance results that are proven with the normal Var[] operator but it allows it to be done with matrices and vectors in an arbitrary fashion.

    A multi-variate statistics textbook should have it (or any other similar resource).
     
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