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Covariance ellipse

  1. Dec 7, 2009 #1
    Dear all, I was wondering how one in reality produces the so called "Covariance ellipse"?

    Lets say I have a set of data points with their error and fit a function to that data using 2 parameters just for simplicity.

    Now, I know that the covariance ellipse is an ellipse of equal probability contours. But how do we do this in reality? Do I evaluate the chi-squared for different configurations of my 2 parameters (which we assume I have estimated using e.g. chi-squared minimization).. and then what? Should I, for instance if I want to state confidence limit intervals, assume that the center of my ellipse has value = 1 in probablity and then seek those boundaries where chi-squared as reduced to the value exp(-0.5) = 0.683?

    Or should I go from my minimum chi-squared value thus obtained from my parameters and then go the boundaries where the chi-squared has reduced by a FACTOR exp(-0.5) = 0.683?
  2. jcsd
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