Covariance Error Ellipse - sqrt of Eigen value as ellipse axis length
Axis-aligned confidence ellipses In general, the equation of an axis-aligned ellipse with a major axis of length and a minor axis of length , centered at the origin, is defined by the following equation: In our case, the length of the axes are defined by the standard deviations and of the data such that the equation of the error ellipse becomes: where s defines the scale of the ellipse and could be any arbitrary number (e.g. s=1). The question is now how to choose , such that the scale of the resulting ellipse represents a chosen confidence level (e.g. a 95% confidence level corresponds to s=5.991). The left hand side of equation ( 2 ) actually represents the sum of squares of independent normally distributed data samples, cov is zero. The sum of squared Gaussian data points is known to be distributed according to a so called Chi-Square distribution . A Chi-Square distribution is defined in terms of ‘degrees of fre...
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