error_analysis.covariance_matrix

Synopsis

Parameter error estimation via the covariance matrix.

Defaults

error_analysis.covariance_matrix(epsrel=0.0, verbosity=1)

Keyword arguments

epsrel: The parameter to remove linear-dependent columns when J is rank deficient.

verbosity: The higher the value, the greater the verbosity.

Description

This is a new experimental feature from version 3.3.

This will estimate parameter errors by using the exponential decay Jacobian matrix `J' to compute the covariance matrix of the best-fit parameters.

This can be used to for comparison to Monte-Carlo simulations.

This method is inspired from the GNU Scientific Library (GSL).

The covariance matrix is given by: covar = Qxx = (J^T.W.J)^-1, where the weight matrix W is constructed by the multiplication of an Identity matrix I and a weight array w. The weight array is 1/errors^2, which then gives W = I.w = I x 1/errors^2.

Qxx is computed by QR decomposition, J^T.W.J=QR, Qxx=R^-1. Q^T. The columns of $\mathfrak{R}$ which satisfy: |R_{kk}| ≤ epsrel |R_{11}| are considered linearly-dependent and are excluded from the covariance matrix (the corresponding rows and columns of the covariance matrix are set to zero).

The parameter `epsrel' is used to remove linear-dependent columns when J is rank deficient.