Selecting the Correct Model Complexity

If the measures at each of the N datapoints are uncorrelated, we can sum over the individual B values (obtained from (2)):


 equation191

We get rid of any correlations by orthogonalising the covariance matrix tex2html_wrap_inline492 by singular value decomposition. The residuals tex2html_wrap_inline494 are calculated by projecting the correlated residuals along the axis of the eigenvectors of tex2html_wrap_inline470 and the eigenvalues of tex2html_wrap_inline470 give the probable errors at each point.

We used the script model_complexity_estimate.m to generate the results in figure 6.

  figure197
Figure 6: Estimating the correct model complexity