Cross Validation Using Excision of Fourier Data from the 3D Reference

In section 7.6, we have already mentioned the problem of reference dependence and the idea of cross-validation. Particularly, we now proceed with an outline of the method introduced by Shaikh et al. (2003), where data are left out from the 3D reference in Fourier space.

The choice of shells as loci from where data are removed is motivated twofold: (i) each projection is affected equally, namely, according to the projection theorem, by excision of a corresponding ring in 2D Fourier space; and (ii) this choice also lends itself naturally to an evaluation by the FSC.

When such a modified 3D reference is used, the alignment of experimental data is not affected by the Fourier components lying on the selected shell. Hence, during refinement, Fourier components building up in the selected shell are free from model bias. The FSC curve of a reconstruction that is done using the modified 3D reference during refinement differs from the FSC obtained with the original 3D reference: we see a dip at the Fourier radius of the shell from which data have been excised (figure 5.32a). The size of the dip is an indicator for the degree of model dependence. Moreover, when the data consist of pure noise, the dip in the FSC extends all the way to the curve that indicates the FSC of pure noise (figure 5.32b).

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