Bayesian methods and maximum entropy reconstruction of spin densities

Jacques Schweizer

CEA-Grenoble, DSM/DRFMC/SPSMS/MDN, 38054 Grenoble Cedex 9, France

Magnetic structure factors are the Fourier components of the periodic spin (magnetization) density in magnetic crystals. The usual way to retrieve the spin density from experimental structure factors is the inverse Fourier transformation.

This method however suffers several drawbacks, as for instance in treating in the same way all the data, whatever their uncertainty is, or also in providing a map which is in complete agreement (chi2=0) with the experimental data.

Bayesian methods propose another approach which optimizes together the agreement with experimental data, but also the intrinsic probability of the map. This intrinsic probability is represented by the entropy of the map in terms of the theory of information and optimizing the intrinsic probability implies maximizing the entropy of the map.