  Statistical methodology is proposed for comparing unlabeled marked point
sets, with an application to aligning steroid molecules in chemoinformatics.
Methods from statistical shape analysis are combined with techniques for
predicting random fields in spatial statistics in order to define a suitable
measure of similarity between two marked point sets. Bayesian modeling of the
predicted field overlap between pairs of point sets is proposed, and posterior
inference of the alignment is carried out using Markov chain Monte Carlo
simulation. By representing the fields in reproducing kernel Hilbert spaces,
the degree of overlap can be computed without expensive numerical integration.
Superimposing entire fields rather than the configuration matrices of point
coordinates thereby avoids the problem that there is usually no clear
one-to-one correspondence between the points. In addition, mask parameters are
introduced in the model, so that partial matching of the marked point sets can
be carried out. We also propose an adaptation of the generalized Procrustes
analysis algorithm for the simultaneous alignment of multiple point sets. The
methodology is illustrated with a simulation study and then applied to a data
set of 31 steroid molecules, where the relationship between shape and binding
activity to the corticosteroid binding globulin receptor is explored.
