The problem of matching unlabelled point sets using Bayesian inference is
considered. Two recently proposed models for the likelihood are compared, based
on the Procrustes size-and-shape and the full configuration. Bayesian inference
is carried out for matching point sets using Markov chain Monte Carlo
simulation. An improvement to the existing Procrustes algorithm is proposed
which improves convergence rates, using occasional large jumps in the burn-in
period. The Procrustes and configuration methods are compared in a simulation
study and using real data, where it is of interest to estimate the strengths of
matches between protein binding sites. The performance of both methods is
generally quite similar, and a connection between the two models is made using
a Laplace approximation