Bayesian multidimensional scaling and choice of dimension

Multidimensional scaling is widely used to handle data that consist of simi larity or dissimilarity measures between pairs of objects. We deal with two major problems in metric multidimensional scaling-configuration of objects and determination of the dimension of object configuration-within a Bayesi an framework. A Markov chain Monte Carlo algorithm is proposed for object c onfiguration, along with a simple Bayesian criterion, called MDSIC, for cho osing their dimension, Simulation results are presented, as are real data. Our method provides better results than does classical multidimensional sca ling and ALSCAL for object configuration, and MDSIC seems to work well for dimension choice in the examples considered.