Bayesian Analysis

Bayesian Matching of Unlabeled Point Sets Using Procrustes and Configuration Models

Kim Kenobi and Ian L. Dryden

Full-text: Open access


The problem of matching unlabeled 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.

Article information

Bayesian Anal. Volume 7, Number 3 (2012), 547-566.

First available in Project Euclid: 28 August 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Gibbs Markov chain Monte Carlo Metropolis-Hastings molecule protein Procrustes size shape


Kenobi, Kim; Dryden, Ian L. Bayesian Matching of Unlabeled Point Sets Using Procrustes and Configuration Models. Bayesian Anal. 7 (2012), no. 3, 547--566. doi:10.1214/12-BA718.

Export citation


  • Dryden, I. L. (2011). shapes package. R Foundation for Statistical Computing, Vienna, Austria. Contributed package. URL
  • Dryden, I. L., Hirst, J. D., and Melville, J. L. (2007). “Statistical analysis of unlabeled point sets: comparing molecules in cheminformatics.” Biometrics, 63: 237–251.
  • Dryden, I. L. and Mardia, K. V. (1992). “Size and shape analysis of landmark data.” Biometrika, 79: 57–68.
  • — (1998). Statistical Shape Analysis. Chichester: Wiley.
  • Green, P. J. and Mardia, K. V. (2004). “Bayesian alignment using hierarchical models, with applications in protein bioinformatics.” Technical report, University of Bristol. ArXiv:math/0503712v1.
  • — (2006). “Bayesian alignment using hierarchical models, with applications in protein bioinformatics.” Biometrika, 93: 235–254.
  • Kendall, D. G. (1989). “A Survey Of The Statistical Theory Of Shape (with discussion).” Statistical Science, 4: 87–120.
  • Kent, J. T. and Mardia, K. V. (2001). “Shape, tangent projections and bilateral symmetry.” Biometrika, 88: 469–485.
  • Khatri, C. G. and Mardia, K. V. (1977). “The von Mises-Fisher matrix distribution in orientation statistics.” Journal of the Royal Statistical Society. Series B., 39(1): 95–106.
  • Mardia, K., Nyirongo, V., Green, P., Gold, N., and Westhead, D. (2007). “Bayesian refinement of protein functional site matching.” BMC Bioinformatics, 8: 257.
  • Mardia, K. V., Nyirongo, V. B., Fallaize, C. J., Barber, S., and Jackson, R. M. (2011). “Hierarchical Bayesian Modeling of Pharmacophores in Bioinformatics.” Biometrics, 67: 611–619.
  • Moss, S. and Hancock, E. R. (1996). “Registering Incomplete Radar Images using the EM Algorithm.” In Fisher, R. B. and Trucco, E. (eds.), Proceedings of the Seventh British Machine Vision Conference, 685–694. British Machine Vision Association.
  • R Development Core Team (2011). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. URL
  • Rangarajan, A., Chui, H., and Bookstein, F. L. (1997). “The Softassign Procrustes Matching Algorithm.” In Duncan, J. and Gindi, G. (eds.), Information Processing in Medical Imaging, 29–42. Springer.
  • Ruffieux, Y. and Green, P. J. (2009). “Alignment of multiple configurations using hierarchical models.” Journal of Computational and Graphical Statistics, 18: 756–773.
  • Schmidler, S. C. (2007). “Fast Bayesian Shape Matching Using Geometric Algorithms.” In Bernado, J. M., Herckerman, D., Berger, J. O., and Dawid, A. P. (eds.), Bayesian Statistics, 8. Oxford University Press.
  • Stuelpnagel, J. (1964). “On the parametrization of the three-dimensional rotation group.” Society for Industrial and Applied Mathematics Review, 6: 422–430.
  • Tierney, L. and Kadane, J. B. (1986). “Accurate approximations for posterior moments and marginal densities.” Journal of the American Statistical Association, 81(393): 82–86.
  • Tjelmeland, H. and Eidsvik, J. (2004). “On the use of local optimizations within Metropolis-Hastings updates.” Journal of the Royal Statistical Society. Series B., 66(2): 411–427.
  • Tjelmeland, H. and Hegstad, B. K. (2001). “Mode jumping proposals in MCMC.” Scandinavian Journal of Statistics., 28(1): 205–223.