Statistical Computing '99 - Schloß Reisensburg

Application of MCMC with highly correlated parameters

Ulrich Halekoh and Werner Vach
Freiburger Zentrum fuer Datenanalyse und Modellbildung
Eckerstrasse 1, D-79110 Freiburg i. Br.

Department of Statistics and Demography
University of Southern Denmark
Campusvej 55, DK-5230 Odense M

We proposed a Bayesian model based approach for the construction of a chronological ranking (seriation) of graves in archaeology. Main parameters of interest are the probabilities describing the course over time of the gravegoods found with the graves and the ranks of the graves themselves. The posterior distribution of these parameters is analysed by sampling with the Markov chain Monte Carlo (MCMC) technique. Due to the high-dimensionality and the strong correlation among the parameters special care is needed in specifying the update-steps in order to achieve sufficient convergence of the generated chain. Besides a general idea of Geyer (1991) proposing to combine samples from chains with successively flatter posteriors we use several additional techniques whose application will be demonstrated in the archaeological context. Furthermore, we present proposals to assess the convergence of the chain and - more specific to the prior assumptions in our Bayesian approach than to the MCMC sampling - we give a sensitivity analysis of our results.

Geyer, C. J. (1991): Markov chain Monte Carlo maximum likelihood. in M. Keramidas (Ed.) Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, Fairfax Station: Interface Foundation, 156-163.

31. Statistical Computing '99