Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 98086, 13 pages
Review Article

Putting Markov Chains Back into Markov Chain Monte Carlo

Richard J. Barker and Matthew R. Schofield

Department of Mathematics and Statistics, University of Otago, P.O. Box 56, Dunedin 9010, New Zealand

Received 7 May 2007; Accepted 8 August 2007

Academic Editor: Graeme Charles Wake

Copyright © 2007 Richard J. Barker and Matthew R. Schofield. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Markov chain theory plays an important role in statistical inference both in the formulation of models for data and in the construction of efficient algorithms for inference. The use of Markov chains in modeling data has a long history, however the use of Markov chain theory in developing algorithms for statistical inference has only become popular recently. Using mark-recapture models as an illustration, we show how Markov chains can be used for developing demographic models and also in developing efficient algorithms for inference. We anticipate that a major area of future research involving mark-recapture data will be the development of hierarchical models that lead to better demographic models that account for all uncertainties in the analysis. A key issue is determining when the chains produced by Markov chain Monte Carlo sampling have converged.