Journal of Applied Mathematics and Decision Sciences
Volume 2007 (2007), Article ID 98086, 13 pages
Putting Markov Chains Back into Markov Chain Monte Carlo
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.