Parallel tempering with equi-energy moves
- 410 Downloads
The Equi-Energy Sampler (EES) introduced by Kou et al. (in Ann. Stat. 34(4), 1581–1619, 2006) is based on a population of chains which are updated by local moves and global moves, also called equi-energy jumps. The state space is partitioned into energy rings, and the current state of a chain can jump to a past state of an adjacent chain that has an energy level close to its level. This algorithm has been developed to facilitate global moves between different chains, resulting in a good exploration of the state space by the target chain. This method seems to be more efficient than the classical Parallel Tempering (PT) algorithm. However it is difficult to use in combination with a Gibbs sampler and it necessitates increased storage. We propose an adaptation of this EES that combines PT with the principle of swapping between chains with the same level of energy. This adaptation, that we shall call Parallel Tempering with Equi-Energy Moves (PTEEM), keeps the original idea of the EES method while ensuring good theoretical properties, and practical implementation. Performances of the PTEEM algorithm are compared with those of the EES and of the standard PT algorithms in the context of mixture models, and in a problem of identification of transcription factor binding motifs.
KeywordsEqui-energy sampler Parallel tempering Population-based Monte Carlo Markov chains Mixture models Binding sites for transcription factors
Unable to display preview. Download preview PDF.
- Atchadé, Y., Roberts, G., Rosenthal, S.: Towards optimal scaling of Metropolis-coupled Markov chain Monte Carlo. Stat Comput (2010) Google Scholar
- Atchadé, Y., Fort, G., Moulines, E., Priouret, P.: Inference and Learning in Dynamic Models. Cambridge University Press, Cambridge (2011), pp. 33–53 Google Scholar
- Behrens, G., Friel, N., Hurn, M.: Tuning tempered transitions. Unpublished manuscript (2009) Google Scholar
- Geyer, C.: Markov chain Monte Carlo maximum likelihood. In: Computing Science and Statistics: Proceedings of the 23rd Symposium on the Interface, pp. 156–163 (1991) Google Scholar
- Hastings, W.: Monte Carlo sampling methods using Markov chains and their applications. Biometrika 88, 1035–1053 (1970) Google Scholar
- Hua, X., Kou, S.: Convergence of the equi-energy sampler and its application to the Ising model. Stat. Sin. (2010, in press) Google Scholar
- Liu, X., Brutlag, D., Liu, J.: Bioprospector: Discovering conserved DNA motifs in upstream regulatory regions of co-expressed genes. Pac. Symp. Biocomput. 6, 127–138 (2001) Google Scholar