TY - GEN A1 - Fischer, Alexander T1 - An Uncoupling-Coupling Technique for Markov Chain Monte Carlo Methods N2 - Uncoupling-coupling Monte Carlo (UCMC) combines uncoupling techniques for finite Markov chains with Markov chain Monte Carlo methodology. By determining almost invariant sets of the associated Markov operator, the Monte Carlo sampling splits by a hierarchical annealing process into the essential regions of the state space; therefore UCMC aims at avoiding the typical metastable behavior of Monte Carlo techniques. From the viewpoint of Monte Carlo, a slowly converging long-time Markov chain is replaced by a limited number of rapidly mixing short-time ones. The correct weighting factors for the various Markov chains are obtained via a coupling matrix, that connects the samplings from the different almost invariant sets. The underlying mathematical structure of this approach is given by a general examination of the uncoupling-coupling procedure. Furthermore, the overall algorithmic scheme of UCMC is applied to the $n$-pentane molecule, a well-known example from molecular dynamics. T3 - ZIB-Report - 00-04 KW - almost invariant sets KW - bridge sampling KW - cluster analysis KW - hierarchical annealing KW - Markov chains KW - Monte Carlo KW - $n$-pentane molecule KW - ratio of no Y1 - 2000 UR - https://opus4.kobv.de/opus4-zib/frontdoor/index/index/docId/572 UR - https://nbn-resolving.org/urn:nbn:de:0297-zib-5720 ER -