# Markov chain Monte Carlo sampling with and without detailed balance

#### Markov chain Monte Carlo sampling with and without detailed balance

- Event time: 11:30am
- Event date: 2nd February 2011
- Speaker: Katrin Wolff (Formerly School of Physics & Astronomy, University of Edinburgh)
- Location: Room 2511, James Clerk Maxwell Building (JCMB) James Clerk Maxwell Building Peter Guthrie Tait Road Edinburgh EH9 3FD GB

### Event details

Detailed balance is often named as a necessary condition for Markov Chain Monte Carlo sampling to converge to a limiting distribution (e.g. the Boltzmann distribution). Here I will show that indeed a weaker balance condition (and regular sampling) is sufficient for convergence [1]. This proves that sequential updating schemes in Monte Carlo methods, which break detailed balance, are correct assuming that regular sampling is maintained. I will then present an algorithm which minimises rejection rates in Monte Carlo sampling by breaking detailed balance [2].

[1] V. I. Manousiouthakis and M. W. Deem, J. Chem. Phys. 110, 2753 (1999) [2] H. Suwa and S. Todo, Phys. Rev. Lett. 105, 120603 (2010)

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