The Annals of Applied Probability

Minimising MCMC variance via diffusion limits, with an application to simulated tempering

Gareth O. Roberts and Jeffrey S. Rosenthal

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We derive new results comparing the asymptotic variance of diffusions by writing them as appropriate limits of discrete-time birth–death chains which themselves satisfy Peskun orderings. We then apply our results to simulated tempering algorithms to establish which choice of inverse temperatures minimises the asymptotic variance of all functionals and thus leads to the most efficient MCMC algorithm.

Article information

Ann. Appl. Probab., Volume 24, Number 1 (2014), 131-149.

First available in Project Euclid: 9 January 2014

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Zentralblatt MATH identifier

Primary: 60J22: Computational methods in Markov chains [See also 65C40]
Secondary: 62M05: Markov processes: estimation 62F10: Point estimation

Markov chain Monte Carlo simulated tempering optimal scaling diffusion limits


Roberts, Gareth O.; Rosenthal, Jeffrey S. Minimising MCMC variance via diffusion limits, with an application to simulated tempering. Ann. Appl. Probab. 24 (2014), no. 1, 131--149. doi:10.1214/12-AAP918.

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