Irreversible simulated tempering

Abstract

An extended ensemble Monte Carlo algorithm is proposed by introducing a violation of the detailed balance condition to the update scheme of the inverse temperature in simulated tempering. Our method, irreversible simulated tempering, is constructed based on the framework of the skew detailed balance condition. By applying this method to the ferromagnetic Ising model in two dimensions on a square lattice as a benchmark, the dynamical behavior of the inverse temperature and an autocorrelation function of the magnetization are studied numerically. It is found that the relaxation dynamics of the inverse temperature changes qualitatively from diffusive to ballistic by violating the detailed balance condition. Consequently, the autocorrelation time of magnetization is several times smaller than that for the conventional algorithm satisfying the detailed balance condition.

8 pages, 9 figures

References in corpus (3)

• Markov Chain Monte Carlo Method without Detailed Balance
• Eigenvalue analysis of an irreversible random walk with skew detailed balance conditions
• Determining efficient temperature sets for the simulated tempering method

Cited by in corpus (7)

• Non-Reversible Parallel Tempering: a Scalable Highly Parallel MCMC Scheme
• Efficient Irreversible Monte Carlo samplers
• An asymptotic Peskun ordering and its application to lifted samplers
• Parallel Tempering on Optimized Paths
• Simulated tempering with irreversible Gibbs sampling techniques
• Academic Meeting Scheduling Using an Antiferromagnetic Potts Model
• Theoretical guarantees for lifted samplers