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About 1,308 papers for “Parallel tempering”

Anytime Parallel Tempering

d'Avigneau, A. Marie, Singh, S. S., Murray, L. M. · arXiv (Cornell University) · 2020

Developing efficient MCMC algorithms is indispensable in Bayesian inference. In parallel tempering, multiple interacting MCMC chains run to more efficiently explore the state space and improve performance. The multiple chains advance independently through local moves, and the performance enhancement steps are exchange moves, where the chains pause to exchange their current sample amongst each other. To accelerate the independent local moves, they may be performed simultaneously on multiple processors. Another problem is then encountered: depending on the MCMC implementation and inference problem, local moves can take a varying and random amount of time to complete. There may also be infrastructure-induced variations, such as competing jobs on the same processors, which arises in cloud computing. Before exchanges can occur, all chains must complete the local moves they are engaged in to avoid introducing a potentially substantial bias (Proposition 2.1). To solve this issue of randomly varying local move completion times in multi-processor parallel tempering, we adopt the Anytime Monte Carlo framework of Murray et al. (2016): we impose real-time deadlines on the parallel local moves and perform exchanges at these deadlines without any processor idling. We show our methodology for exchanges at real-time deadlines does not introduce a bias and leads to significant performance enhancements over the naïve approach of idling until every processor's local moves complete. The methodology is then applied in an ABC setting, where an Anytime ABC parallel tempering algorithm is derived for the difficult task of estimating the parameters of a Lotka-Volterra predator-prey model, and similar efficiency enhancements are observed.

Cited by 0Open access

Adaptive parallel tempering algorithm

Błażej Miasojedow, Éric Moulines, Matti Vihola · arXiv (Cornell University) · 2012

Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler depend strongly on the choice of tuning parameters, such as the temperature schedule and the proposal distribution used for local exploration. We propose an adaptive algorithm which tunes both the temperature schedule and the parameters of the random-walk Metropolis kernel automatically. We prove the convergence of the adaptation and a strong law of large numbers for the algorithm. We illustrate the performance of our method with examples. Our empirical findings indicate that the algorithm can cope well with different kind of scenarios without prior tuning.

Cited by 9Open access

Virtual‐Move Parallel Tempering

Ivan Coluzza, Daan Frenkel · ChemPhysChem · 2005

Efficient sampling: Free-energy landscapes for the refolding of a model protein are computed with the conventional adaptive parallel-tempering (APT) scheme and the virtual-move parallel-tempering (VMPT) algorithm (a and b, respectively, in the picture). There is a striking difference in the sampling efficiency of the two methods. VMPT generates a fairly complete free-energy landscape, whereas APT only generates fragments.

Cited by 89

Likelihood-Free Parallel Tempering

Meïli Baragatti, Agnès Grimaud, Denys Pommeret · HAL (Le Centre pour la Communication Scientifique Directe) · 2011

Approximate Bayesian Computational (ABC) methods (or likelihood-free methods) have appeared in the past fifteen years as useful methods to perform Bayesian analyses when the likelihood is analytically or computationally intractable. Several ABC methods have been proposed: Monte Carlo Markov Chains (MCMC) methods have been developped by Marjoramet al. (2003) and by Bortotet al. (2007) for instance, and sequential methods have been proposed among others by Sissonet al. (2007), Beaumont et al. (2009) and Del Moral et al. (2009). Until now, while ABC-MCMC methods remain the reference, sequential ABC methods have appeared to outperforms them (see for example McKinley et al. (2009) or Sisson et al. (2007)). In this paper a new algorithm combining population-based MCMC methods with ABC requirements is proposed, using an analogy with the Parallel Tempering algorithm (Geyer, 1991). Performances are compared with existing ABC algorithms on simulations and on a real example.

Cited by 0Open access

Feedback-optimized parallel tempering

Helmut G. Katzgraber, D avid Ah, Matthias Troyer · 2006

We intro duce an algorithm for systematically improving the efficiency of parallel tempering Monte Carlo simulations by optimizing the simulated temperature set. Our approach is closely related to a recently introduced adaptive algorithm that optimizes the simulated statistical ensemble in generalized broad-histogram Monte Carlo simulations. Conventionally, a temperature set is chosen in such a way that the acceptance rates for replica swaps between adjacent temperatures are independent of the temperature and large enough to ensure frequent swaps. In this paper, we show that by choosing the temperatures with a modified version of the optimized ensemble feedback method we can minimize the round-trip times between the lowest and highest temperatures which effectively increases the efficiency of the parallel tempering algorithm. In particular, the density of temperatures in the optimized temperature set increases at the 'bottlenecks' of the simulation, such as phase transitions. In turn, the acceptance rates are now temperature dependent in the optimized temperature ensemble. We illustrate the feedback-optimized parallel tempering algorithm by studying the two-dimensional Ising ferromagnet and the two-dimensional fully frustrated Ising model, and briefly discuss possible feedback schemes for systems that require configurational averages, such as spin glasses.

Cited by 16

Parallel Tempering sans vraisemblance

Meïli Baragatti, Agnès Grimaud, Denys Pommeret · HAL (Le Centre pour la Communication Scientifique Directe) · 2012

International audience

Cited by 0

From Parallel Tempering Monte Carlo

K. Pinn, C. Wieczerkowski · 1998

There are 880 magic squares of size 4 by 4, and 275,305,224 of size 5 by 5. It seems very difficult if not impossible to count exactly the number of higher order magic squares. We propose a method to estimate these numbers by Monte Carlo simulating magic squares at finite temperature. One is led to perform low temperature simulations of a system with many ground states that are separated by energy barriers. The Parallel Tempering Monte Carlo method turns out to be of great help here. Our estimate for the number of 6 by 6 magic squares Magic squares involve using all the numbers 1, 2, 3,..., n 2 to fill the squares of an n × n board so that each row, each column, and both main diagonals sum up to the same number. Interesting information about magic squares is collected at the WEB site of M. Suzuki [1].

Cited by 0

Speeding up parallel tempering simulations

Martin Hasenbusch, Stefan Schaefer · Physical Review E · 2010

We discuss methods that allow us to increase the step size in a parallel tempering simulation of statistical models and test them at the example of the three-dimensional Heisenberg spin glass. We find an overall speedup of about 2 for contemporary lattices.

Cited by 15Open access

An Adaptive Parallel Tempering Algorithm

Błażej Miasojedow, Éric Moulines, Matti Vihola · Journal of Computational and Graphical Statistics · 2013

Abstract Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler depend strongly on the choice of tuning parameters, such as the temperature schedule and the proposal distribution used for local exploration. We propose an adaptive algorithm with fixed number of temperatures which tunes both the temperature schedule and the parameters of the random-walk Metropolis kernel automatically. We prove the convergence of the adaptation and a strong law of large numbers for the algorithm under general conditions. We also prove as a side result the geometric ergodicity of the parallel tempering algorithm. We illustrate the performance of our method with examples. Our empirical findings indicate that the algorithm can cope well with different kinds of scenarios without prior tuning. Supplementary materials including the proofs and the Matlab implementation are available online. Key Words: Adaptive MCMCLaw of large numbersMultimodality SUPPLEMENTARY MATERIALS Proofs: The proofs of all the results in this article are given in the supplementary document (supplemental-pt.tex, LaTeX file) Matlab implementation: Matlab implementation of the adaptive parallel tempering algorithm. (apt-codes.zip, Zip file) ACKNOWLEDGMENTS The first two authors were supported by the French National Research Agency under the contract ANR-08-BLAN-0218 "BigMC." The third author was supported by the Academy of Finland (project 250575) and by the Finnish Academy of Science and Letters, Vilho, Yrjö and Kalle Väisälä Foundation. Notes The Matlab-implementation is available at http://iki.fi/mvihola/apt-codes.zip.

Cited by 105

Parallel Tempering for DSGE Estimation

Brault, Joshua · Econstor (Econstor) · 2024

In this paper, I develop a population-based Markov chain Monte Carlo (MCMC) algorithm known as parallel tempering to estimate dynamic stochastic general equilibrium (DSGE) models. Parallel tempering approximates the posterior distribution of interest using a family of Markov chains with tempered posteriors. At each iteration, two randomly selected chains in the ensemble are proposed to swap parameter vectors, after which each chain mutates via Metropolis-Hastings. The algorithm results in a fast-mixing MCMC, particularly well suited for problems with irregular posterior distributions. Also, due to its global nature, the algorithm can be initialized directly from the prior distributions. I provide two empirical examples with complex posteriors: a New Keynesian model with equilibrium indeterminacy and the Smets-Wouters model with more diffuse prior distributions. In both examples, parallel tempering overcomes the inherent estimation challenge, providing extremely consistent estimates across different runs of the algorithm with large effective sample sizes. I provide code compatible with Dynare mod files, making this routine straightforward for DSGE practitioners to implement.

Cited by 0Open access

HagesLab/MetroTRPL: Parallel Tempering Patch

cfai2304, amurad2 · Zenodo (CERN European Organization for Nuclear Research) · 2023

In this update, annealing is being dropped in favor of parallel tempering, which we consider a more versatile usage of multiple chains. See ## for further details. Added setting "parallel_tempering" to MCMC_fields, which may be None or a list of temperature values. Activating this setting creates an ensemble of one chain per temperature. Otherwise, the program runs with a single chain as before (essentially, an ensemble of size 1 with temperature 1). Added setting "temper_freq" to MCMC_fields, which may be a positive integer n. If the ensemble contains more than one chain, the program will attempt a chain swapping move every n iterations. A successful swap interchanges the positions of two chains with adjacent temperatures in the ensemble, which hopefully allows low-temperature chains to escape local likelihood extrema more easily. Defaults to n=10. Deprecated all settings and behaviors referring to annealing. Pickle files now export chain ensembles containing lists of MetroStates instead of individual MetroStates. GUI adapted to read both types of pickle files. Deprecated some settings that turned out not to be so useful: One-param-at-a-time delayed_acceptance proposal_function (now always uses uniform box) self_normalize resample noise_level equal_mu_override and equal_s_override Deprecated some objects, as it was better for performance just to store many quantities as arrays rather than dictionaries: Covariance Parameters Solution Known issues: The parallel tempering does not use CPU parallelism - having multiple chains/temperatures will proportionally increase the runtime. We are working on some MPI interfaces to synchronize the different temperatures. MLE and Dense_Sampling still need retesting and may throw errors in this version.

Cited by 0Open access