scholarly journals Accelerating parallel tempering: Quantile tempering algorithm (QuanTA)

2019 ◽  
Vol 51 (03) ◽  
pp. 802-834 ◽  
Author(s):  
Nicholas G. Tawn ◽  
Gareth O. Roberts
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Theoretical Analysis ◽  
Parallel Tempering ◽  
Mcmc Methods ◽  
Regularity Conditions ◽  
Population Approach ◽  
Multimodal Problems ◽  
Established Population

AbstractIt is well known that traditional Markov chain Monte Carlo (MCMC) methods can fail to effectively explore the state space for multimodal problems. Parallel tempering is a well-established population approach for such target distributions involving a collection of particles indexed by temperature. However, this method can suffer dramatically from the curse of dimensionality. In this paper we introduce an improvement on parallel tempering called QuanTA. A comprehensive theoretical analysis quantifying the improved efficiency and scalability of the approach is given. Under weak regularity conditions, QuanTA gives accelerated mixing through the temperature space. Empirical evidence of the effectiveness of this new algorithm is illustrated on canonical examples.

scholarly journals Mapping-Linked Quantitative Trait Loci Using Bayesian Analysis and Markov Chain Monte Carlo Algorithms

Genetics ◽  
1997 ◽  
Vol 146 (2) ◽  
pp. 735-743 ◽  
Author(s):  
Pekka Uimari ◽  
Ina Hoeschele
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Quantitative Trait Loci ◽  
Quantitative Trait ◽  
Allele Frequencies ◽  
Mcmc Methods ◽  
Substitution Effects ◽  
Indicator Variable ◽  
Trait Loci

A Bayesian method for mapping linked quantitative trait loci (QTL) using multiple linked genetic markers is presented. Parameter estimation and hypothesis testing was implemented via Markov chain Monte Carlo (MCMC) algorithms. Parameters included were allele frequencies and substitution effects for two biallelic QTL, map positions of the QTL and markers, allele frequencies of the markers, and polygenic and residual variances. Missing data were polygenic effects and multi-locus marker-QTL genotypes. Three different MCMC schemes for testing the presence of a single or two linked QTL on the chromosome were compared. The first approach includes a model indicator variable representing two unlinked QTL affecting the trait, one linked and one unlinked QTL, or both QTL linked with the markers. The second approach incorporates an indicator variable for each QTL into the model for phenotype, allowing or not allowing for a substitution effect of a QTL on phenotype, and the third approach is based on model determination by reversible jump MCMC. Methods were evaluated empirically by analyzing simulated granddaughter designs. All methods identified correctly a second, linked QTL and did not reject the one-QTL model when there was only a single QTL and no additional or an unlinked QTL.

A Distributed Computer System for Parallel Markov Chain Monte Carlo (MCMC)

2018 ◽  
Author(s):  
Michael Hynes
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Parameter Space ◽  
Heterogeneous Computing ◽  
Peer To Peer ◽  
Parallel Tempering ◽  
Single Chain ◽  
Distributed Computing Systems ◽  
Mcmc Algorithms

A ubiquitous problem in physics is to determine expectation values of observables associated with a system. This problem is typically formulated as an integration of some likelihood over a multidimensional parameter space. In Bayesian analysis, numerical Markov Chain Monte Carlo (MCMC) algorithms are employed to solve such integrals using a fixed number of samples in the Markov Chain. In general, MCMC algorithms are computationally expensive for large datasets and have difficulties sampling from multimodal parameter spaces. An MCMC implementation that is robust and inexpensive for researchers is desired. Distributed computing systems have shown the potential to act as virtual supercomputers, such as in the SETI@home project in which millions of private computers participate. We propose that a clustered peer-to-peer (P2P) computer network serves as an ideal structure to run Markovian state exchange algorithms such as Parallel Tempering (PT). PT overcomes the difficulty in sampling from multimodal distributions by running multiple chains in parallel with different target distributions andexchanging their states in a Markovian manner. To demonstrate the feasibility of peer-to-peer Parallel Tempering (P2P PT), a simple two-dimensional dataset consisting of two Gaussian signals separated by a region of low probability was used in a Bayesian parameter fitting algorithm. A small connected peer-to-peer network was constructed using separate processes on a linux kernel, and P2P PT was applied to the dataset. These sampling results were compared with those obtained from sampling the parameter space with a single chain. It was found that the single chain was unable to sample both modes effectively, while the P2P PT method explored the target distribution well, visiting both modes approximately equally. Future work will involve scaling to many dimensions and large networks, and convergence conditions with highly heterogeneous computing capabilities of members within the network.

scholarly journals Markov chain Monte Carlo inference for Markov jump processes via the linear noise approximation

2013 ◽  
Vol 371 (1984) ◽  
pp. 20110541 ◽  
Author(s):  
Vassilios Stathopoulos ◽  
Mark A. Girolami
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Jump Processes ◽  
Mcmc Methods ◽  
Computationally Efficient ◽  
Markov Jump ◽  
Riemann Manifold ◽  
Exact Inference ◽  
Markov Jump Processes

Bayesian analysis for Markov jump processes (MJPs) is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding, thus its applicability is limited to a small class of problems. In this paper, we describe the application of Riemann manifold Markov chain Monte Carlo (MCMC) methods using an approximation to the likelihood of the MJP that is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient whereas the convergence rate and mixing of the chains allow for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology.

scholarly journals Measuring Stellar Radial Velocity using Markov Chain Monte Carlo(MCMC) Method

2013 ◽  
Vol 9 (S298) ◽  
pp. 441-441
Author(s):  
Yihan Song ◽  
Ali Luo ◽  
Yongheng Zhao
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Probability Distribution ◽  
Radial Velocity ◽  
Mcmc Methods ◽  
Mcmc Method ◽  
Stellar Spectra ◽  
Mcmc Simulation ◽  
Template Fitting

AbstractStellar radial velocity is estimated by using template fitting and Markov Chain Monte Carlo(MCMC) methods. This method works on the LAMOST stellar spectra. The MCMC simulation generates a probability distribution of the RV. The RV error can also computed from distribution.

scholarly journals Improved Markov Chain Monte Carlo method for cryptanalysis substitution-transposition cipher

2016 ◽  
Vol 22 (4) ◽  
Author(s):  
Behrouz Fathi-Vajargah ◽  
Mohadeseh Kanafchian
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Monte Carlo Method ◽  
Mcmc Methods ◽  
Random Numbers ◽  
Simple Substitution

AbstractIn this paper we first investigate the use of Markov Chain Monte Carlo (MCMC) methods to attack classical ciphers. MCMC has previously been used to break simple substitution, transposition and substitution-transposition ciphers. Here, we improve the accuracy of obtained results by these algorithms and we show the performance of the algorithms using quasi random numbers such as Faure, Sobol and Niederreiter sequences.

scholarly journals On the convergence rates of some adaptive Markov chain Monte Carlo algorithms

2015 ◽  
Vol 52 (3) ◽  
pp. 811-825
Author(s):  
Yves Atchadé ◽  
Yizao Wang
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Convergence Rates ◽  
Mixing Time ◽  
Regularity Conditions ◽  
Monte Carlo Algorithms ◽  
Mcmc Algorithms ◽  
Variation Distance ◽  
Importance Resampling

In this paper we study the mixing time of certain adaptive Markov chain Monte Carlo (MCMC) algorithms. Under some regularity conditions, we show that the convergence rate of importance resampling MCMC algorithms, measured in terms of the total variation distance, is O(n-1). By means of an example, we establish that, in general, this algorithm does not converge at a faster rate. We also study the interacting tempering algorithm, a simplified version of the equi-energy sampler, and establish that its mixing time is of order O(n-1/2).

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