scholarly journals Nested Adaptation of MCMC Algorithms

2020 ◽  
Vol 15 (4) ◽  
pp. 1323-1343
Author(s):  
Dao Nguyen ◽  
Perry de Valpine ◽  
Yves Atchade ◽  
Daniel Turek ◽  
Nicholas Michaud ◽  
...  
Keyword(s):  
Mcmc Algorithms

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 A reduced order approach for probabilistic inversions of 3-D magnetotelluric data I: general formulation

2020 ◽  
Vol 223 (3) ◽  
pp. 1837-1863
Author(s):  
M C Manassero ◽  
J C Afonso ◽  
F Zyserman ◽  
S Zlotnik ◽  
I Fomin
Keyword(s):  
Large Scale ◽  
Computational Cost ◽  
Forward Problem ◽  
Parallel Structure ◽  
Data Sets ◽  
Magnetotelluric Data ◽  
Reduced Order ◽  
Mcmc Algorithms ◽  
Simulation Based ◽  
And Performance

SUMMARY Simulation-based probabilistic inversions of 3-D magnetotelluric (MT) data are arguably the best option to deal with the nonlinearity and non-uniqueness of the MT problem. However, the computational cost associated with the modelling of 3-D MT data has so far precluded the community from adopting and/or pursuing full probabilistic inversions of large MT data sets. In this contribution, we present a novel and general inversion framework, driven by Markov Chain Monte Carlo (MCMC) algorithms, which combines (i) an efficient parallel-in-parallel structure to solve the 3-D forward problem, (ii) a reduced order technique to create fast and accurate surrogate models of the forward problem and (iii) adaptive strategies for both the MCMC algorithm and the surrogate model. In particular, and contrary to traditional implementations, the adaptation of the surrogate is integrated into the MCMC inversion. This circumvents the need of costly offline stages to build the surrogate and further increases the overall efficiency of the method. We demonstrate the feasibility and performance of our approach to invert for large-scale conductivity structures with two numerical examples using different parametrizations and dimensionalities. In both cases, we report staggering gains in computational efficiency compared to traditional MCMC implementations. Our method finally removes the main bottleneck of probabilistic inversions of 3-D MT data and opens up new opportunities for both stand-alone MT inversions and multi-observable joint inversions for the physical state of the Earth’s interior.

The Move-to-Front Rule: A Case Study for two Perfect Sampling Algorithms

1998 ◽  
Vol 12 (3) ◽  
pp. 283-302 ◽  
Author(s):  
James Allen Fill
Keyword(s):  
Finite Population ◽  
Mixing Time ◽  
Test Case ◽  
Perfect Sampling ◽  
Mcmc Algorithms ◽  
Time Result ◽  
Elementary Problem ◽  
Sampling Algorithms ◽  
Coupling Algorithm

The elementary problem of exhaustively sampling a finite population without replacement is used as a nonreversible test case for comparing two recently proposed MCMC algorithms for perfect sampling, one based on backward coupling and the other on strong stationary duality. The backward coupling algorithm runs faster in this case, but the duality-based algorithm is unbiased for user impatience. An interesting by-product of the analysis is a new and simple stochastic interpretation of a mixing-time result for the move-to-front rule.

scholarly journals Weak Convergence Rates of Population Versus Single-Chain Stochastic Approximation MCMC Algorithms

2014 ◽  
Vol 46 (04) ◽  
pp. 1059-1083 ◽  
Author(s):  
Qifan Song ◽  
Mingqi Wu ◽  
Faming Liang
Keyword(s):  
Monte Carlo ◽  
Weak Convergence ◽  
Stochastic Approximation ◽  
Convergence Rates ◽  
Gain Factor ◽  
Single Chain ◽  
Practical Applications ◽  
Mcmc Algorithms ◽  
Factor Sequence ◽  
Number Of Iterations

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than O(1 / t), where t indexes the number of iterations. This is of interest for practical applications.

scholarly journals Bayesian-Based Methods for the Estimation of the Unknown Model’s Parameters in the Case of the Localization of the Atmospheric Contamination Source

2012 ◽  
Vol 37 (4) ◽  
pp. 253-270 ◽  
Author(s):  
M. Borysiewicz ◽  
A. Wawrzynczak ◽  
P. Kopka
Keyword(s):  
Model Parameters ◽  
Contamination Source ◽  
Contaminant Source ◽  
Distributed Sensor ◽  
Distributed Sensor Network ◽  
Mcmc Algorithms ◽  
On Line ◽  
A Current ◽  
The Bayesian Approach ◽  
Atmospheric Release

AbstractIn many areas of application it is important to estimate unknown model parameters in order to model precisely the underlying dynamics of a physical system. In this context the Bayesian approach is a powerful tool to combine observed data along with prior knowledge to gain a current (probabilistic) understanding of unknown model parameters. We have applied the methodology combining Bayesian inference with Markov chain Monte Carlo (MCMC) to the problem of the atmospheric contaminant source localization. The algorithm input data are the on-line arriving information about concentration of given substance registered by distributed sensor network. We have examined different version of the MCMC algorithms in effectiveness to estimate the probabilistic distributions of atmospheric release parameters. The results indicate the probability of a source to occur at a particular location with a particular release rate.

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