The Multiple-Try Method and Local Optimization in Metropolis Sampling

Liu, Jun S.; Liang, Faming; Wong, Wing Hung

doi:10.2307/2669532

Cited by 59 publications

(62 citation statements)

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“…The use of multiple chains has several desirable advantages, particularly when dealing with complex posterior distributions involving long tails, correlated parameters, multi-modality, and numerous local optima Liu et al, 2000;ter Braak, 2006;ter Braak and Vrugt, 2008;Vrugt et al, 2009a;Radu et al, 2009). The use of multiple chains offers a robust protection against premature convergence, and opens up the use of a wide arsenal of statistical measures to test whether convergence to a limiting distribution has been achieved (Gelman and Rubin, 1992).…”

Section: Multi-chain Methods: De-mcmentioning

confidence: 99%

“…It can be shown that this method satisfies the detailed balance condition and therefore produces a reversible Markov chain with the target distribution as the stationary distribution (Liu et al, 2000).…”

Section: Mt-dream (Zs)mentioning

confidence: 99%

“…The MT-DREAM (ZS) algorithm uses multiple-try sampling (Liu et al, 2000), snooker updating, and sampling from an archive of past states to enhance the convergence speed of CPU-intensive and parameter rich models. Benchmark experiments in geophysics, hydrology and hydrogeology have shown that this sampler is able to sample correctly high-dimensional target distributions Laloy et al, , 2013Linde and Vrugt, 2013;Carbajal et al, 2014;Lochbühler et al, 2014Lochbühler et al, , 2015.…”

Section: Mt-dream (Zs)mentioning

confidence: 99%

See 2 more Smart Citations

Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

Vrugt

2016

Environmental Modelling & Software

596

532

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Section: Multi-chain Methods: De-mcmentioning

confidence: 99%

Section: Mt-dream (Zs)mentioning

confidence: 99%

Section: Mt-dream (Zs)mentioning

confidence: 99%

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Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

Vrugt

2016

Environmental Modelling & Software

596

532

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“…This line sampling strategy overcomes the drawback of Gibbs line sampling. Furthermore, as Liu et al (2000) propose, this sampling strategy can be easily combined with a local optimization algorithm such as the Conjugate Gradient method. While Gilks et al (1994) did not mention exactly how to sample from the adjusted distribution, Liu et al (2000) developed a multiple-try method (MTM) for this purpose and named the new sampler the Conjugate Gradient Monte Carlo (CGMC) sampler.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation in nonlinear environmental problems

Liu

Cardiff

Kitanidis

2010

Stoch Environ Res Risk Assess

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Popular parameter estimation methods, including least squares, maximum likelihood, and maximum a posteriori (MAP), solve an optimization problem to obtain a central value (or best estimate) followed by an approximate evaluation of the spread (or covariance matrix). A different approach is the Monte Carlo (MC) method, and particularly Markov chain Monte Carlo (MCMC) methods, which allow sampling from the posterior distribution of the parameters. Though available for years, MC methods have only recently drawn wide attention as practical ways for solving challenging highdimensional parameter estimation problems. They have a broader scope of applications than conventional methods and can be used to derive the full posterior pdf but can be computationally very intensive. This paper compares a number of different methods and presents improvements using as case study a nonlinear DNAPL source dissolution and solute transport model. This depth-integrated semianalytical model approximates dissolution from the DNAPL source zone using nonlinear empirical equations with partially known parameters. It then calculates the DNAPL plume concentration in the aquifer by solving the advection-dispersion equation with a flux boundary. The comparison is among the classical MAP and some versions of computer-intensive Monte Carlo methods, including the Metropolis-Hastings (MH) method and the adaptive direction sampling (ADS) method.

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“…This not only makes it difficult to rapidly explore multidimensional parameter spaces, but also complicates assessment of convergence, and effective use of multiprocessor resources. Prefetching [Brockwell, 2006] and multitry Metropolis sampling [Liu et al, 2000] offer some options for distributed, multicore implementation of single chains. What is more, the use of a single chain increases chances of premature convergence.…”

Section: Comparison With Other Posterior Sampling Methods 331 Compmentioning

confidence: 99%

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

Laloy

Linde

Jacques

et al. 2015

Water Resources Research

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We present a Bayesian inversion method for the joint inference of high-dimensional multiGaussian hydraulic conductivity fields and associated geostatistical parameters from indirect hydrological data. We combine Gaussian process generation via circulant embedding to decouple the variogram from grid cell specific values, with dimensionality reduction by interpolation to enable Markov chain Monte Carlo (MCMC) simulation. Using the Matern variogram model, this formulation allows inferring the conductivity values simultaneously with the field smoothness (also called Matern shape parameter) and other geostatistical parameters such as the mean, sill, integral scales and anisotropy direction(s) and ratio(s). The proposed dimensionality reduction method systematically honors the underlying variogram and is demonstrated to achieve better performance than the Karhunen-Loè ve expansion. We illustrate our inversion approach using synthetic (error corrupted) data from a tracer experiment in a fairly heterogeneous 10,000-dimensional 2-D conductivity field. A 40-times reduction of the size of the parameter space did not prevent the posterior simulations to appropriately fit the measurement data and the posterior parameter distributions to include the true geostatistical parameter values. Overall, the posterior field realizations covered a wide range of geostatistical models, questioning the common practice of assuming a fixed variogram prior to inference of the hydraulic conductivity values. Our method is shown to be more efficient than sequential Gibbs sampling (SGS) for the considered case study, particularly when implemented on a distributed computing cluster. It is also found to outperform the method of anchored distributions (MAD) for the same computational budget.

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The Multiple-Try Method and Local Optimization in Metropolis Sampling

Cited by 59 publications

References 0 publications

Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

Parameter estimation in nonlinear environmental problems

Probabilistic inference of multi‐Gaussian fields from indirect hydrological data using circulant embedding and dimensionality reduction

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