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Differential Evolution Markov Chain with snooker updater and fewer chains

STATISTICS AND COMPUTING 2008年第4期18卷 435-446页

作者： ter Braak, Cajo J. F. Vrugt, Jasper A. Wageningen Univ & Res Ctr NL-6700 AC Wageningen Netherlands Los Alamos Natl Lab CNLS Los Alamos NM 87545 USA

Differential Evolution Markov Chain (DE-MC) is an adaptive MCMC algorithm, in which multiple chains are run in parallel. Standard DE-MC requires at least N=2d chains to be run in parallel, where d is the dimensionality of the posterior. This paper extends DE-MC with a snooker updater and shows by simulation and real examples that DE-MC can work for d up to 50-100 with fewer parallel chains (e.g. N=3) by exploiting information from their past by generating jumps from differences of pairs of past states. This approach extends the practical applicability of DE-MC and is shown to be about 5-26 times more efficient than the optimal Normal random walk metropolis sampler for the 97.5% point of a variable from a 25-50 dimensional Student t (3) distribution. In a nonlinear mixed effects model example the approach outperformed a block-updater geared to the specific features of the model.

关键词： Evolutionary Monte Carlo metropolis algorithm Adaptive Markov chain Monte Carlo Theophylline kinetics Adaptive direction sampling Parallel computing Differential evolution

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Monte Carlo Simulations

Monte Carlo Simulations

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作者： David J. Earl Michael W. Deem

A description of Monte Carlo methods for simulation of proteins is given. Advantages and disadvantages of the Monte Carlo approach are presented. The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented. Some of the standard and some of the more recent ways of performing Monte Carlo on proteins are presented. A discussion of the estimation of errors in properties calculated by Monte Carlo is given. less

关键词： Monte Carlo Simulations Monte Carlo Markov chain metropolis algorithm Protein simulation Stochastic methods

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Numerical results for the metropolis algorithm

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EXPERIMENTAL MATHEMATICS 2004年第2期13卷 207-213页

作者： Diaconis, P Neuberger, JW Stanford Univ Dept Math Palo Alto CA 94305 USA Univ N Texas Dept Math Denton TX 76203 USA

This paper deals with the spectrum of an operator associated with a special kind of random walk. The operator is related to the metropolis algorithm, an important tool of large-scale scientific computing. The spectrum of this operator has both discrete and continuous parts. There is an interesting challenge due to the fact that any finite-dimensional approximation has only eigenvalues. Patterns are presented which give an idea of the full spectrum of this operator.

关键词： metropolis algorithm random walk continuous spectrum

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Simulated annealing versus metropolis for a TSP instance

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INFORMATION PROCESSING LETTERS 2007年第6期104卷 216-219页

作者： Meer, Klaus Syddansk Univ Odense Dept Math & Comp Sci DK-5230 Odense M Denmark

In a recent paper [I. Wegener, Simulated Annealing beats metropolis in combinatorial optimization, in: L. Caires, G.F. Italiano, L. Monteiro, C. Palamidessi, M. Yung (Eds.), Proc. ICALP 2005, in: LNCS, vol. 3580, 2005, pp. 589-601] Wegener gave a first natural example of a combinatorial optimization problem where for certain instances a Simulated Annealing algorithm provably performs better than the metropolis algorithm for any fixed temperature. Wegener's example deals with a special instance of the Minimum Spanning Tree problem. In this short note we show that Wegener's technique as well can be used to prove a similar result for another important problem in combinatorial optimization, namely the Traveling Salesman Problem. The main task is to construct a suitable TSP instance for which SA outperforms MA when using the well known 2-Opt local search heuristic. (C) 2007 Elsevier B.V. All rights reserved.

关键词： analysis of algorithms simulated annealing metropolis algorithm 2-Opt heuristic for TSP

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Convergence of metropolis-type algorithms for a large canonical ensemble

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MATHEMATICAL NOTES 2007年第3-4期82卷 464-468页

作者： Vabishchevich, N. P. Moscow MV Lomonosov State Univ Moscow Russia

In this paper, we study the convergence of metropolis-type algorithms used in modeling statistical systems with a fluctuating number of particles located in a finite volume. We justify the use of metropolis algorithms for a particular class of Such statistical systems. We prove a theorem oil the geometric ergodicity of the Markov process modeling the behavior of an ensemble with a fluctuating number of particles in a finite Volume whose interaction is described by a potential bounded below and decreasing according to the law r(-3-a), alpha >= 0, as r -> 0.

关键词： metropolis algorithm Markov process geometric ergodicity drift condition

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Estimation of parameters in complex ¹⁵N tracing models by Monte Carlo sampling

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SOIL BIOLOGY & BIOCHEMISTRY 2007年第3期39卷 715-726页

作者： Mueller, Christoph Ruetting, T. Kattge, J. Laughlin, R. J. Stevens, R. J. Univ Giessen Dept Plant Ecol D-35392 Giessen Germany Max Planck Inst Biogeochem D-07745 Jena Germany Agri Food & Biosci Inst Agr Food & Environm Sci Div Belfast BT9 5PX Antrim North Ireland

The most widely used method to quantify gross N transforination rates in soils is based on N-15 dilution and enrichment principles. To identify rate parameters, N-15-tracing experiments are analysed by models that are linked to algorithins that try to minimize the misfit between modelled and observed data. In Currently available N-15-tracing models optimization algorithms are based oil the Levenberg-Marquardt method that is suitable for the determination of small number of parameters. Therefore, these models are restricted to a few processes. Methods based on Monte Carlo sampling have the potential to overcome restrictions on parameter numbers but have not been tested for application in N-15-tracing models. Here, for the first time, we use a Markov chain Monte Carlo (MCMC) method with a tracing model to simultaneously determine the probability density functions (PDFs) of the whole set of parameters for a previously published data set [Muller, C., Stevens, R.J., Laughlin, R.J., 2004. A N-15 tracing model to analyse N transformations in old grassland soil. Soil Biology & Biochemistry 36, 619-632]. We show that the MCMC method can simultaneously determine PDFs of more than 8 parameters and demonstrate for the first time that it is possible to optimize models where transformations are described by Michaelis-Menten kinetics. Setting the NH4+ oxidation rate to Michaelis-Menten kinetics reduced the misfit by 19%. Together with monitoring diagnostics for parameter convergence, the MCMC method is a very efficient and robust technique to determine PDFs for parameters in N-15-tracing models that Contain large number of N transformations and complex process descriptions. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： N-15 tracing model N transformations metropolis algorithm Monte Carlo sampling Markov chain Michaelis-Menten kinetics

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¹⁵N tracing models with a Monte Carlo optimization procedure provide new insights on gross N transformations in soils

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SOIL BIOLOGY & BIOCHEMISTRY 2007年第9期39卷 2351-2361页

作者： Ruetting, Tobias Mueller, Christoph Univ Giessen Dept Plant Ecol D-35392 Giessen Germany Natl Univ Ireland Univ Coll Dublin Sch Biol & Environm Sci Dublin 4 Ireland

N-15 tracing studies in combination with analyses via process-based models are the current "state-of-the-art" technique to quantify gross nitrogen (N) transformation rates in soils. A crucial component of this technique is the optimization algorithm which primarily decides how many model parameters can simultaneously be estimated. Recently, we published a Markov chain Monte Carlo (MCMC) method which has the potential to simultaneously estimate large number of parameters in N-15 tracing models [Muller et al., 2007. Estimation of parameters in complex N-15 tracing models by Monte Carlo sampling. Soil Biology & Biochemistry 39, 715-726]. Here, we present the results of a reanalysis of datasets by Kirkham and Bartholomew [1954. Equations for following nutrient transformations in soil, utilizing tracer data. Soil Science Society of America Proceedings 18, 33-34], Myrold and Tiedje [1986. Simultaneous estimation of several nitrogen cycle rates using N-15: theory and application. Soil Biology & Biochemistry 18, 559-568] and Watson et al. [2000. Overestimation of gross N transformation rates in grassland soils due to non-uniform exploitation of applied and native pools. Soil Biology & Biochemistry 32, 2019-2030] using the MCMC technique. Analytical solutions such as the ones derived by Kirkham and Bartholomew [1954. Equations for following nutrient transformations in soil, utilizing tracer data. Soil Science Society of America Proceedings 18, 33-34] result in gross rates without uncertainties. We show that the analysis of the same data sets with the MCMC method provides standard deviations for gross N transformations. The standard deviations are further reduced if realistic data uncertainties are considered. Reanalyzing data by Myrold and Tiedje [1986. Simultaneous estimation of several nitrogen cycle rates using 15N: theory and application. Soil Biology & Biochemistry 18, 559-568] (Capac soil) resulted in a model fit similar to the one of the original analysis but with mor

关键词： N-15 tracing model gross rates N transformations metropolis algorithm monte carlo sampling michaelis-menten kinetics reanalysis overestimation

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Quantifying hydrological modeling errors through a mixture of normal distributions

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JOURNAL OF HYDROLOGY 2007年第3-4期332卷 303-315页

作者： Schaefli, Bettina Talamba, Daniela Balin Musy, Andre Ecole Polytech Fed Lausanne Hydrol & Land Improvement Lab CH-1015 Lausanne Switzerland

Bayesian inference of posterior parameter distributions has become widely used in hydrological modeling to estimate the associated modeling uncertainty. The classical underlying statistical model assumes a Gaussian modeling error with zero mean and a given variance. For hydrological modeling residuals, this assumption however rarely holds;the present paper proposes the use of a mixture of normal distributions as a simple solution to overcome this problem in parameter inference studies. The hydrological and the statistical model parameters are inferred using a Markov chain Monte Carlo method known as the Metropotis-Hastings algorithm. The proposed methodology is illustrated for a rainfall-runoff model applied to a highly glacierized alpine catchment. The associated total modeling error is modeled using a mixture of two normal distributions, the mixture components referring respectively to the tow and the high flow discharge regime. The obtained results show that the use of a finite mixture model constitutes a promising solution to model hydrological modeling errors in parameter inference studies and could give additional insights into the model behavior. (c) 2006 Elsevier B.V. All rights reserved.

关键词： Gaussian mixtures modeling error parameter uncertainty Bayesian inference rainfall-runoff models metropolis algorithm

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Monte Carlo techniques for real-time quantum dynamics

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JOURNAL OF COMPUTATIONAL PHYSICS 2007年第2期220卷 549-567页

作者： Dowling, Mark R. Davis, Matthew J. Drummond, Peter D. Corney, Joel F. Univ Queensland Dept Phys Sch Phys Sci ARC Ctr Excellence Quantum Atom Opt Brisbane Qld 4072 Australia

The stochastic-gauge representation is a method of mapping the equation of motion for the quantum mechanical density operator onto a set of equivalent stochastic differential equations. One of the stochastic variables is termed the "weight", and its magnitude is related to the importance of the stochastic trajectory. We investigate the use of Monte Carlo algorithms to improve the sampling of the weighted trajectories and thus reduce sampling error in a simulation of quantum dynamics. The method can be applied to calculations in real time, as well as imaginary time for which Monte Carlo algorithms are more-commonly used. The Monte-Carlo algorithms are applicable when the weight is guaranteed to be real, and we demonstrate how to ensure this is the case. Examples are given for the anharmonic oscillator, where large improvements over stochastic sampling are observed. (c) 2006 Elsevier Inc. All rights reserved.

关键词： quantum dynamics Monte Carlo metropolis algorithm branching algorithm stochastic gauges Bose-Einstein condensation

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Genetic CONDENSATION for motion tracking

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SOFT COMPUTING 2007年第4期11卷 349-354页

作者： Ye, Zhu Liu, Zhi-Qiang City Univ Hong Kong Sch Creat Media Hong Kong Hong Kong Peoples R China

Tracking serves as a means to prepare data for pose estimation and action recognition. The CONDENSATION algorithm is a conditional density propagation method for motion tracking. This algorithm combines factored sampling with learned dynamic models to propagate an entire probability distributes for object position and shape over time. It can accomplish highly robust tracking of object motion. However, it usually requires a large number of samples to ensure a fair maximum likelihood estimation of the current state. In this paper, we use the mutation and crossover operators of the genetic algorithm to find appropriate samples. With this approach, we are able to improve robustness, accuracy and flexibility in CONDENSATION for visual tracking.

关键词： tracking CONDENSATION algorithm factored sampling genetic algorithm metropolis algorithm

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