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The multiple-try method and local optimization in metropolis sampling

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2000年第449期95卷 121-134页

作者： Liu, JS Liang, FM Wong, WH Stanford Univ Dept Stat Stanford CA 94305 USA Univ Calif Los Angeles Dept Stat Los Angeles CA 90095 USA

This article describes a new metropolis-like transition rule, the multiple-try metropolis, for Markov chain Monte Carlo (MCMC) simulations. By using this transition rule together with adaptive direction sampling. we propose a novel method for incorporating local optimization steps into a MCMC sampler in continuous state-space. Numerical studies show that the new method performs significantly better than the traditional metropolis-Hastings (M-H) sampler. With minor tailoring in using the rule, the multiple-try method can also be exploited to achieve the effect of a griddy Gibbs sampler without having to bear with griddy approximations, and the effect of a hit-and-run algorithm without having to figure out the required conditional distribution in a random direction.

关键词： adaptive direction sampling conjugate gradient damped sinusoidal Gibbs sampling griddy Gibbs sampler hit-and-run algorithm Markov chain Monte Carlo metropolis algorithm mixture model orientational bias Monte Carlo

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ADAPTIVE REJECTION metropolis SAMPLING WITHIN GIBBS SAMPLING

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JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES C-APPLIED STATISTICS 1995年第4期44卷 455-472页

作者： GILKS, WR BEST, NG TAN, KKC ADDENBROOKES HOSP CAMBRIDGE ENGLAND

Gibbs sampling is a powerful technique for statistical inference. It involves little more than sampling from full conditional distributions, which can be both complex and computationally expensive to evaluate. Gilks and Wild have shown that in practice full conditionals are often log-concave, and they proposed a method of adaptive rejection sampling for efficiently sampling from univariate log-concave distributions. In this paper, to deal with non-log-concave full conditional distributions, we generalize adaptive rejection sampling to include a Hastings-metropolis algorithm step. One important field of application in which statistical models may lead to non-log-concave full conditionals is population pharmacokinetics. Here, the relationship between drug dose and blood or plasma concentration in a group of patients typically is modelled by using non-linear mixed effects models. Often, the data used for analysis are routinely collected hospital measurements, which tend to be noisy and irregular. Consequently, a robust (t-distributed) error structure is appropriate to account for outlying observations and/or patients. We propose a robust non-linear full probability model for population pharmacokinetic data. We demonstrate that our method enables Bayesian inference for this model. through an analysis of antibiotic administration in new-born babies.

关键词： BAYESIAN COMPUTATION GIBBS SAMPLING MARKOV CHAIN MONTE CARLO METHOD metropolis algorithm PHARMACOKINETIC MODEL RANDOM VARIATE GENERATION

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Optimal scaling of metropolis algorithms: Heading toward general target distributions

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Canadian Journal of Statistics 2008年第4期36卷 483-503页

作者： Bédard, Mylène Rosenthal, Jeffrey S. Département de Mathématiques et de Statistique Université de Montréal Montréal QC H3C 3J7 C. P. 6128 succursale Centre-ville Canada Department of Statistics University of Toronto Toronto ON M5S 3G3 100 St. George Street Canada

The authors provide an overview of optimal scaling results for the metropolis algorithm with Gaussian proposal distribution. They address in more depth the case of high-dimensional target distributions formed of independent, but not identically distributed components. They attempt to give an intuitive explanation as to why the well-known optimal acceptance rate of 0.234 is not always suitable. They show how to find the asymptotically optimal acceptance rate when needed, and they explain why it is sometimes necessary to turn to inhomogeneous proposal distributions. Their results are illustrated with a simple example.

关键词： Acceptance rate Langevin diffusion Marginal process metropolis algorithm Scaling Weak convergence

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Storage Assignment Using Nested metropolis Sampling and Approximations of Order Batching Travel Costs

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SN Computer Science 2024年第5期5卷 477页

作者： Oxenstierna, Johan Malec, Jacek Krueger, Volker Dept. of Computer Science Lund University Lund Sweden Kairos Logic AB Lund Sweden

The Storage Location Assignment Problem (SLAP) is of central importance in warehouse operations. An important research challenge lies in generalizing the SLAP such that it is not tied to certain order-picking methodologies, constraints, or warehouse layouts. We propose the OBP-based SLAP, where the quality of a location assignment is obtained by optimizing an Order Batching Problem (OBP). For the optimization of the OBP-based SLAP, we propose a nested metropolis algorithm. The algorithm includes an OBP-optimizer to obtain the cost of an assignment, as well as a filter which approximates OBP costs using a model based on the Quadratic Assignment Problem (QAP). In experiments, we tune two key parameters in the QAP model, and test whether its predictive quality warrants its use within the SLAP optimizer. Results show that the QAP model’s per-sample accuracy is only marginally better than a random baseline, but that it delivers predictions much faster than the OBP optimizer, implying that it can be used as an effective filter. We then run the SLAP optimizer with and without using the QAP model on industrial data. We observe a cost improvement of around 23% over 1 h with the QAP model, and 17% without it. We share results for public instances on the TSPLIB format. © The Author(s) 2024.

关键词： metropolis algorithm Order batching problem Quadratic assignment problem Storage location assignment problem Warehousing

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Inference for a Failure Counting Process Partially Observed

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IEEE TRANSACTIONS ON RELIABILITY 2015年第1期64卷 311-319页

作者： Guerineau, Lise Gouno, Evans Elect France Res & Dev Dept Reliabil Availabil Elect Networks Paris France Univ Bretagne Sud Lab Math Bretagne Atlantique Vannes France

We consider a system defined as a collection of two types of components. The number of failures of each component is described as a stochastic process, with one of the processes depending on the other. None of the processes is observed directly. The only available information is the number of type 1 components at risk in the system. Because of this missing data situation, different algorithms relying on an Expectation Maximization (EM) strategy are proposed to obtain the MLE of the intensity parameters for both processes so we can assess the reliability of type 1 and type 2 components. To overcome the computational limits of EM, a Monte Carlo EM (MCEM) algorithm using a metropolis procedure is presented. Stochastic EM (SEM) algorithms including a Bayesian approach are also described. The methods are applied to simulated data to demonstrate their efficiency.

关键词： Bayesian estimation birth process expectation maximization algorithm maximum likelihood metropolis algorithm Monte Carlo methods Poisson process

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An Energy-Based Model for the Image Edge-Histogram Specification Problem

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IEEE TRANSACTIONS ON IMAGE PROCESSING 2012年第1期21卷 379-+页

作者： Mignotte, Max Univ Montreal Dept Informat & Rech Operat Fac Arts & Sci Montreal PQ H3C 3J7 Canada

In this correspondence, we present an original energy-based model that achieves the edge-histogram specification of a real input image and thus extends the exact specification method of the image luminance (or gray level) distribution recently proposed by Coltuc et al. Our edge-histogram specification approach is stated as an optimization problem in which each edge of a real input image will tend iteratively toward some specified gradient magnitude values given by a target edge distribution (or a normalized edge histogram possibly estimated from a target image). To this end, a hybrid optimization scheme combining a global and deterministic conjugate-gradient-based procedure and a local stochastic search using the metropolis criterion is proposed herein to find a reliable solution to our energy-based model. Experimental results are presented, and several applications follow from this procedure.

关键词： Conjugate gradient edge-histogram specification energy-based model gradient magnitude local stochastic search metropolis algorithm

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Monte Carlo study of the phase transitions in the classical XY ferromagnets with random anisotropy

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PHASE TRANSITIONS 2023年第9-10期96卷 668-686页

作者： Mallick, Olivia Acharyya, Muktish Presidency Univ Dept Phys Kolkata India

The three-dimensional anisotropic classical XY ferromagnet has been investigated by extensive Monte Carlo simulation using the metropolis single spin flip algorithm. The magnetisation (M) and the susceptibility (.) are measured and studied as functions of the temperature of the system. For constant anisotropy, the ferro-para phase transition has been found to take place at a higher temperature than that observed in the isotropic case. The system gets ordered at higher temperatures for higher values of the strength of anisotropy. The opposite scenario is observed in the case of random anisotropy. For all three different kinds of statistical distributions (uniform, Gaussian, and bimodal) of random anisotropy, the system gets ordered at lower temperatures for higher values of the width of the distribution of anisotropy. We have provided the phase boundaries in the case of random anisotropy. The critical exponents for the scaling laws M similar to L (beta/nu) and x similar to L (gamma/nu) are estimated through the finite size analysis.

关键词： XY ferromagnet anisotropy Monte Carlo simulation metropolis algorithm finite size analysis binder cumulant

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Field percolation-switching in soft ternary anisotropic system

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 520卷 11-25页

作者： Ambrozic, M. Kralj, S. Univ Maribor Fac Math & Nat Sci Koroska 160 Maribor Slovenia Jozef Stefan Inst Jamova 39 Ljubljana Slovenia Fac Ind Engn Segova 112 Novo Mesto Slovenia

We study numerically external electric or magnetic field driven switching between percolated and non-percolated configuration of nanoparticles in soft matter ternary systems. The system consists of nematic liquid crystal, impurities and elongated nanoparticles. We use the Lebwohl-Lasher lattice-type modeling to determine the orientational order of nanoparticles and consequently the metropolis algorithm to find the percolation threshold. In our model the external field acts directly only on the liquid crystal component, which in turn tends to reorient nanoparticles. We determine regimes where an external field relatively robustly switches between percolated and non-percolated states. The main variable physical parameters are volume concentration and length-to-width ratio of nanoparticles, concentration of impurities and temperature. We have revealed that impurities imposing static orientational disorder are a significant part of the system. A possible application is also proposed. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Nematic liquid crystals Nanoparticles Lebwohl-Lasher model metropolis algorithm Percolation threshold

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The use of discrete Markov random fields in reservoir characterization

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JOURNAL OF PETROLEUM SCIENCE AND ENGINEERING 2001年第2-4期32卷 257-264页

作者： Salomao, MC Remacre, AZ Univ Estadual Campinas Inst Geosci Dept Mineral Resources Policy & Management BR-13083970 Campinas SP Brazil

In this work, we discuss relevant aspects concerning the use of discrete Markov random fields (MRF) in the simulation of rock properties in petroleum reservoirs. The Strauss multi-color model is useful to describe complex image configurations, by handling with parameters of repulsion between the different rock facies, symbolized in this case, by the different colors. The transition between the facies and the porous medium anisotropy are imposed to the system, and it is possible to generate various types of arrangement of the facies on the image, in contrast to Gaussian stochastic process, that can only simulate diffusion-type images. Another point focused is the behavior of the spatial correlation in discrete Markov random fields, here studied by the calculus of the practical semivariogram. function in the binary Markov images, generated by using the metropolis algorithm. These images have a correspondence to Gaussian images with Gaussian-type correlation, after truncated in binary facies. This similarity is validated by analysis in the behavior of the semivariogram function of the discrete Gaussian processes. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： Markov random fields metropolis algorithm Gaussian stochastic process spatial correlation

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Convergence control methods for Markov chain Monte Carlo algorithms

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STATISTICAL SCIENCE 1995年第3期10卷 231-253页

作者： Robert, CP Statistics Laboratory CREST-INSEE France

Markov chain Monte Carlo methods have been increasingly popular since their introduction by Gelfand and Smith. However, while the breadth and variety of Markov chain Monte Carlo applications are properly astounding, progress in the control of convergence for these algorithms has been slow, despite its relevance in practical implementations. We present here different approaches toward this goal based on functional and mixing theories, while paying particular attention to the central limit theorem and to the approximation of the limiting variance. Renewal theory in the spirit of Mykland, Tierney and Yu is presented as the most promising technique in this regard, and we illustrate its potential in several examples. In addition, we stress that many strong convergence properties can be derived from the study of simple subchains which are produced by Markov chain Monte Carlo algorithms, due to a duality principle obtained in Diebolt and Robert for mixture estimation. We show here the generality of this principle which applies, for instance, to most missing data models. A more empirical stopping rule for Markov chain Monte Carlo algorithms is related to the simultaneous convergence of different estimators of the quantity of interest. Besides the regular ergodic average,we propose the Rao-Blackwellized version as well as estimates based on importance sampling and trapezoidal approximations of the integrals.

关键词： Gibbs sampling metropolis algorithm central limit theorem asymptotic variance renewal theory duality principle finite state Markov chains missing data ergodic theorem Rao-Blackwellization importance sampling trapezoidal integration

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