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A Bayes analysis of modified Weibull distribution via Markov chain Monte Carlo simulation

JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 2010年第3期80卷 241-254页

作者： Upadhyay, S. K. Gupta, Ashutosh Banaras Hindu Univ DST Ctr Interdisciplinary Math Sci Varanasi 221005 Uttar Pradesh India Banaras Hindu Univ Dept Stat Varanasi 221005 Uttar Pradesh India

This paper presents the posterior analysis of a new family defined in the literature as modified Weibull distribution. This family is a modification of the two-parameter Weibull model in the sense that it, besides covering increasing and decreasing hazard rates, also represents bathtub-shaped behaviour. Both the Gibbs sampler and the metropolis algorithms have been used to provide complete analysis of the concerned posterior surfaces. The paper also considers examining the issue of model validation using predictive simulation ideas and the Bayesian p-value. Finally, numerical illustration has been provided based on two real data sets.

关键词： modified Weibull distribution bathtub hazard rate Markov chain Monte Carlo Gibbs sampler metropolis algorithm predictive simulation partial predictive p-value

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MOLECULAR DYNAMICAL SIMULATION OF THE CANONICAL ENSEMBLE

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JOURNAL OF STATISTICAL PHYSICS 1985年第1-2期39卷 167-180页

作者： BONOMI, E 1.Centre de Physique Théorique de l'école Polytechnique Plateau de Palaiseau-91128 Palaiseau-Cedex France

We apply a technique to simulate the canonical ensemble, mixing molecular dynamics and Monte Carlo techniques, in which particles suffer virtual hard shocks. In the limit of infinite time the system approaches a Boltzmann distribution. A good approximation to the Boltzmann distribution is achieved in computationally accessible time for some model systems including the one-dimensional jellium.

关键词： metropolis algorithm Brownian dynamics molecular dynamics computer simulation

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Honest exploration of intractable probability distributions via Markov chain Monte Carlo

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STATISTICAL SCIENCE 2001年第4期16卷 312-334页

作者： Jones, GL Hobert, JP Univ Minnesota Sch Stat Minneapolis MN 55455 USA Univ Florida Dept Stat Gainesville FL 32611 USA

Two important questions that must be answered whenever a Markov chain Monte Carlo (MCMC) algorithm is used are (Q1) What is an appropriate burn-in? and (Q2) How long should the sampling continue after burn-in? Developing rigorous answers to these questions presently requires a detailed study of the convergence properties of the underlying Markov chain. Consequently, in most practical applications of MCMC, exact answers to (Q1) and (Q2) are not sought. The goal of this paper is to demystify the analysis that leads to honest answers to (Q1) and (Q2). The authors hope that this article will serve as a bridge between those developing Markov chain theory and practitioners using MCMC to solve practical problems. The ability to address (Q1) and (Q2) formally comes from establishing a drift condition and an associated minorization condition, which together imply that the underlying Markov chain is geometrically ergodic. In this article, we explain exactly what drift and minorization are as well as how and why these conditions can be used to form rigorous answers to (Q1) and (Q2). The basic ideas are as follows. The results of Rosenthal (1995) and Roberts and Tweedie (1999) allow one to use drift and minorization conditions to construct a formula giving an analytic upper bound on the distance to stationarity, A rigorous answer to (Q1) can be calculated using this formula. The desired characteristics of the target distribution are typically estimated using ergodic averages. Geometric ergodicity of the underlying Markov chain implies that there are central limit theorems available for ergodic averages (Chan and Geyer 1994). The regenerative simulation technique (Mykland, Tierney and Yu, 1995;Robert, 1995) can be used to get a consistent estimate of the variance of the asymptotic normal distribution. Hence, an asymptotic standard error can be calculated, which provides an answer to (Q2) in the sense that an appropriate time to stop sampling can be determined. The methods are il

关键词： central limit theorem convergence rate coupling inequality drift condition general state space geometric ergodicity Gibbs sampler hierarchical random effects model metropolis algorithm minorization condition regeneration splitting uniform ergodicity

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Slice sampling

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ANNALS OF STATISTICS 2003年第3期31卷 705-741页

作者： Neal, RM Univ Toronto Dept Stat Toronto ON M5S 3G3 Canada

Markov chain sampling methods that adapt to characteristics of the distribution being sampled can be constructed using the principle that one can sample from a distribution by sampling uniformly from the region under the plot of its density function. A Markov chain that converges to this uniform distribution can be constructed by alternating uniform sampling in the vertical direction with uniform sampling from the horizontal "slice" defined by the current vertical position, or more generally, with some update that leaves the uniform distribution over this slice invariant. Such "slice sampling" methods are easily implemented for univariate distributions, and can be used to sample from a multivariate distribution by updating each variable in turn. This approach is often easier to implement than Gibbs sampling and more efficient than simple metropolis updates, due to the ability of slice sampling to adaptively choose the magnitude of changes made. It is therefore attractive for routine and automated use. Slice sampling methods that update all variables simultaneously are also possible. These methods can adaptively choose the magnitudes of changes made to each variable, based on the local properties of the density function. More ambitiously, such methods could potentially adapt to the dependencies between variables by constructing local quadratic approximations. Another approach is to improve sampling efficiency by suppressing random walks. This can be done for univariate slice sampling by "overrelaxation," and for multivariate slice sampling by "reflection" from the edges of the slice.

关键词： Markov chain Monte Carlo auxiliary variables adaptive methods Gibbs sampling metropolis algorithm overrelaxation dynamical methods

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Monte Carlo simulation of magnetic multi-core nanoparticles

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JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS 2009年第10期321卷 1400-1403页

作者： Schaller, Vincent Wahnstrom, Goran Sanz-Velasco, Anke Enoksson, Peter Johansson, Christer Chalmers Univ Technol Dept Microtechnol & Nanosci MC2 BioNano Syst Lab SE-41296 Gothenburg Sweden Chalmers Univ Technol Dept Appl Phys SE-41296 Gothenburg Sweden Imego Inst SE-40014 Gothenburg Sweden

In this paper, a Monte Carlo simulation is carried out to evaluate the equilibrium magnetization of magnetic multi-core nanoparticles in a liquid and subjected to a static magnetic field. The particles contain a magnetic multi-core consisting of a cluster of magnetic single-domains of magnetite. We show that the magnetization of multi-core nanoparticles cannot be fully described by a Langevin model. Inter-domain dipolar interactions and domain magnetic anisotropy contribute to decrease the magnetization of the particles, whereas the single-domain size distribution yields an increase in magnetization. Also, we show that the interactions affect the effective magnetic moment of the multicore nanoparticles. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Magnetic multi-core nanoparticle Monte Carlo simulation metropolis algorithm Magnetic dipolar interaction Magnetic anisotropy Magnetization

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The computational complexity of generating random fractals

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JOURNAL OF STATISTICAL PHYSICS 1996年第5-6期82卷 1299-1326页

作者： Machta, J Greenlaw, R UNIV NEW HAMPSHIRE DEPT COMP SCIDURHAMNH 03824

We examine a number of models that generate random fractals. The models are studied using the tools of computational complexity theory from the perspective of parallel computation. Diffusion-limited aggregation and several widely used algorithms for equilibrating the Ising model are shown to be highly sequential;it is unlikely they can be simulated efficiently in parallel. This is in contrast to Mandelbrot percolation, which can be simulated in constant parallel time. Our research helps shed light on the intrinsic complexity of these models relative to each other and to different growth processes that have been recently studied using complexity theory. In addition, the results may serve as a guide to simulation physics.

关键词： cluster algorithms computational complexity diffusion-limited aggregation Ising model metropolis algorithm P-completeness

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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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Nonequilibrium tricritical behavior in anisotropic XY ferromagnet driven by elliptically polarized propagating magnetic field wave

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2024年 651卷

作者： Mallick, Olivia Acharyya, Muktish Presidency Univ Dept Phys 86-1 Coll St Kolkata 700073 India

The three-dimensional anisotropic XY ferromagnet, driven by an elliptically polarized propagating magnetic field wave, has been extensively investigated by Monte Carlo simulation with the metropolis single spin flip algorithm. Both the effects of the bilinear exchange type and the single-site anisotropies are thoroughly investigated. The time-averaged magnetization (over the complete cycle of the elliptically polarized propagating magnetic field wave) components play the role of the dynamic order parameter. For a fixed set of values of the strength of anisotropy and the field amplitudes, the system has been found to get dynamically ordered at a pseudocritical temperature. The pseudocritical temperature of such a dynamic nonequilibrium phase transition has been found to depend both on the strength of anisotropy and the amplitudes of the elliptically polarized propagating magnetic field wave. A comprehensive phase diagram is represented here in the form of an image plot of the pseudocritical temperature in the plane formed by the strength of anisotropy and field amplitudes. Interestingly, this nonequilibrium phase transition has been found to be discontinuous (first order) for higher values of the field amplitude. On the other hand, the continuous (second order) transition has been noticed for lower values of the field amplitude. Such an interesting nonequilibrium tricritical behavior has been observed in driven XY ferromagnet. The order of such a nonequilibrium phase transition has been confirmed by the thermal variation (near the transition) of the statistical distribution of the order parameter and by the thermal variation of the fourth-order Binder cumulant. In the plane formed by field amplitude and anisotropy, a tricritical line has been shown as the accompanying (and complementary) phase diagram. The dependence of the pseudocritical temperature, on the frequency and wavelength of the elliptically polarized propagating magnetic field wave, has also been reported

关键词： XY model Anisotropy Monte Carlo simulation metropolis algorithm Polarized field wave Tricritical behavior Finite size analysis

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Trading accuracy for speed in parallel simulated annealing with simultaneous moves

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PARALLEL COMPUTING 2000年第1期26卷 135-150页

作者： Durand, MD White, SR Princeton Univ Dept Mol Biol Princeton NJ 08544 USA IBM Corp Thomas J Watson Res Ctr Yorktown Heights NY 10598 USA

A common approach to parallelizing simulated annealing is to generate several perturbations to the current solution simultaneously, requiring synchronization to guarantee correct evaluation of the cost function. The cost of this synchronization may be reduced by allowing inaccuracies in the cost calculations. We provide a framework for understanding the theoretical implications of this approach based on a model of processor interaction under reduced synchronization that demonstrates how errors in cost calculations occur and how to estimate them. We show how bounds on error in the cost calculations in a simulated annealing algorithm can be translated into worst-case bounds on perturbations in the parameters which describe the behavior of the algorithm. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： parallel simulated annealing metropolis algorithm Boltzmann distribution

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Bayesian Estimation of the Log-linear Exponential Regression Model with Censorship and Collinearity

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2016年第1期45卷 152-164页

作者： Ariza-Hernandez, Francisco J. Godinez-Jaimes, Flaviano Reyes-Carreto, Ramon Univ Autonoma Guerrero Unidad Acad Matemat Chilpancingo Mexico

In this work, a simulation study is conducted to evaluate the performance of Bayesian estimators for the log-linear exponential regression model under different levels of censoring and degrees of collinearity for two covariates. The diffuse normal, independent Student-t and multivariate Student-t distributions are considered as prior distributions and to draw from the posterior distributions, the metropolis algorithm is implemented. Also, the results are compared with the maximum likelihood estimators in terms of the mean squared error, coverages and length of the credibility and confidence intervals.

关键词： Bayes' estimator Censorship Collinearity Coverages Log-linear regression metropolis algorithm Simulation study

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