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REGENERATION IN MARKOV-CHAIN SAMPLERS

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 1995年第429期90卷 233-241页

作者： MYKLAND, P TIERNEY, L YU, B UNIV MINNESOTA SCH STATMINNEAPOLISMN 55455 UNIV CALIF BERKELEY BERKELEYCA 94720

Markov chain sampling has recently received considerable attention, in particular in the context of Bayesian computation and maximum likelihood estimation. This article discusses the use of Markov chain splitting, originally developed for the theoretical analysis of general state-space Markov chains, to introduce regeneration into Markov chain samplers. This allows the use of regenerative methods for analyzing the output of these samplers and can provide a useful diagnostic of sampler performance. The approach is applied to several samplers, including certain metropolis samplers that can be used on their own or in hybrid samplers, and is illustrated in several examples.

关键词： GIBBS SAMPLING HYBRID SAMPLER MARKOV CHAIN MONTE CARLO metropolis algorithm SIMULATION OUTPUT ANALYSIS SPLIT CHAIN

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Monte Carlo methods

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GEM-INTERNATIONAL JOURNAL ON GEOMATHEMATICS 2018年第1期9卷 117-143页

作者： Koch, Karl-Rudolf Univ Bonn Inst Geodesy & Geoinformat Theoret Geodesy Grp Nussallee 17 D-53115 Bonn Germany

Monte Carlo methods deal with generating random variates from probability density functions in order to estimate unknown parameters or general functions of unknown parameters and to compute their expected values, variances and covariances. One generally works with the multivariate normal distribution due to the central limit theorem. However, if random variables with the normal distribution and random variables with a different distribution are combined, the normal distribution is not valid anymore. The Monte Carlo method is then needed to get the expected values, variances and covariances for the random variables with distributions different from the normal distribution. The error propagation by Monte Carlo methods is discussed and methods for generating random variates from the multivariate normal distribution and from the multivariate uniform distribution. The Monte Carlo integration is presented leading to the sampling-importance-resampling algorithm. Markov chain Monte Carlo methods provide by the metropolis algorithm and the Gibbs sampler additional ways of generating random variates. A special topic is the Gibbs sampler for computing and propagating large covariance matrices. This task arises, for instance, when the geopotential is determined from satellite observations. The example of the minimal detectable outlier shows, how the Monte Carlo method is used to determine the power of a hypothesis test.

关键词： Bayesian statistics SIR algorithm metropolis algorithm Gibbs sampler Markov chain Monte Carlo methods

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Real-parameter evolutionary Monte Carlo with applications to Bayesian mixture models

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2001年第454期96卷 653-666页

作者： Liang, FM Wong, WH Natl Univ Singapore Dept Stat & Appl Probabil Singapore 117543 Singapore Harvard Univ Sch Publ Hlth Dept Biostat Boston MA 02115 USA

We propose an evolutionary Monte Carlo algorithm to sample from a target distribution with real-valued parameters. The attractive features of the algorithm include the ability to learn from the samples obtained in previous steps and the ability to improve the mixing of a system by sampling along a temperature ladder. The effectiveness of the algorithm is examined through three multimodal examples and Bayesian neural networks. The numerical results confirm that the real-coded evolutionary algorithm is a promising general approach for simulation and optimization.

关键词： crossover evolutionary Monte Carlo exchange genetic algorithm Markov chain Monte Carlo metropolis algorithm mixture model mutation neural network parallel tempering

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Quantitative contraction rates for Markov chains on general state spaces

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ELECTRONIC JOURNAL OF PROBABILITY 2019年第none期24卷 1-36页

作者： Eberle, Andreas Majka, Mateusz B. Univ Bonn Inst Angew Math Endenicher Allee 60 D-53115 Bonn Germany Univ Warwick Dept Stat Coventry CV4 7AL W Midlands England

We investigate the problem of quantifying contraction coefficients of Markov transition kernels in Kantorovich (L-1 Wasserstein) distances. For diffusion processes, relatively precise quantitative bounds on contraction rates have recently been derived by combining appropriate couplings with carefully designed Kantorovich distances. In this paper, we partially carry over this approach from diffusions to Markov chains. We derive quantitative lower bounds on contraction rates for Markov chains on general state spaces that are powerful if the dynamics is dominated by small local moves. For Markov chains on R(d )with isotropic transition kernels, the general bounds can be used efficiently together with a coupling that combines maximal and reflection coupling. The results are applied to Euler discretizations of stochastic differential equations with non-globally contractive drifts, and to the metropolis adjusted Langevin algorithm for sampling from a class of probability measures on high dimensional state spaces that are not globally log-concave.

关键词： Markov chains Wasserstein distances quantitative bounds couplings Euler schemes metropolis algorithm

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A subpixel image restoration algorithm

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JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS 1997年第2期6卷 182-201页

作者： Gavin, J Jennison, C [a] School of Mathematical Sciences University of Bath Bath BA2 7AY United Kingdom

In statistical image reconstruction, data are often recorded on a regular grid of squares, known as pixels, and the reconstructed image is defined on the same pixel grid. Thus, the reconstruction of a continuous planar image is piecewise constant on pixels, and boundaries in the image consist of horizontal and vertical edges lying between pixels. This approximation to the true boundary can result in a loss of information that may be quite noticeable for small objects, only a few pixels in size. increasing the resolution of the sensor may not be a practical alternative. If some prior assumptions are made about the true image, however, reconstruction to a greater accuracy than that of the recording sensor's pixel grid is possible. We adopt a Bayesian approach, incorporating prior information about the true image in a stochastic model that attaches higher probability to images with shorter total edge length. in reconstructions, pixels may be of a single color or split between two colors. The model is illustrated using both real and simulated data.

关键词： Bayesian statistical image reconstruction confocal microscopy deconvolution edge detection Gibbs sampler Markov chain Monte Carlo metropolis algorithm subpixel resolution

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PARAMETRIC LINK MODIFICATION OF BOTH TAILS IN BINARY REGRESSION

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STATISTICAL PAPERS 1994年第3期35卷 189-201页

作者： CZADO, C YORK UNIV DEPT MATH & STATN YORK M3J 1P3ONCANADA

Common binary regression models such as logistic or probit regression have been extended to include parametric link transformation families. These binary regression models with parametric link are designed to avoid possible link misspecification and improve fit in some data sets. One and two parameter link families have been proposed in the literature (for a review see Stukel (1988)). However in real data examples published so far only one parameter link families have found to improve the fit significantly. This paper introduces a two parameter link family involving the modification of both tails of the link. An analysis based on computationally tractable Bayesian inference involving Monte Carlo sampling algorithms is presented extending earlier work of Czado (1992, 1993b). Finally, the usefulness of the two tailed link modification will be demonstrated in an example where single tail modification can be significantly improved upon by using a two tailed modification.

关键词： BINARY REGRESSION PARAMETRIC LINK TRANSFORMATION MAXIMUM LIKELIHOOD BAYESIAN INFERENCE MARKOV CHAIN MONTE-CARLO METHODS GIBBS SAMPLER metropolis algorithm REJECTION SAMPLING

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An integrated hydrologic Bayesian multimodel combination framework: Confronting input, parameter, and model structural uncertainty in hydrologic prediction

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WATER RESOURCES RESEARCH 2007年第1期43卷 W01403.1-W01403.1页

作者： Ajami, Newsha K. Duan, Qingyun Sorooshian, Soroosh Univ Calif Berkeley Dept Civil & Environm Engn Berkeley Water Ctr Berkeley CA 94720 USA Lawrence Livermore Natl Lab Livermore CA 94551 USA Univ Calif Irvine Dept Civil & Environm Engn Ctr Hydrometeorol & Remote Sensing Irvine CA 92679 USA

The conventional treatment of uncertainty in rainfall-runoff modeling primarily attributes uncertainty in the input-output representation of the model to uncertainty in the model parameters without explicitly addressing the input, output, and model structural uncertainties. This paper presents a new framework, the Integrated Bayesian Uncertainty Estimator (IBUNE), to account for the major uncertainties of hydrologic rainfall-runoff predictions explicitly. IBUNE distinguishes between the various sources of uncertainty including parameter, input, and model structural uncertainty. An input error model in the form of a Gaussian multiplier has been introduced within IBUNE. These multipliers are assumed to be drawn from an identical distribution with an unknown mean and variance which were estimated along with other hydrological model parameters by a Monte Carlo Markov Chain (MCMC) scheme. IBUNE also includes the Bayesian model averaging (BMA) scheme which is employed to further improve the prediction skill and address model structural uncertainty using multiple model outputs. A series of case studies using three rainfall-runoff models to predict the streamflow in the Leaf River basin, Mississippi, are used to examine the necessity and usefulness of this technique. The results suggest that ignoring either input forcings error or model structural uncertainty will lead to unrealistic model simulations and incorrect uncertainty bounds.

关键词： RAINFALL-RUNOFF MODELS metropolis algorithm MAXIMUM-LIKELIHOOD VARIABLESELECTION DATA ASSIMILATION OPTIMIZATION SIMULATIONS CALIBRATION ENSEMBLES FILTER

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Constant hazard function models with a change point: A Bayesian analysis using Markov chain Monte Carlo methods

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BIOMETRICAL JOURNAL 1998年第5期40卷 543-555页

作者： Achcar, JA Loibel, S Univ Sao Paulo Inst Ciencias Math BR-13560970 Sao Carlos SP Brazil

metropolis algorithms along with Gibbs steps are proposed to perform a Bayesian analysis for change-point constant hazard function models considering different prior densities for the parameters and censored survival data. We also present some generalizations for the comparison of two treatments. The methodology is illustrated with some examples.

关键词： constant hazard change-point Gibbs sampling metropolis algorithm

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Exploring anisotropic pressure and spatial correlations in strongly confined hard-disk fluids: Exact results

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Physical Review E 2024年第2期110卷 L022601-L022601页

作者： Ana M. Montero Andrés Santos Departamento de Física Instituto de Computación Científica Avanzada (ICCAEx)

This study examines the transverse and longitudinal properties of hard disks confined in narrow channels. Employing an exact mapping of the system onto a one-dimensional polydisperse, nonadditive mixture of hard rods with equal chemical potentials, we compute various thermodynamic properties, including the transverse and longitudinal equations of state, along with their behaviors at both low and high densities. Structural properties are analyzed using the two-body correlation function and the radial distribution function, tailored for the highly anisotropic geometry of this system. The results are corroborated by computer simulations.

关键词： Classical statistical mechanics Confinement Equations of state 2-dimensional systems Polydisperse systems Exact solutions for many-body systems metropolis algorithm

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Bayesian analysis for uncertainty estimation of a canopy transpiration model

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WATER RESOURCES RESEARCH 2007年第4期43卷 4424-1-4424-1页

作者： Samanta, S. Mackay, D. S. Clayton, M. K. Kruger, E. L. Ewers, B. E. Univ Wisconsin Dept Forest Ecol & Management Madison WI 53706 USA Univ Wisconsin Dept Plant Pathol Madison WI 53706 USA SUNY Buffalo Dept Geog Buffalo NY 14261 USA

[1] A Bayesian approach was used to fit a conceptual transpiration model to half-hourly transpiration rates for a sugar maple ( Acer saccharum) stand collected over a 5-month period and probabilistically estimate its parameter and prediction uncertainties. The model used the Penman-Monteith equation with the Jarvis model for canopy conductance. This deterministic model was extended by adding a normally distributed error term. This extension enabled using Markov chain Monte Carlo simulations to sample the posterior parameter distributions. The residuals revealed approximate conformance to the assumption of normally distributed errors. However, minor systematic structures in the residuals at fine timescales suggested model changes that would potentially improve the modeling of transpiration. Results also indicated considerable uncertainties in the parameter and transpiration estimates. This simple methodology of uncertainty analysis would facilitate the deductive step during the development cycle of deterministic conceptual models by accounting for these uncertainties while drawing inferences from data.

关键词： RECURSIVE PARAMETER-ESTIMATION ACER-SACCHARUM SEEDLINGS VAPOR-PRESSUREDEFICIT CHAIN MONTE-CARLO STOMATAL CONDUCTANCE HYDROLOGIC-MODELS metropolis algorithm IMPROVEDCALIBRATION CATCHMENT MODELS ESTIMATION GLUE

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