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Bayesian inference for a random tessellation process

BIOMETRICS 2001年第2期57卷 502-507页

作者： Blackwell, PG Univ Sheffield Dept Probabil & Stat Sheffield S3 7RH S Yorkshire England

This article describes an inhomogeneous Poisson point process in the plane with an intensity function based on a Dirichlet tessellation process and a method for using observations on the point process to make fully Bayesian inferences about the underlying tessellation. The method is implemented using a Markov chain Monte Carlo approach. An application to modeling the territories of clans of badgers, Meles meles, is described.

关键词： animal territories Cox process inhomogeneous Poisson process Markov chain Monte Carlo metropolis-hastings algorithm polygon decomposition tessellation reconstruction Thiessen polygon Voronoi tessellation

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Uncertainty analysis for the integration of seismic and controlled source electro-magnetic data

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GEOPHYSICAL PROSPECTING 2011年第4期59卷 609-626页

作者： Kwon, Myoung Jae Snieder, Roel Colorado Sch Mines Ctr Wave Phenomena Dept Geophys Golden CO 80401 USA

We study the appraisal problem for the joint inversion of seismic and controlled source electro-magnetic (CSEM) data and utilize rock-physics models to integrate these two disparate data sets. The appraisal problem is solved by adopting a Bayesian model and we incorporate four representative sources of uncertainty. These are uncertainties in 1) seismic wave velocity, 2) electric conductivity, 3) seismic data and 4) CSEM data. The uncertainties in porosity and water saturation are quantified by a posterior random sampling in the model space of porosity and water saturation in a marine one-dimensional structure. We study the relative contributions from the four individual sources of uncertainty by performing several statistical experiments. The uncertainties in the seismic wave velocity and electric conductivity play a more significant role on the variation of posterior uncertainty than do the seismic and CSEM data noise. The numerical simulations also show that the uncertainty in porosity is most affected by the uncertainty in the seismic wave velocity and that the uncertainty in water saturation is most influenced by the uncertainty in electric conductivity. The framework of the uncertainty analysis presented in this study can be utilized to effectively reduce the uncertainty of the porosity and water saturation derived from the integration of seismic and CSEM data.

关键词： Controlled source electro-magnetic metropolis-hastings algorithm Uncertainty analysis

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Population Markov Chain Monte Carlo

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MACHINE LEARNING 2003年第1-2期50卷 175-196页

作者： Laskey, KB Myers, JW George Mason Univ Dept Syst Engn & Operat Res Fairfax VA 22030 USA TRW Co Inc Reston VA 20190 USA

Stochastic search algorithms inspired by physical and biological systems are applied to the problem of learning directed graphical probability models in the presence of missing observations and hidden variables. For this class of problems, deterministic search algorithms tend to halt at local optima, requiring random restarts to obtain solutions of acceptable quality. We compare three stochastic search algorithms: a metropolis-hastings Sampler (MHS), an Evolutionary algorithm (EA), and a new hybrid algorithm called Population Markov Chain Monte Carlo, or popMCMC. PopMCMC uses statistical information from a population of MHSs to inform the proposal distributions for individual samplers in the population. Experimental results show that popMCMC and EAs learn more efficiently than the MHS with no information exchange. Populations of MCMC samplers exhibit more diversity than populations evolving according to EAs not satisfying physics-inspired local reversibility conditions.

关键词： Markov chain Monte Carlo metropolis-hastings algorithm graphical probabilistic models Bayesian networks Bayesian learning evolutionary algorithms

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Monte Carlo EM with importance reweighting and its applications in random effects models

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 1999年第4期29卷 429-444页

作者： Quintana, FA Liu, JS del Pino, GE Pontificia Univ Catolica Chile Fac Matemat Dept Probabilidad & Estad Santiago Chile Stanford Univ Dept Stat Stanford CA 94305 USA

In this paper we propose a new Monte Carlo EM algorithm to compute maximum likelihood estimates in the context of random effects models. The algorithm involves the construction of efficient sampling distributions for the Monte Carlo implementation of the E-step, together with a reweighting procedure that allows repeatedly using a same sample of random effects. In addition, we explore the use of stochastic approximations to speed up convergence once stability has been reached. Our algorithm is compared with that of McCulloch (1997). Extensions to more general problems are discussed. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： importance sampling metropolis-hastings algorithm stochastic approximations

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metropolis INTEGRATION SCHEMES FOR SELF-ADJOINT DIFFUSIONS

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MULTISCALE MODELING & SIMULATION 2014年第2期12卷 781-831页

作者： Bou-Rabee, Nawaf Donev, Aleksandar Vanden-Eijnden, Eric Rutgers State Univ Dept Math Sci Camden NJ 08102 USA NYU Courant Inst New York NY 10012 USA

We present explicit methods for simulating diffusions whose generator is self-adjoint with respect to a known (but possibly not normalizable) density. These methods exploit this property and combine an optimized Runge Kutta algorithm with a metropolis hastings Monte Carlo scheme. The resulting numerical integration scheme is shown to be weakly accurate at finite noise and to gain higher order accuracy in the small noise limit. It also permits the user to avoid computing explicitly certain terms in the equation, such as the divergence of the mobility tensor, which can be tedious to calculate. Finally, the scheme is shown to be ergodic with respect to the exact equilibrium probability distribution of the diffusion when it exists. These results are illustrated in several examples, including a Brownian dynamics simulation of DNA in a solvent. In this example, the proposed scheme is able to accurately compute dynamics at time step sizes that are an order of magnitude (or more) larger than those permitted with commonly used explicit predictor-corrector schemes.

关键词： explicit integrators Brownian dynamics with hydrodynamic interactions metropolis-hastings algorithm small noise limit predictor-corrector schemes DNA simulations ergodicity fluctuation-dissipation theorem

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Bayesian interface technique-based inverse estimation of closure coefficients of standard k - ε turbulence model by limiting the number of DNS data points for flow over a periodic hill

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INVERSE PROBLEMS 2024年第8期40卷 085004-085004页

作者： Kumar Chaurasia, Nagendra Chakraborty, Shubhankar Indian Inst Informat Technol Design & Mfg Kancheep Dept Mech Engn Chennai 600127 India

Among different numerical methods for modeling turbulent flow, Reynolds-averaged Navier-Stokes (RANS) is the most commonly used and computationally reasonable. However, the accuracy of RANS is lower than that of other high-fidelity numerical methods. In this work, the uncertainties associated with the coefficients of the standard k - epsilon RANS turbulence model are estimated and calibrated to improve the accuracy. The calibration is performed by considering the coefficients individually as well as collectively. The first three coefficients of the standard k - epsilon turbulence model are calibrated among the five coefficients (C-mu, C-epsilon 1, C-epsilon 2, sigma(epsilon). and sigma(k)). The Bayesian inference technique using the metropolis-hastings algorithm is applied to quantify uncertainties and calibration. Flow over a periodic hill is selected as a test case. The separation height of the bubble at x/h = 2 and x/h = 4, along with the streamwise velocity at various locations, has been chosen as the quantities of interest for comparing the results with DNS. The calibration is performed using known high-fidelity data (direct numerical simulation) from the available data set. The velocity field is re-calculated from the calibrated closure coefficients and compared with the same calculated with the standard coefficients of k - epsilon turbulence model (baseline). The deviation of calibrated C-mu is almost 50%-60% from baseline and for C-epsilon 1 and C-epsilon 2 it is 3%-12% and 6%-9% respectively. The algorithm is tested for different Reynold numbers and data points. A sensitivity analysis is also performed.

关键词： Bayesian inference technique metropolis-hastings algorithm Markov Chain Monte Carlo turbulence models RANS DNS

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Bayesian ordinal and binary regression models with a parametric family of mixture links

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 1999年第1期31卷 59-87页

作者： Lang, JB Univ Iowa Dept Stat & Actuarial Sci Iowa City IA 52242 USA

An ordinal and binary regression model with parametric link is introduced. The link is a member of a one-parameter family of "mixture links", a family that comprises smooth mixtures of the extreme minimum-value, extreme maximum-value, and logistic distributions. A Bayesian version of this flexible model serves as a vehicle for introducing a priori information regarding the choice of link. Owing to non-conjugacy, posterior and predictive distributions are approximated using Markov chain Monte Carlo simulation methods. Link-independent, Bayesian interpretations of covariate effects are described. The method is illustrated through the analyses of several data sets. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： categorical data cumulative link model LD50 logistic regression mixture distribution Markov chain Monte Carlo metropolis-hastings algorithm ordinal data predictive posterior distribution tolerance distribution

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Markov chain Monte Carlo sampling using a reservoir method

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2019年 139卷 64-74页

作者： Wang, Zhonglei Xiamen Univ Wang Yanan Inst Studies Econ MOE Key Lab Econometr Xiamen 361005 Fujian Peoples R China Xiamen Univ Sch Econ Xiamen 361005 Fujian Peoples R China

Markov chain Monte Carlo methods are widely used to draw a sample from a target distribution which is hard to characterize analytically, and reservoir sampling is developed to obtain a sample from a data stream sequentially in a single pass. A stochastic thinning algorithm using reservoir sampling is proposed, and it can be embedded in most Markov chain Monte Carlo methods to reduce the autocorrelation among the generated sample. The distribution of the sample generated by the proposed sampling algorithm converges in total variation to the target distribution in probability under mild conditions. A practical method is introduced to detect the convergence of the proposed sampling algorithm. Two simulation studies are conducted to compare the proposed sampling algorithm and the corresponding Markov chain Monte Carlo methods without thinning, and results show that the estimation bias of the proposed sampling algorithm is approximately the same as the corresponding Markov chain Monte Carlo method, but the proposed sampling algorithm has a smaller Monte Carlo variance. The proposed sampling algorithm saves computer memory in the sense that the storage of a small portion of the Markov chain is required in each iteration. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Convergence metropolis-hastings algorithm Removal procedure Stochastic thinning

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REVERSIBLE MARKOV DECISION PROCESSES WITH AN AVERAGE-REWARD CRITERION

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 2013年第1期51卷 402-418页

作者： Cogill, Randy Peng, Cheng Univ Virginia Dept Syst & Informat Engn Charlottesville VA 22902 USA

A wide variety of stochastic models have an important property known as reversibility. The analysis of reversible Markov chains is often significantly simpler than analysis of general Markov chains, particularly since there are often simple closed-form expressions for their invariant probability mass functions. In this paper we study the structure of optimal control policies for Markov decision processes with reversible dynamics. For optimal control of Markov decision processes, significant analytical and computational simplifications can arise as a result of reversibility. Here we present an analysis of a special class of reversible Markov decision processes, namely those that contain a cycle through their communication graph under any policy. These results provide encouraging evidence that similar simplifications hold for more general models, such as reversible processes without cycles and partition reversible processes. These results are demonstrated on a control-based variant of the metropolis-hastings algorithm, yielding faster convergence and better asymptotic performance than a conventional algorithm when applied to a combinatorial optimization problem.

关键词： Markov decision processes reversible Markov chains metropolis-hastings algorithm

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Reconciling individual-based forest growth models with landscape-level studies through a meta-modelling approach

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CANADIAN JOURNAL OF FOREST RESEARCH 2022年第8期52卷 1140-1153页

作者： Fortin, Mathieu Lavoie, Jean-Francois Canadian Wood Fibre Ctr Canadian Forest Serv Nat Resources Canada 580 Booth St Ottawa ON Canada Canadian Wood Fibre Ctr Canadian Forest Serv Nat Resources Canada 1055 Rue PEPS Quebec City PQ Canada

Landscape-level studies such as those on forest management planning and carbon accounting rely on large-area growth projections provided by forest growth models. Nowadays, most of these models are individual tree-based models. The detailed input they require and their complexity are a challenge for the integration into a landscape-level study. A possible alternative consists of approximating the complex model through a meta-model. A meta-model mimics the behaviour of the original model, while being simpler in terms of input and computation. In this study, we developed a Bayesian meta-modelling approach that can be used to obtain a simplified growth model from an individual tree-based model. The approach was exemplified through a real-world case study, namely a forest management unit in the province of Quebec, Canada. Using a Markov chain Monte Carlo method, we managed to fit meta-models based on the Chapman-Richards equation or its derivative for the main potential vegetation types. This meta-modelling approach has the advantages of (i) being an effective method of upscaling, (ii) providing simple meta-models suitable for landscape-level studies, and (iii) ensuring a proper error propagation from the original individual tree-based model into the meta-model.

关键词： meta-model Bayesian statistics Markov chain Monte Carlo metropolis-hastings algorithm individual tree-based models upscaling forest growth models forest management planning

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