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On the geometric ergodicity of metropolis-hastings algorithms

STATISTICS 2007年第1期41卷 77-84页

作者： Atchade, Yves F. Perron, Francois Univ Ottawa Dept Math & Stat Ottawa ON K1N 6N5 Canada Univ Montreal Dept Math & Stat Montreal PQ H3C 3J7 Canada

Under a compactness assumption, we show that a phi-irreducible and aperiodic metropolis-hastings chain is geometrically ergodic if and only if its rejection probability is bounded away from unity. In the particular case of the independence metropolis-hastings algorithm, we obtain that the whole spectrum of the induced operator is contained in (and in many cases equal to) the essential range of the rejection probability of the chain as conjectured by [Liu, J. S., 1996, Metropolized independent sampling with comparaisons to rejection sampling and importance sampling. Statistics and Computing, 6, 113-119.].

关键词： geometric ergodicity Markov chain operators metropolis-hastings algorithm

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A VANILLA RAO-BLACKWELLIZATION OF metropolis-hastings algorithmS

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ANNALS OF STATISTICS 2011年第1期39卷 261-277页

作者： Douc, Randal Robert, Christian P. TELECOM SudParis F-91011 Evry France INSEE CREST F-92245 Malakoff France Univ Paris 09 F-75775 Paris 16 France

Casella and Robert [Biometrika 83 (1996) 81-94] presented a general Rao-Blackwellization principle for accept-reject and metropolis-hastings schemes that leads to significant decreases in the variance of the resulting estimators, but at a high cost in computation and storage. Adopting a completely different perspective, we introduce instead a universal scheme that guarantees variance reductions in all metropolis-hastings-based estimators while keeping the computation cost under control. We establish a central limit theorem for the improved estimators and illustrate their performances on toy examples and on a probit model estimation.

关键词： metropolis-hastings algorithm Markov chain Monte Carlo (MCMC) probit model central limit theorem variance reduction conditioning

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Bayesian identification of clustered outliers in multiple regression

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2007年第8期51卷 3955-3967页

作者： Mohr, Donna L. Univ N Florida Dept Math & Stat Jacksonville FL 32224 USA

We propose a Bayesian model for clustered outliers in multiple regression. In the literature, outliers are frequently modeled as coming from a subgroup where the variance of the errors is much larger than in the rest of the data. By contrast, when a cluster of outliers exists, we show that it can be more informative to model them as coming from a subgroup where different regression coefficients hold. We can explicitly model the clustering phenomenon by assuming that the probability of an outlier is a function of the explanatory variables. Fitting proceeds via the Gibbs sampler, using the metropolis-hastings algorithm to produce variates from the more unusual distributions. Initialization uses a least median of squares fit, and in some ways this method can be viewed as a Bayesian version of the many algorithms that use this fit as a start to some more efficient estimator. This method works very well in a variety of test data sets. We illustrate its use in a data set of sailboat prices, where it yields information both on the identity of the outliers and on their location, spread, and the regression coefficients inside the minority subgroup. (c) 2006 Elsevier B.V. All rights reserved.

关键词： switching regression least median of squares Gibbs samplers metropolis-hastings algorithm

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Spatial risk assessment of typhoon cumulated rainfall: a case study in Taipei area

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2012年第4期26卷 509-517页

作者： Lee, Yun-Huan Yang, Hong-Ding Chen, Chun-Shu Natl Changhua Univ Educ Inst Stat & Informat Sci Changhua Taiwan Ming Chuan Univ Dept Finance Taipei Taiwan Natl Changhua Univ Educ Dept Math Changhua Taiwan

Typhoon is one of the most destructive disasters in Taiwan, which usually causes many floods and mudslides and prevents the electrical and water supply. Prior to its arrival, how to accurately forecast the path and rainfall of typhoon are important issues. In the past, a regression-based model was the most applied statistical method to evaluate the associated problems. However, it generally ignored the spatial dependence in the data, resulting in less accurate estimation and prediction, and the importance of particular explanatory variables may not be apparent. Therefore, in this paper we focus on assessing the spatial risk variations regarding the typhoon cumulated rainfall at Taipei with respect to typhoon locations by using the spatial hierarchical Bayesian model combined with the spatial conditional autoregressive model, where the model parameters are estimated by designing a family of stochastic algorithms based on a Markov chain Monte Carlo technique. The proposed method is applied to a real data set of Taiwan for illustration. Also, some important explanatory variables regarding the typhoon cumulated rainfall at Taipei are indicated as well.

关键词： Conditional autoregressive model Cumulated rainfall Hierarchical Bayesian model Markov chain Monte Carlo metropolis-hastings algorithm Spatial risk assessment

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Bayesian forecasting of grape moth emergence

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ECOLOGICAL MODELLING 2006年第3-4期197卷 478-489页

作者： Moravie, M. -A. Davison, A. C. Pasquier, D. Charmillot, P. -J. Ecole Polytech Fed Lausanne Sch Basic Sci Inst Math CH-1015 Lausanne Switzerland AGROSCOPE Dept Plant Protect CH-1260 Nyon Switzerland

Wine production is an important industry in Western Switzerland, but vineyards must contend with grape vine and grape berry moths, the larval stages of which feed on grape flower buds and berries. This paper proposes a stochastic model for prediction of the emergence times of the moths, in order to aid treatment aimed at their control. Observed moth counts are treated as a realization of an inhomogeneous Poisson process whose probabilities are related to the distribution of time to emergence. We use a hierarchical model to account for the variability of this distribution between sites and years. Maximum likelihood and Bayesian fitting of the model to data are described, the latter using Markov chain Monte Carlo simulation, and the Bayesian approach is used for forecasting in future years. Grape vine moth flights proved much more variable than grape berry moth flights among sites and years;depending on the site, the flights of the two species can overlap or be completely distinct. Credibility intervals are provided for each site for a random future year, and the predictions can be updated and refined once 15-20% of the flight for a new year has emerged. The paper ends with discussion of the role of such models in similar applications. (c) 2006 Elsevier B.V All rights reserved.

关键词： Bayesian hierarchical model Gibbs sampler Markov chain Monte Carlo metropolis-hastings algorithm pest management Poisson process

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metropolis-hastings reversiblizations of non-reversible Markov chains

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2020年第2期130卷 1041-1073页

作者： Choi, Michael C. H. Chinese Univ Hong Kong Inst Data & Decis Analyt Shenzhen 518172 Guangdong Peoples R China

We study two types of metropolis-hastings (MH) reversiblizations for non-reversible Markov chains with Markov kernel P. While the first type is the classical metropolised version of P, we introduce a new self-adjoint kernel which captures the opposite transition effect of the first type, that we call the second MH kernel. We investigate the spectral relationship between P and the two MH kernels. Along the way, we state a version of Weyl's inequality for the spectral gap of P (and hence its additive reversiblization), as well as an expansion of P. Both results are expressed in terms of the spectrum of the two MH kernels. In the spirit of Fill (1991) and Paulin (2015), we define a new pseudo-spectral gap based on the two MH kernels, and show that the total variation distance from stationarity can be bounded by this gap. We give variance bounds of the Markov chain in terms of the proposed gap, and offer spectral bounds in metastability and Cheeger's inequality in terms of the two MH kernels by comparison of Dirichlet form and Peskun ordering. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Non-reversible Markov chain Spectral gap metropolis-hastings algorithm Mixing time Weyl's inequality Variance bounds

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A brief introduction to computer-intensive methods, with a view towards applications in spatial statistics and stereology

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JOURNAL OF MICROSCOPY 2011年第1期242卷 1-9页

作者： Mattfeldt, Torsten Univ Ulm Inst Pathol D-89081 Ulm Germany

P>Computer-intensive methods may be defined as data analytical procedures involving a huge number of highly repetitive computations. We mention resampling methods with replacement (bootstrap methods), resampling methods without replacement (randomization tests) and simulation methods. The resampling methods are based on simple and robust principles and are largely free from distributional assumptions. Bootstrap methods may be used to compute confidence intervals for a scalar model parameter and for summary statistics from replicated planar point patterns, and for significance tests. For some simple models of planar point processes, point patterns can be simulated by elementary Monte Carlo methods. The simulation of models with more complex interaction properties usually requires more advanced computing methods. In this context, we mention simulation of Gibbs processes with Markov chain Monte Carlo methods using the metropolis-hastings algorithm. An alternative to simulations on the basis of a parametric model consists of stochastic reconstruction methods. The basic ideas behind the methods are briefly reviewed and illustrated by simple worked examples in order to encourage novices in the field to use computer-intensive methods.

关键词： Bootstrap computer-intensive methods high performance computing clusters Markov chain Monte Carlo methods metropolis-hastings algorithm point processes randomization tests simulation spatial statistics stereology stochastic reconstruction

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Parameter estimation with the Markov Chain Monte Carlo method aided by evolutionary neural networks in a water hammer model

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COMPUTATIONAL & APPLIED MATHEMATICS 2023年第1期42卷 1-31页

作者： Carvalho, Raphael Costa Herzog, Iasmin Louzada Barreto Orlande, Helcio Rangel Colaco, Marcelo Jose Madeira, Italo Marcio Chakraborti, Nirupam Univ Fed Rio de Janeiro Politecn COPPE Dept Mech Engn UFRJ POB 68503 BR-21941972 Rio De Janeiro RJ Brazil Petrobras SA CENPES Res & Dev Ctr Av Horacio De Macedo 950 BR-21941915 Rio De Janeiro RJ Brazil Czech Tech Univ Fac Mech Engn Prague 6 Czech Republic

Fast transients in pumps and valves may induce significant variations in pressures and flow rates throughout pipelines that can even cause structural damages. This computational work deals with parameter estimation of a water hammer model, with focus on a transient friction coefficient and an empirical parameter related to the pipeline elasticity. The hyperbolic water hammer model was solved with a total variation diminishing version of the weighted average flux finite volume scheme. Simulated pressure and flow rate measurements taken near the inlet and the outlet of the pipeline were used for the solution of the parameter estimation problem with Markov Chain Monte Carlo methods. This work aimed at the reduction of the computational time of the inverse problem solution with two different strategies: (1) the application of a recent parallel computation version of the metropolis-hastings algorithm;and (2) the use of a machine learning metamodel obtained with the evolutionary neural network algorithm and the approximation error model approach. These two approaches are compared in terms of the parameter estimation accuracies and associated computational times.

关键词： Bayesian statistics metropolis-hastings algorithm Parallel computation Machine learning EvoNN Approximation error model

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Bayesian model selection in logistic regression for the detection of adverse drug reactions

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BIOMETRICAL JOURNAL 2016年第6期58卷 1376-1389页

作者： Marbac, Matthieu Tubert-Bitter, Pascale Sedki, Mohammed Inst Pasteur INSERM B2PHI UMR 1181 Paris France Univ Versailles St Quentin Versailles France Univ Paris 11 Fac Med Orsay France

Spontaneous adverse event reports have a high potential for detecting adverse drug reactions. However, due to their dimension, the analysis of such databases requires statistical methods. In this context, disproportionality measures can be used. Their main idea is to project the data onto contingency tables in order to measure the strength of associations between drugs and adverse events. However, due to the data projection, these methods are sensitive to the problem of coprescriptions and masking effects. Recently, logistic regressions have been used with a Lasso type penalty to perform the detection of associations between drugs and adverse events. On different examples, this approach limits the drawbacks of the disproportionality methods, but the choice of the penalty value is open to criticism while it strongly influences the results. In this paper, we propose to use a logistic regression whose sparsity is viewed as a model selection challenge. Since the model space is huge, a metropolis-hastings algorithm carries out the model selection by maximizing the BIC criterion. Thus, we avoid the calibration of penalty or threshold. During our application on the French pharmacovigilance database, the proposed method is compared to well-established approaches on a reference dataset, and obtains better rates of positive and negative controls. However, many signals (i.e., specific drug-event associations) are not detected by the proposed method. So, we conclude that this method should be used in parallel to existing measures in pharmacovigilance. Code implementing the proposed method is available at the following url: .https://***/masedki/MHTrajectoryR.

关键词： Bayesian Information Criterion Binary data Logistic regression metropolis-hastings algorithm Model selection Pharmacovigilance Spontaneous reporting

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WEAK CONVERGENCE RATES OF POPULATION VERSUS SINGLE-CHAIN STOCHASTIC APPROXIMATION MCMC algorithmS

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ADVANCES IN APPLIED PROBABILITY 2014年第4期46卷 1059-1083页

作者： Song, Qifan Wu, Mingqi Liang, Faming Texas A&M Univ College Stn TX 77843 USA Shell Global Solut US Inc The Hague Netherlands

In this paper we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation Markov chain Monte Carlo (MCMC) algorithms (SAMCMC algorithms). Based on the theory, we give an explicit ratio of convergence rates for the population SAMCMC algorithm and the single-chain SAMCMC algorithm. Our results provide a theoretic guarantee that the population SAMCMC algorithms are asymptotically more efficient than the single-chain SAMCMC algorithms when the gain factor sequence decreases slower than 0 (1/t), where t indexes the number of iterations. This is of interest for practical applications.

关键词： Asymptotic normality Markov chain Monte Carlo stochastic approximation metropolis-hastings algorithm

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