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Bayesian analysis of ARMA-GARCH models: A Markov chain sampling approach

JOURNAL OF ECONOMETRICS 2000年第1期95卷 57-69页

作者： Nakatsuma, T Hitotsubashi Univ Inst Ecol Res Kunitachi Tokyo 1868603 Japan

We develop a Markov chain Monte Carlo method for a linear regression model with an ARMA(p, q)-GARCH(r, s) error. To generate a Monte Carlo sample from the joint posterior distribution, we employ a Markov chain sampling with the metropolis-hastings algorithm. As illustration, we estimate an ARMA-GARCH model of simulated time series data. (C) 2000 Elsevier Science S.A. All righter reserved. JEL classification: C11;C22.

关键词： ARMA process Bayesian inference GARCH Markov chain Monte carlo metropolis-hastings algorithm

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Bayesian analysis of the flutter margin method in aeroelasticity

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JOURNAL OF SOUND AND VIBRATION 2016年 384卷 56-74页

作者： Khalil, Mohammad Poirel, Dominique Sarkar, Abhijit Carleton Univ Dept Civil & Environm Engn Mackenzie BldgColonel By Dr Ottawa ON K1S 5B6 Canada Royal Mil Coll Canada Dept Mech & Aerosp Engn Kingston ON K7K 7B4 Canada Sandia Natl Labs POB 969 MS 9051 Livermore CA 94551 USA

A Bayesian statistical framework is presented for Zimmerman and Weissenburger flutter margin method which considers the uncertainties in aeroelastic modal parameters. The proposed methodology overcomes the limitations of the previously developed least square based estimation technique which relies on the Gaussian approximation of the flutter margin probability density function (pdf). Using the measured free-decay responses at subcritical (preflutter) airspeeds, the joint non-Gaussain posterior pdf of the modal parameters is sampled using the metropolis-hastings (MH)Markov chain Monte Carlo (MCMC) algorithm. The posterior MCMC samples of the modal parameters are then used to obtain the flutter margin pdfs and finally the flutter speed pdf. The usefulness of the Bayesian flutter margin method is demonstrated using synthetic data generated from a two-degree-of-freedom pitch-plunge aeroelastic model. The robustness of the statistical framework is demonstrated using different sets of measurement data. It will be shown that the probabilistic (Bayesian) approach reduces the number of test points required in providing a flutter speed estimate for a given accuracy and precision. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Aeroelasticity Coalescence Flutter Bayesian estimation metropolis-hastings algorithm Non-Gaussian Parameter Estimation

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Multilevel Markov Chain Monte Carlo

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SIAM REVIEW 2019年第3期61卷 509-545页

作者： Dodwell, T. J. Ketelsen, C. Scheichl, R. Teckentrup, A. L. Univ Exeter Coll Engn Math & Phys Sci Inst Data Sci & Artificial Intelligence Exeter EX4 4QF Devon England Alan Turing Inst London NW1 2DB England Maxar Technol Westminster CO 80234 USA Heidelberg Univ Inst Appl Math & Interdisciplinary Ctr Sci Comp Neuenheimer Feld 205 D-69120 Heidelberg Germany Univ Edinburgh Sch Math James Clerk Maxwell Bldg Edinburgh EH9 3FD Midlothian Scotland

In this paper we address the problem of the prohibitively large computational cost of existing Markov chain Monte Carlo methods for large-scale applications with high-dimensional parameter spaces, e.g., in uncertainty quantification in porous media flow. We propose a new multilevel metropolis-hastings algorithm and give an abstract, problem-dependent theorem on the cost of the new multilevel estimator based on a set of simple, verifiable assumptions. For a typical model problem in subsurface flow, we then provide a detailed analysis of these assumptions and show significant gains over the standard metropolis-hastings estimator. Numerical experiments confirm the analysis and demonstrate the effectiveness of the method with consistent reductions of more than an order of magnitude in the cost of the multilevel estimator over the standard metropolis-hastings algorithm for tolerances epsilon < 10(-2).

关键词： elliptic PDEs with random coefficients log-normal coefficients finite element analysis Bayesian approach metropolis-hastings algorithm multilevel Monte Carlo

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Bayesian analysis of the Logit model and comparison of two metropolis-hastings strategies

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2002年第2期39卷 137-152页

作者： Altaleb, A Chauveau, D Univ Damascus Fac Engn Dept Math & Stat Damascus Syria Univ Marne La Vallee Equipe Anal & Math Appl F-77454 Marne La Vallee 2 France

We examine some Markov chain Monte Carlo (MCMC) methods for a generalized non-linear regression model, the Logit model. It is first shown that MCMC algorithms may be used since the posterior is proper under the choice of non-informative priors. Then two non-standard MCMC methods are compared: a metropolis-hastings algorithm with a bivariate normal proposal resulting from an approximation, and a metropolis-hastings algorithm with an adaptive proposal. The results presented here are illustrated by simulations, and show the good behavior of both methods, and superior performances of the method with an adaptive proposal in terms of convergence to the stationary distribution and exploration of the posterior distribution surface. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： Bayesian statistic Markov chain Monte Carlo metropolis-hastings algorithm adaptive algorithm stationarity convergence assessment

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Bayesian blind turbo receiver for coded OFDM systems with frequency offset and frequency-selective fading

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2001年第12期19卷 2516-2527页

作者： Lu, B Wang, XD Texas A&M Univ Dept Elect Engn College Stn TX 77843 USA

The design of a blind receiver for coded orthogonal frequency-division multiplexing communication systems in the presence of frequency offset and frequency-selective fading is investigated. The proposed blind receiver iterates between a Bayesian demodulation stage and a maximum a posteriori channel decoding stage. The extrinsic a posteriori probabilities of data symbols are iteratively exchanged between these two stages to achieve successively improved performance. The Bayesian demodulator computes the a posteriori data symbol probabilities, based on the received signals (without knowing or explicitly estimating the frequency offset and the fading channel states), by using Markov chain Monte Carlo (MCMC) techniques. In particular, two MCMC methods-the metropolis-hastings algorithm and the Gibbs sampler-are studied for this purpose. Computer simulation results show that the proposed Bayesian blind turbo receiver can achieve good performance and is robust against modeling mismatch.

关键词： blind receiver coded orthogonal frequency-division multiplexing (OFDM) frequency offset frequency-selective fading Gibbs sampler Markov chain Monte Carlo metropolis-hastings algorithm turbo principle

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A Bayesian algorithm for Joint Symbol Timing Synchronization and Channel Estimation in Two-Way Relay Networks

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IEEE TRANSACTIONS ON COMMUNICATIONS 2013年第10期61卷 4271-4283页

作者： Jiang, Zhe Wang, Haiyan Ding, Zhi Northwestern Polytech Univ Sch Marine Sci & Technol Xian 710072 Peoples R China Univ Calif Davis Dept Elect & Comp Engn Davis CA 95616 USA

This work investigates joint estimation of symbol timing synchronization and channel response in two-way relay networks (TWRN) that utilize amplify-and-forward (AF) relay strategy. With unknown relay channel gains and unknown timing offset, the optimum maximum likelihood (ML) algorithm for joint timing recovery and channel estimation can be overly complex. We develop a new Bayesian based Markov chain Monte Carlo (MCMC) algorithm in order to facilitate joint symbol timing recovery and effective channel estimation. In particular, we present a basic metropolis-hastings algorithm (BMH) and a metropolis-hastings-ML (MH-ML) algorithm for this purpose. We also derive the Cramer-Rao lower bound (CRLB) to establish a performance benchmark. Our test results of ML, BMH, and MH-ML estimation illustrate near-optimum performance in terms of mean-square errors (MSE) and estimation bias. We further present bit error rate (BER) performance results.

关键词： Two-way relay network amplify-and-forward synchronization channel estimation Cramer-Rao lower bound Markov chain Monte Carlo metropolis-hastings algorithm

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Tailored randomized block MCMC methods with application to DSGE models

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JOURNAL OF ECONOMETRICS 2010年第1期155卷 19-38页

作者： Chib, Siddhartha Ramamurthy, Srikanth Washington Univ John M Olin Sch Business St Louis MO 63130 USA Loyola Univ Maryland Sellinger Sch Business Baltimore MD 21210 USA

In this paper we develop new Markov chain Monte Carlo schemes for the estimation of Bayesian models. One key feature of our method, which we call the tailored randomized block metropolis-hastings (TaRB-MH) method, is the random clustering of the parameters at every iteration into all arbitrary number of blocks. Then each block is sequentially updated through an M-H step. Another feature is that the proposal density for each block is tailored to the location and curvature of the target density based on the output of simulated annealing, following Chib and Greenberg ( 1994, 1995) and Chib and Ergashev (in press). We also provide all extended version of our method for sampling multi-modal distributions in which at a pre-specified mode jumping iteration, a single-block proposal is generated from one of the modal regions using a Mixture proposal density, and this proposal is then accepted according to all M-H probability of move. At the non-mode jumping iterations, the draws are obtained by applying the TaRB-MH algorithm. We also discuss flow the approaches of Chib (1995) and Chib and Jeliazkov (2001) call be adapted to these sampling schemes for estimating the model marginal likelihood. The methods are illustrated in several problems. In the DSGE model of Smets and Wouters (2007), for example, which involves a 36-dimensional posterior distribution, we show that the autocorrelations of the sampled draws from the TaRB-MH algorithm decay to zero within 30-40 lags for most parameters. In contrast, the sampled draws from the random-walk M-H method, the algorithm that has been used to date in the context of DSGE models, exhibit significant autocorrelations even at lags 2500 and beyond. Additionally, the RW-MH does not explore the same high density regions of the posterior distribution as the TaRB-MH algorithm. Another example concerns the model of An and Schorfheide (2007) where the posterior distribution is Multimodal. While the RW-MH algorithm is Unable to jump from the low

关键词： Dynamic stochastic general equilibrium models Markov chain Monte Carlo metropolis-hastings algorithm Marginal likelihood Randomized blocks Tailored proposal densities Multi modal densities Simulated annealing

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Componentwise adaptation for high dimensional MCMC

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COMPUTATIONAL STATISTICS 2005年第2期20卷 265-273页

作者： Haario, H Saksman, E Tamminen, J Univ Helsinki Dept Math & Stat FIN-00014 Helsinki Finland Univ Jyvaskyla Dept Math & Stat FIN-40014 Jyvaskyla Finland Finnish Meteorol Inst Geophys Res Div FIN-00101 Helsinki Finland

We introduce a new adaptive MCMC algorithm, based on the traditional single component metropolis-hastings algorithm and on our earlier adaptive metropolis algorithm (AM). In the new algorithm the adaption is performed component by component. The chain is no more Markovian, but it remains ergodic. The algorithm is demonstrated to work well in varying test cases up to 1000 dimensions.

关键词： MCMC adaptive MCMC metropolis-hastings algorithm

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Analysis of generalized linear mixed models via a stochastic approximation algorithm with Markov chain Monte-Carlo method

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STATISTICS AND COMPUTING 2002年第2期12卷 175-183页

作者： Zhu, HT Lee, SY Yale Univ Sch Med Dept Epidemiol & Publ Hlth New Haven CT 06520 USA Chinese Univ Hong Kong Dept Stat Shatin Hong Kong Peoples R China

In recent years much effort has been devoted to maximum likelihood estimation of generalized linear mixed models. Most of the existing methods use the EM algorithm, with various techniques in handling the intractable E-step. In this paper, a new implementation of a stochastic approximation algorithm with Markov chain Monte Carlo method is investigated. The proposed algorithm is computationally straightforward and its convergence is guaranteed. A simulation and three real data sets, including the challenging salamander data, are used to illustrate the procedure and to compare it with some existing methods. The results indicate that the proposed algorithm is an attractive alternative for problems with a large number of random effects or with high dimensional intractable integrals in the likelihood function.

关键词： completed-data log-likelihood metropolis-hastings algorithm generalized linear mixed model Markov chain Monte-Carlo salamander data stochastic approximation

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A semiparametric Bayesian approach to joint mean and variance models

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STATISTICS & PROBABILITY LETTERS 2013年第7期83卷 1624-1631页

作者： Xu, Dengke Zhang, Zhongzhan Beijing Univ Technol Coll Appl Sci Beijing 100124 Peoples R China

We propose a fully Bayesian inference for semiparametric joint mean and variance models on the basis of B-spline approximations of nonparametric components. An efficient MCMC method which combines Gibbs sampler and metropolis-hastings algorithm is suggested for the inference, and the methodology is illustrated through a simulation study and a real example. (c) 2013 Elsevier B.V. All rights reserved.

关键词： Bayesian analysis Joint mean and variance models Gibbs sampler metropolis-hastings algorithm B-spline

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