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• catalog abstract "This monograph proposes several approaches to convergence monitoring for MCMC algorithms which are centered on the theme of discrete Markov chains. After a short introduction to MCMC methods, including recent developments like perfect simulation and Langevin Metropolis-Hastings algorithms, and to the current convergence diagnostics, the contributors present the theoretical basis for a study of MCMC convergence using discrete Markov chains and their specificities. The contributors stress in particular that this study applies in a wide generality, starting with latent variable models like mixtures, then extending the scope to chains with renewal properties, and concluding with a general Markov chain. They then relate the different connections with discrete or finite Markov chains with practical convergence diagnostics which are either graphical plots (allocation map, divergence graph, variance stabilizing, normality plot), stopping rules (normality, stationarity, stability tests), or confidence bounds (divergence, asymptotic variance, normality). Most of the quantitative tools take advantage of manageable versions of the CLT. The different methods proposed here are first evaluated on a set of benchmark examples and then studied on three full scale realistic applications, along with the standard convergence diagnostics: A hidden Markov modelling of DNA sequences, including a perfect simulation implementation, a latent stage modelling of the dynamics of HIV infection, and a modelling of hospitalization duration by exponential mixtures. The monograph is the outcome of a monthly research seminar held at CREST, Paris, since 1995. The seminar involved the contributors to this monograph and was led by Christian P. Robert, Head of the Satistics Laboratory at CREST and Professor of Statistics at the University of Rouen since 1992.".
• catalog contributor b10916081.
• catalog created "1998.".
• catalog date "1998".
• catalog date "1998.".
• catalog dateCopyrighted "1998.".
• catalog description "Includes bibliographical references and indexes.".
• catalog description "Markov Chain Monte Carlo Methods -- Convergence Control of MCMC Algorithms -- Linking Discrete and Continuous Chains -- Valid Discretization via Renewal Theory -- Control by the Central Limit Theorem -- Convergence Assessment in Latent Variable Models: DNA Applications -- Convergence Assessment in Latent Variable Models: Application to the Longitudinal Modelling of a Marker of HIV Progression -- Estimation of Exponential Mixtures.".
• catalog description "This monograph proposes several approaches to convergence monitoring for MCMC algorithms which are centered on the theme of discrete Markov chains. After a short introduction to MCMC methods, including recent developments like perfect simulation and Langevin Metropolis-Hastings algorithms, and to the current convergence diagnostics, the contributors present the theoretical basis for a study of MCMC convergence using discrete Markov chains and their specificities. The contributors stress in particular that this study applies in a wide generality, starting with latent variable models like mixtures, then extending the scope to chains with renewal properties, and concluding with a general Markov chain. They then relate the different connections with discrete or finite Markov chains with practical convergence diagnostics which are either graphical plots (allocation map, divergence graph, variance stabilizing, normality plot), stopping rules (normality, stationarity, stability tests), or confidence bounds (divergence, asymptotic variance, normality). Most of the quantitative tools take advantage of manageable versions of the CLT. The different methods proposed here are first evaluated on a set of benchmark examples and then studied on three full scale realistic applications, along with the standard convergence diagnostics: A hidden Markov modelling of DNA sequences, including a perfect simulation implementation, a latent stage modelling of the dynamics of HIV infection, and a modelling of hospitalization duration by exponential mixtures. The monograph is the outcome of a monthly research seminar held at CREST, Paris, since 1995. The seminar involved the contributors to this monograph and was led by Christian P. Robert, Head of the Satistics Laboratory at CREST and Professor of Statistics at the University of Rouen since 1992.".
• catalog extent "x, 192 p. :".
• catalog identifier "0387985913 (alk. paper)".
• catalog isPartOf "Lecture notes in statistics (Springer-Verlag) ; v. 135.".
• catalog isPartOf "Lecture notes in statistics ; 135".
• catalog issued "1998".
• catalog issued "1998.".
• catalog language "eng".
• catalog publisher "New York : Springer,".
• catalog subject "519.2 21".
• catalog subject "Convergence.".
• catalog subject "Markov processes.".
• catalog subject "Monte Carlo method.".
• catalog subject "QA295 .D46 1998".
• catalog subject "Statistics.".
• catalog tableOfContents "Markov Chain Monte Carlo Methods -- Convergence Control of MCMC Algorithms -- Linking Discrete and Continuous Chains -- Valid Discretization via Renewal Theory -- Control by the Central Limit Theorem -- Convergence Assessment in Latent Variable Models: DNA Applications -- Convergence Assessment in Latent Variable Models: Application to the Longitudinal Modelling of a Marker of HIV Progression -- Estimation of Exponential Mixtures.".
• catalog title "Discretization and MCMC convergence assessment / Christian P. Robert (editor).".
• catalog type "text".