The Resource Discretization and MCMC convergence assessment, Christian P. Robert (editor), (electronic resource)

Discretization and MCMC convergence assessment, Christian P. Robert (editor), (electronic resource)

Label
Discretization and MCMC convergence assessment
Title
Discretization and MCMC convergence assessment
Statement of responsibility
Christian P. Robert (editor)
Contributor
Subject
Genre
Language
eng
Summary
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
Member of
Cataloging source
VT2
Dewey number
519.2
Illustrations
illustrations
Index
index present
LC call number
QA276-280
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorDate
1961-
http://library.link/vocab/relatedWorkOrContributorName
Robert, Christian P.
Series statement
Lecture notes in statistics
Series volume
135
http://library.link/vocab/subjectName
  • Convergence
  • Markov processes
  • Monte Carlo method
  • Convergence
  • Markov processes
  • Monte Carlo method
Label
Discretization and MCMC convergence assessment, Christian P. Robert (editor), (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4612-1716-9
Instantiates
Publication
Bibliography note
Includes bibliographical references (p. [175]-183) and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
1 online resource (x, 192 pages)
Form of item
online
Isbn
9781461217169
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Specific material designation
remote
System control number
  • (OCoLC)828772117
  • (OCoLC)ocn828772117
Label
Discretization and MCMC convergence assessment, Christian P. Robert (editor), (electronic resource)
Link
http://dx.doi.org/10.1007/978-1-4612-1716-9
Publication
Bibliography note
Includes bibliographical references (p. [175]-183) and indexes
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Dimensions
unknown
Extent
1 online resource (x, 192 pages)
Form of item
online
Isbn
9781461217169
Isbn Type
(electronic bk.)
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other physical details
illustrations.
Specific material designation
remote
System control number
  • (OCoLC)828772117
  • (OCoLC)ocn828772117

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