rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Discretization and MCMC convergence assessment
  name:
    name part: Robert, Christian P.
    name part: 1961-
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1998
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (x, 192 pages) : illustrations.
  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.
  table of 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.
  note: Christian P. Robert (editor).
  note: Electronic resource.
  note: Includes bibliographical references (pages [175]-183) and indexes.
  subject:
    topic: Convergence
  subject:
    topic: Markov processes
  subject:
    topic: Monte Carlo method
  subject:
    topic: Convergence
  subject:
    topic: Markov processes
  subject:
    topic: Monte Carlo method
  classification: QA276-280
  classification: 519.2
  related item:
    title info:
      title: Discretization and MCMC convergence assessment
    origin info:
      publisher: New York : Springer, ©1998
    identifier: (DLC) 98008676
  related item:
    title info:
      title: Lecture notes in statistics (Springer-Verlag) ; v. 135
  identifier: 9781461217169 (electronic bk.)
  identifier: 1461217164 (electronic bk.)
  identifier: 0387985913
  identifier: 9780387985916
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: VT2
    record creation date: 980609
    record change date: 20260422203208.4
    record identifier: in00003553418
    language of cataloging:
      language term: eng