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The Resource Discretization and MCMC Convergence Assessment, edited by Christian P. Robert, (electronic resource)
Discretization and MCMC Convergence Assessment, edited by Christian P. Robert, (electronic resource)
Resource Information
The item Discretization and MCMC Convergence Assessment, edited by Christian P. Robert, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Discretization and MCMC Convergence Assessment, edited by Christian P. Robert, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 The exponential increase in the use of MCMC methods and the corre sponding applications in domains of even higher complexity have caused a growing concern about the available convergence assessment methods and the realization that some of these methods were not reliable enough for allpurpose analyses. Some researchers have mainly focussed on the con vergence to stationarity and the estimation of rates of convergence, in rela tion with the eigenvalues of the transition kernel. This monograph adopts a different perspective by developing (supposedly) practical devices to assess the mixing behaviour of the chain under study and, more particularly, it proposes methods based on finite (state space) Markov chains which are obtained either through a discretization of the original Markov chain or through a duality principle relating a continuous state space Markov chain to another finite Markov chain, as in missing data or latent variable models. The motivation for the choice of finite state spaces is that, although the resulting control is cruder, in the sense that it can often monitor con vergence for the discretized version alone, it is also much stricter than alternative methods, since the tools available for finite Markov chains are universal and the resulting transition matrix can be estimated more accu rately. Moreover, while some setups impose a fixed finite state space, other allow for possible refinements in the discretization level and for consecutive improvements in the convergence monitoring
 Language

 eng
 eng
 Edition
 1st ed. 1998.
 Extent
 1 online resource (XI, 192 p. 20 illus.)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Contents

 1 Markov Chain Monte Carlo Methods
 1.1 Motivations
 1.2 MetropolisHastings algorithms
 1.3 The Gibbs sampler
 1.4 Perfect sampling
 1.5 Convergence results from a Duality Principle
 2 Convergence Control of MCMC Algorithms
 2.1 Introduction
 2.2 Convergence assessments for single chains
 2.3 Convergence assessments based on parallel chains
 2.4 Coupling techniques
 3 Linking Discrete and Continuous Chains
 3.1 Introduction
 3.2 RaoBlackwellization
 3.3 Riemann sum control variates
 3.4 A mixture example
 4 Valid Discretization via Renewal Theory
 4.1 Introduction
 4.2 Renewal theory and small sets
 4.3 Discretization of a continuous Markov chain
 4.4 Convergence assessment through the divergence criterion
 4.5 Illustration for the benchmark examples
 4.6 Renewal theory for variance estimation
 5 Control by the Central Limit Theorem
 5.1 Introduction
 5.2 CLT and Renewal Theory
 5.3 Two control methods with parallel chains
 5.4 Extension to continuous state chains
 5.5 Illustration for the benchmark examples
 5.6 Testing normality on the latent variables
 6 Convergence Assessment in Latent Variable Models: DNA Applications
 6.1 Introduction
 6.2 Hidden Markov model and associated Gibbs sampler
 6.3 Analysis of thebIL67bacteriophage genome: first convergence diagnostics
 6.4 Coupling from the past for theM1M0model
 6.5 Control by the Central Limit Theorem
 7 Convergence Assessment in Latent Variable Models: Application to the Longitudinal Modelling of a Marker of HIV Progression
 7.1 Introduction
 7.2 Hierarchical Model
 7.3 Analysis of the San Francisco Men’s Health Study
 7.4 Convergence assessment
 8 Estimation of Exponential Mixtures
 8.1 Exponential mixtures
 8.2 Convergence evaluation
 References
 Author Index
 Isbn
 9781461217169
 Label
 Discretization and MCMC Convergence Assessment
 Title
 Discretization and MCMC Convergence Assessment
 Statement of responsibility
 edited by Christian P. Robert
 Language

 eng
 eng
 Summary
 The exponential increase in the use of MCMC methods and the corre sponding applications in domains of even higher complexity have caused a growing concern about the available convergence assessment methods and the realization that some of these methods were not reliable enough for allpurpose analyses. Some researchers have mainly focussed on the con vergence to stationarity and the estimation of rates of convergence, in rela tion with the eigenvalues of the transition kernel. This monograph adopts a different perspective by developing (supposedly) practical devices to assess the mixing behaviour of the chain under study and, more particularly, it proposes methods based on finite (state space) Markov chains which are obtained either through a discretization of the original Markov chain or through a duality principle relating a continuous state space Markov chain to another finite Markov chain, as in missing data or latent variable models. The motivation for the choice of finite state spaces is that, although the resulting control is cruder, in the sense that it can often monitor con vergence for the discretized version alone, it is also much stricter than alternative methods, since the tools available for finite Markov chains are universal and the resulting transition matrix can be estimated more accu rately. Moreover, while some setups impose a fixed finite state space, other allow for possible refinements in the discretization level and for consecutive improvements in the convergence monitoring
 Dewey number
 519.2
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsedt
 2HcEQPnYXTM
 Image bit depth
 0
 Language note
 English
 LC call number
 T5757.97
 Literary form
 non fiction
 Nature of contents
 dictionaries
 http://library.link/vocab/relatedWorkOrContributorName
 Robert, Christian P.
 Series statement
 Lecture Notes in Statistics,
 Series volume
 135
 http://library.link/vocab/subjectName

 Mathematics
 Applications of Mathematics
 Label
 Discretization and MCMC Convergence Assessment, edited by Christian P. Robert, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 Markov Chain Monte Carlo Methods  1.1 Motivations  1.2 MetropolisHastings algorithms  1.3 The Gibbs sampler  1.4 Perfect sampling  1.5 Convergence results from a Duality Principle  2 Convergence Control of MCMC Algorithms  2.1 Introduction  2.2 Convergence assessments for single chains  2.3 Convergence assessments based on parallel chains  2.4 Coupling techniques  3 Linking Discrete and Continuous Chains  3.1 Introduction  3.2 RaoBlackwellization  3.3 Riemann sum control variates  3.4 A mixture example  4 Valid Discretization via Renewal Theory  4.1 Introduction  4.2 Renewal theory and small sets  4.3 Discretization of a continuous Markov chain  4.4 Convergence assessment through the divergence criterion  4.5 Illustration for the benchmark examples  4.6 Renewal theory for variance estimation  5 Control by the Central Limit Theorem  5.1 Introduction  5.2 CLT and Renewal Theory  5.3 Two control methods with parallel chains  5.4 Extension to continuous state chains  5.5 Illustration for the benchmark examples  5.6 Testing normality on the latent variables  6 Convergence Assessment in Latent Variable Models: DNA Applications  6.1 Introduction  6.2 Hidden Markov model and associated Gibbs sampler  6.3 Analysis of thebIL67bacteriophage genome: first convergence diagnostics  6.4 Coupling from the past for theM1M0model  6.5 Control by the Central Limit Theorem  7 Convergence Assessment in Latent Variable Models: Application to the Longitudinal Modelling of a Marker of HIV Progression  7.1 Introduction  7.2 Hierarchical Model  7.3 Analysis of the San Francisco Men’s Health Study  7.4 Convergence assessment  8 Estimation of Exponential Mixtures  8.1 Exponential mixtures  8.2 Convergence evaluation  References  Author Index
 Dimensions
 unknown
 Edition
 1st ed. 1998.
 Extent
 1 online resource (XI, 192 p. 20 illus.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461217169
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461217169
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089670
 (SSID)ssj0000805874
 (PQKBManifestationID)11530556
 (PQKBTitleCode)TC0000805874
 (PQKBWorkID)10747220
 (PQKB)10273826
 (DEHe213)9781461217169
 (MiAaPQ)EBC3076613
 (EXLCZ)993400000000089670
 Label
 Discretization and MCMC Convergence Assessment, edited by Christian P. Robert, (electronic resource)
 Note
 Bibliographic Level Mode of Issuance: Monograph
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Contents
 1 Markov Chain Monte Carlo Methods  1.1 Motivations  1.2 MetropolisHastings algorithms  1.3 The Gibbs sampler  1.4 Perfect sampling  1.5 Convergence results from a Duality Principle  2 Convergence Control of MCMC Algorithms  2.1 Introduction  2.2 Convergence assessments for single chains  2.3 Convergence assessments based on parallel chains  2.4 Coupling techniques  3 Linking Discrete and Continuous Chains  3.1 Introduction  3.2 RaoBlackwellization  3.3 Riemann sum control variates  3.4 A mixture example  4 Valid Discretization via Renewal Theory  4.1 Introduction  4.2 Renewal theory and small sets  4.3 Discretization of a continuous Markov chain  4.4 Convergence assessment through the divergence criterion  4.5 Illustration for the benchmark examples  4.6 Renewal theory for variance estimation  5 Control by the Central Limit Theorem  5.1 Introduction  5.2 CLT and Renewal Theory  5.3 Two control methods with parallel chains  5.4 Extension to continuous state chains  5.5 Illustration for the benchmark examples  5.6 Testing normality on the latent variables  6 Convergence Assessment in Latent Variable Models: DNA Applications  6.1 Introduction  6.2 Hidden Markov model and associated Gibbs sampler  6.3 Analysis of thebIL67bacteriophage genome: first convergence diagnostics  6.4 Coupling from the past for theM1M0model  6.5 Control by the Central Limit Theorem  7 Convergence Assessment in Latent Variable Models: Application to the Longitudinal Modelling of a Marker of HIV Progression  7.1 Introduction  7.2 Hierarchical Model  7.3 Analysis of the San Francisco Men’s Health Study  7.4 Convergence assessment  8 Estimation of Exponential Mixtures  8.1 Exponential mixtures  8.2 Convergence evaluation  References  Author Index
 Dimensions
 unknown
 Edition
 1st ed. 1998.
 Extent
 1 online resource (XI, 192 p. 20 illus.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9781461217169
 Level of compression
 uncompressed
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461217169
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (CKB)3400000000089670
 (SSID)ssj0000805874
 (PQKBManifestationID)11530556
 (PQKBTitleCode)TC0000805874
 (PQKBWorkID)10747220
 (PQKB)10273826
 (DEHe213)9781461217169
 (MiAaPQ)EBC3076613
 (EXLCZ)993400000000089670
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