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Discretization and MCMC Convergence Assessment

  • Christian P. Robert

Part of the Lecture Notes in Statistics book series (LNS, volume 135)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Christian P. Robert, Sylvia Richardson
    Pages 1-25
  3. Christian P. Robert, Dominique Cellier
    Pages 27-46
  4. Anne Philippe, Christian P. Robert
    Pages 47-66
  5. Chantal Guihenneuc-Jouyaux, Christian P. Robert
    Pages 67-97
  6. Didier Chauveau, Jean Diebolt, Christian P. Robert
    Pages 99-126
  7. Florence Muri, Didier Chauveau, Dominique Cellier
    Pages 127-146
  8. Marie-Anne Gruet, Anne Philippe, Christian P. Robert
    Pages 161-173
  9. Back Matter
    Pages 175-194

About this book

Introduction

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 all-purpose 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.

Keywords

Latent variable model Markov chain Markov model Variance algorithms renewal theory statistics

Editors and affiliations

  • Christian P. Robert
    • 1
  1. 1.INSEE CrestMalakoff CedexFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4612-1716-9
  • Copyright Information Springer-Verlag New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-98591-6
  • Online ISBN 978-1-4612-1716-9
  • Series Print ISSN 0930-0325
  • Buy this book on publisher's site
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