Discretization and MCMC Convergence Assessment:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1998
|
| Schriftenreihe: | Lecture Notes in Statistics
135 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The exponential increase in the use of MCMC methods and the corresponding 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 convergence to stationarity and the estimation of rates of convergence, in relation 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 convergence 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 accurately. 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 |
| Beschreibung: | 1 Online-Ressource (XI, 192p) |
| ISBN: | 9781461217169 9780387985916 |
| ISSN: | 0930-0325 |
| DOI: | 10.1007/978-1-4612-1716-9 |
Internformat
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| 490 | 1 | |a Lecture Notes in Statistics |v 135 |x 0930-0325 | |
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Datensatz im Suchindex
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| author | Robert, Christian P. 1961- |
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| bvnumber | BV042419897 |
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| dewey-full | 519.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5 |
| dewey-search | 519.5 |
| dewey-sort | 3519.5 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1716-9 |
| format | Electronic eBook |
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| id | DE-604.BV042419897 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461217169 9780387985916 |
| issn | 0930-0325 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855314 |
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| physical | 1 Online-Ressource (XI, 192p) |
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| publishDate | 1998 |
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| publisher | Springer New York |
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| series | Lecture Notes in Statistics |
| series2 | Lecture Notes in Statistics |
| spelling | Robert, Christian P. 1961- Verfasser (DE-588)115436448 aut Discretization and MCMC Convergence Assessment edited by Christian P. Robert New York, NY Springer New York 1998 1 Online-Ressource (XI, 192p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Statistics 135 0930-0325 The exponential increase in the use of MCMC methods and the corresponding 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 convergence to stationarity and the estimation of rates of convergence, in relation 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 convergence 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 accurately. 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 Statistics Statistics, general Statistik Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd rswk-swf Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 s 1\p DE-604 Lecture Notes in Statistics 135 (DE-604)BV036592911 135 https://doi.org/10.1007/978-1-4612-1716-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Robert, Christian P. 1961- Discretization and MCMC Convergence Assessment Lecture Notes in Statistics Statistics Statistics, general Statistik Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd |
| subject_GND | (DE-588)4508520-1 |
| title | Discretization and MCMC Convergence Assessment |
| title_auth | Discretization and MCMC Convergence Assessment |
| title_exact_search | Discretization and MCMC Convergence Assessment |
| title_full | Discretization and MCMC Convergence Assessment edited by Christian P. Robert |
| title_fullStr | Discretization and MCMC Convergence Assessment edited by Christian P. Robert |
| title_full_unstemmed | Discretization and MCMC Convergence Assessment edited by Christian P. Robert |
| title_short | Discretization and MCMC Convergence Assessment |
| title_sort | discretization and mcmc convergence assessment |
| topic | Statistics Statistics, general Statistik Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd |
| topic_facet | Statistics Statistics, general Statistik Markov-Ketten-Monte-Carlo-Verfahren |
| url | https://doi.org/10.1007/978-1-4612-1716-9 |
| volume_link | (DE-604)BV036592911 |
| work_keys_str_mv | AT robertchristianp discretizationandmcmcconvergenceassessment |