Markov chain Monte Carlo: stochastic simulation for Bayesian inference
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton, Fla. [u.a.]
Chapman & Hall
2006
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Texts in statistical science
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz.: S. 289 - 310 |
| Beschreibung: | XVII, 323 S. graph. Darst. |
| ISBN: | 1584885874 9781584885870 |
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Datensatz im Suchindex
| _version_ | 1804145147122810880 |
|---|---|
| adam_text | Titel: Markov chain Monte Carlo
Autor: Gamerman, Dani
Jahr: 2006
Preface to the second edition p. xiii
Preface to the first edition p. xv
Introduction p. 1
Stochastic simulation p. 9
Introduction p. 9
Generation of discrete random quantities p. 10
Bernoulli distribution p. 11
Binomial distribution p. 11
Geometric and negative binomial distribution p. 12
Poisson distribution p. 12
Generation of continuous random quantities p. 13
Probability integral transform p. 13
Bivariate techniques p. 14
Methods based on mixtures p. 17
Generation of random vectors and matrices p. 20
Multivariate normal distribution p. 21
Wishart distribution p. 23
Multivariate Student s t distribution p. 24
Resampling methods p. 25
Rejection method p. 25
Weighted resampling method p. 30
Adaptive rejection method p. 32
Exercises p. 34
Bayesian inference p. 41
Introduction p. 41
Bayes theorem p. 41
Prior, posterior and predictive distributions p. 42
Summarizing the information p. 47
Conjugate distributions p. 49
Conjugate distributions for the exponential family p. 51
Conjugacy and regression models p. 55
Conditional conjugacy p. 58
Hierarchical models p. 60
Dynamic models p. 63
Sequential inference p. 64
Smoothing p. 65
Extensions p. 67
Spatial models p. 68
Model comparison p. 72
Exercises p. 74
Approximate methods of inference p. 81
Introduction p. 81
Asymptotic approximations p. 82
Normal approximations p. 83
Mode calculation p. 86
Standard Laplace approximation p. 88
Exponential form Laplace approximations p. 90
Approximations by Gaussian quadrature p. 93
Monte Carlo integration p. 95
Methods based on stochastic simulation p. 98
Bayes theorem via the rejection method p. 100
Bayes theorem via weighted resampling p. 101
Application to dynamic models p. 104
Exercises p. 106
Markov chains p. 113
Introduction p. 113
Definition and transition probabilities p. 114
Decomposition of the state space p. 118
Stationary distributions p. 121
Limiting theorems p. 124
Reversible chains p. 127
Continuous state spaces p. 129
Transition kernels p. 129
Stationarity and limiting results p. 131
Simulation of a Markov chain p. 132
Data augmentation or substitution sampling p. 135
Exercises p. 136
Gibbs sampling p. 141
Introduction p. 141
Definition and properties p. 142
Implementation and optimization p. 148
Forming the sample p. 148
Scanning strategies p. 150
Using the sample p. 151
Reparametrization p. 152
Blocking p. 155
Sampling from the full conditional distributions p. 156
Convergence diagnostics p. 157
Rate of convergence p. 158
Informal convergence monitors p. 159
Convergence prescription p. 161
Formal convergence methods p. 164
Applications p. 169
Hierarchical models p. 169
Dynamic models p. 172
Spatial models p. 176
MCMC-based software for Bayesian modeling p. 178
BUGS code for Example 5.7 p. 182
BUGS code for Example 5.8 p. 184
Exercises p. 184
Metropolis-Hastings algorithms p. 191
Introduction p. 191
Definition and properties p. 193
Special cases p. 198
Symmetric chains p. 198
Random walk chains p. 198
Independence chains p. 199
Other forms p. 204
Hybrid algorithms p. 205
Componentwise transition p. 206
Metropolis within Gibbs p. 211
Blocking p. 214
Reparametrization p. 216
Applications p. 217
Generalized linear mixed models p. 217
Dynamic linear models p. 223
Dynamic generalized linear models p. 226
Spatial models p. 231
Exercises p. 234
Further topics in MCMC p. 237
Introduction p. 237
Model adequacy p. 237
Estimates of the predictive likelihood p. 238
Uses of the predictive likelihood p. 248
Deviance information criterion p. 253
Model choice: MCMC over model and parameter spaces p. 257
Markov chain for supermodels p. 258
Markov chain with jumps p. 261
Further issues related to RJMCMC algorithms p. 270
Convergence acceleration p. 271
Alterations to the chain p. 271
Alterations to the equilibrium distribution p. 278
Auxiliary variables p. 282
Exercises p. 284
References p. 289
Author index p. 311
Subject index p. 316
Table of Contents provided by Blackwell s Book Services and R.R. Bowker. Used with permission.
|
| any_adam_object | 1 |
| author | Gamerman, Dani Lopes, Hedibert Freitas |
| author_GND | (DE-588)17123779X |
| author_facet | Gamerman, Dani Lopes, Hedibert Freitas |
| author_role | aut aut |
| author_sort | Gamerman, Dani |
| author_variant | d g dg h f l hf hfl |
| building | Verbundindex |
| bvnumber | BV026556061 |
| classification_rvk | QH 239 SK 820 SK 830 |
| ctrlnum | (OCoLC)266086459 (DE-599)BVBBV026556061 |
| dewey-full | 519.542 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.542 |
| dewey-search | 519.542 |
| dewey-sort | 3519.542 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV026556061 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:14:49Z |
| institution | BVB |
| isbn | 1584885874 9781584885870 |
| language | English |
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| spelling | Gamerman, Dani Verfasser aut Markov chain Monte Carlo stochastic simulation for Bayesian inference Dani Gamerman ; Hedibert Freitas Lopes 2. ed. Boca Raton, Fla. [u.a.] Chapman & Hall 2006 XVII, 323 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science Literaturverz.: S. 289 - 310 Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Bayes-Inferenz (DE-588)4648118-7 gnd rswk-swf Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd rswk-swf Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Bayes-Inferenz (DE-588)4648118-7 s Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 s DE-188 Statistische Entscheidungstheorie (DE-588)4077850-2 s Markov-Kette (DE-588)4037612-6 s 1\p DE-604 Monte-Carlo-Simulation (DE-588)4240945-7 s 2\p DE-604 Bayes-Entscheidungstheorie (DE-588)4144220-9 s 3\p DE-604 Lopes, Hedibert Freitas Verfasser (DE-588)17123779X aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022118390&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Gamerman, Dani Lopes, Hedibert Freitas Markov chain Monte Carlo stochastic simulation for Bayesian inference Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Bayes-Inferenz (DE-588)4648118-7 gnd Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Markov-Kette (DE-588)4037612-6 gnd |
| subject_GND | (DE-588)4144220-9 (DE-588)4077850-2 (DE-588)4648118-7 (DE-588)4508520-1 (DE-588)4240945-7 (DE-588)4037612-6 |
| title | Markov chain Monte Carlo stochastic simulation for Bayesian inference |
| title_auth | Markov chain Monte Carlo stochastic simulation for Bayesian inference |
| title_exact_search | Markov chain Monte Carlo stochastic simulation for Bayesian inference |
| title_full | Markov chain Monte Carlo stochastic simulation for Bayesian inference Dani Gamerman ; Hedibert Freitas Lopes |
| title_fullStr | Markov chain Monte Carlo stochastic simulation for Bayesian inference Dani Gamerman ; Hedibert Freitas Lopes |
| title_full_unstemmed | Markov chain Monte Carlo stochastic simulation for Bayesian inference Dani Gamerman ; Hedibert Freitas Lopes |
| title_short | Markov chain Monte Carlo |
| title_sort | markov chain monte carlo stochastic simulation for bayesian inference |
| title_sub | stochastic simulation for Bayesian inference |
| topic | Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Bayes-Inferenz (DE-588)4648118-7 gnd Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd Markov-Kette (DE-588)4037612-6 gnd |
| topic_facet | Bayes-Entscheidungstheorie Statistische Entscheidungstheorie Bayes-Inferenz Markov-Ketten-Monte-Carlo-Verfahren Monte-Carlo-Simulation Markov-Kette |
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