Markov chain Monte Carlo: stochastic simulation for Bayesian inference
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2006
|
| Edition: | 2. ed. |
| Series: | Texts in statistical science series
68 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 323 S. Illustrationen, Diagramme |
| ISBN: | 1584885874 9781584885870 |
Staff View
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Record in the Search Index
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| adam_text | Contents
Preface
to the second edition
xiii
Preface to the first edition
xv
Introduction
1
1
Stochastic simulation
9
1.1
Introduction
9
1.2
Generation of discrete random quantities
10
1.2.1
Bernoulli distribution
11
1.2.2
Binomial distribution
11
1.2.3
Geometric and negative binomial distribution
12
1.2.4
Poisson
distribution
12
1.3
Generation of continuous random quantities
13
1.3.1
Probability integral transform
13
1.3.2
Divariate
techniques
14
1.3.3
Methods based on mixtures
17
1.4
Generation of random vectors and matrices
20
1.4.1
Multivariate normal distribution
21
1.4.2
Wishart
distribution
23
1.4.3
Multivariate Student s
ŕ
distribution
24
1.5
Resampling methods
25
1.5.1
Rejection method
25
1.5.2
Weighted resampling method
30
1.5.3
Adaptive rejection method
32
1.6
Exercises
34
2
Bayesian inference
41
2.1
Introduction
41
2.2
Bayes
theorem
41
2.2.1
Prior, posterior and predictive distributions
42
2.2.2
Summarizing the information
47
2.3
Conjugate distributions
49
2.3.1
Conjugate distributions for the exponential family
51
2.3.2
Conjugacy
and regression models
55
2.3.3
Conditional conjugacy
58
2.4
Hierarchical models
60
2.5
Dynamic models
63
2.5.1
Sequential inference
64
2.5.2
Smoothing
65
2.5.3
Extensions
67
2.6
Spatial models
68
2.7
Model comparison
72
2.8
Exercises
74
3
Approximate methods of inference
81
3.1
Introduction
81
3.2
Asymptotic approximations
82
3.2.1
Normal approximations
83
3.2.2
Mode calculation
86
3.2.3
Standard Laplace approximation
88
3.2.4
Exponential form Laplace approximations
90
3.3
Approximations by Gaussian quadrature
93
3.4
Monte Carlo integration
95
3.5
Methods based on stochastic simulation
98
3.5.1
Bayes
theorem via the rejection method
100
3.5.2
Bayes
theorem via weighted resampling
101
3.5.3
Application to dynamic models
104
3.6
Exercises
106
4
Markov chains
113
4.1
Introduction
113
4.2
Definition and transition probabilities
114
4.3
Decomposition of the state space
118
4.4
Stationary distributions
121
4.5
Limiting theorems
124
4.6
Reversible chains
127
4.7
Continuous state spaces
129
4.7.1
Transition kernels
129
4.7.2
Stationarity and limiting results
131
4.8
Simulation of a Markov chain
132
4.9
Data augmentation or substitution sampling
135
4.10
Exercises
136
5
Gibbs sampling
5.1
Introduction
5.2
Definition and properties
5.3
Implementation and optimization
5.3.1
Forming the sample
148
5.3.2
Scanning strategies
150
5.3.3
Using the sample
151
5.3.4
Reparametrization
152
5.3.5
Blocking
155
5.3.6
Sampling from the full conditional distributions
156
5.4
Convergence diagnostics
157
5.4.1
Rate of convergence
158
5.4.2
Informal convergence monitors
159
5.4.3
Convergence prescription
161
5.4.4
Formal convergence methods
164
5.5
Applications
169
5.5.1
Hierarchical models
169
5.5.2
Dynamic models
172
5.5.3
Spatial models
176
5.6
MCMC-based software for Bayesian modeling
178
Appendix
5.
A: BUGS code for Example
5.7 182
Appendix 5.B: BUGS code for Example
5.8 184
5.7
Exercises
184
Metropolis-Hastings algorithms
191
6.1
Introduction
191
6.2
Definition and properties
193
6.3
Special cases
198
6.3.1
Symmetric chains
198
6.3.2
Random walk chains
198
6.3.3
Independence chains
199
6.3.4
Other forms
204
6.4
Hybrid algorithms
205
6.4.1
Componentwise transition
206
6.4.2
Metropolis within Gibbs
211
6.4.3
Blocking
214
6.4.4
Reparametrization
216
6.5
Applications
217
6.5.1
Generalized linear mixed models
217
6.5.2
Dynamic linear models
223
6.5.3
Dynamic generalized linear models
226
6.5.4
Spatial models
231
6.6
Exercises
234
Further topics in MCMC
237
7.1
Introduction
237
7.2
Model adequacy
237
7.2.1
Estimates of the predictive likelihood
238
7.2.2
Uses of the predictive likelihood
248
7.2.3
Deviance information criterion
253
7.3
Model choice: MCMC over model and parameter spaces
257
7.3.1
Markov chain for supermodels
258
7.3.2
Markov chain with jumps
261
7.3.3
Further issues related to RJMCMC algorithms
270
7.4
Convergence acceleration
271
7.4.1
Alterations to the chain
271
7.4.2
Alterations to the equilibrium distribution
278
7.4.3
Auxiliary variables
282
7.5
Exercises
284
References
289
Author index
311
Subject index
316
|
| adam_txt |
Contents
Preface
to the second edition
xiii
Preface to the first edition
xv
Introduction
1
1
Stochastic simulation
9
1.1
Introduction
9
1.2
Generation of discrete random quantities
10
1.2.1
Bernoulli distribution
11
1.2.2
Binomial distribution
11
1.2.3
Geometric and negative binomial distribution
12
1.2.4
Poisson
distribution
12
1.3
Generation of continuous random quantities
13
1.3.1
Probability integral transform
13
1.3.2
Divariate
techniques
14
1.3.3
Methods based on mixtures
17
1.4
Generation of random vectors and matrices
20
1.4.1
Multivariate normal distribution
21
1.4.2
Wishart
distribution
23
1.4.3
Multivariate Student's
ŕ
distribution
24
1.5
Resampling methods
25
1.5.1
Rejection method
25
1.5.2
Weighted resampling method
30
1.5.3
Adaptive rejection method
32
1.6
Exercises
34
2
Bayesian inference
41
2.1
Introduction
41
2.2
Bayes'
theorem
41
2.2.1
Prior, posterior and predictive distributions
42
2.2.2
Summarizing the information
47
2.3
Conjugate distributions
49
2.3.1
Conjugate distributions for the exponential family
51
2.3.2
Conjugacy
and regression models
55
2.3.3
Conditional conjugacy
58
2.4
Hierarchical models
60
2.5
Dynamic models
63
2.5.1
Sequential inference
64
2.5.2
Smoothing
65
2.5.3
Extensions
67
2.6
Spatial models
68
2.7
Model comparison
72
2.8
Exercises
74
3
Approximate methods of inference
81
3.1
Introduction
81
3.2
Asymptotic approximations
82
3.2.1
Normal approximations
83
3.2.2
Mode calculation
86
3.2.3
Standard Laplace approximation
88
3.2.4
Exponential form Laplace approximations
90
3.3
Approximations by Gaussian quadrature
93
3.4
Monte Carlo integration
95
3.5
Methods based on stochastic simulation
98
3.5.1
Bayes'
theorem via the rejection method
100
3.5.2
Bayes'
theorem via weighted resampling
101
3.5.3
Application to dynamic models
104
3.6
Exercises
106
4
Markov chains
113
4.1
Introduction
113
4.2
Definition and transition probabilities
114
4.3
Decomposition of the state space
118
4.4
Stationary distributions
121
4.5
Limiting theorems
124
4.6
Reversible chains
127
4.7
Continuous state spaces
129
4.7.1
Transition kernels
129
4.7.2
Stationarity and limiting results
131
4.8
Simulation of a Markov chain
132
4.9
Data augmentation or substitution sampling
135
4.10
Exercises
136
5
Gibbs sampling
5.1
Introduction
5.2
Definition and properties
5.3
Implementation and optimization
5.3.1
Forming the sample
148
5.3.2
Scanning strategies
150
5.3.3
Using the sample
151
5.3.4
Reparametrization
152
5.3.5
Blocking
155
5.3.6
Sampling from the full conditional distributions
156
5.4
Convergence diagnostics
157
5.4.1
Rate of convergence
158
5.4.2
Informal convergence monitors
159
5.4.3
Convergence prescription
161
5.4.4
Formal convergence methods
164
5.5
Applications
169
5.5.1
Hierarchical models
169
5.5.2
Dynamic models
172
5.5.3
Spatial models
176
5.6
MCMC-based software for Bayesian modeling
178
Appendix
5.
A: BUGS code for Example
5.7 182
Appendix 5.B: BUGS code for Example
5.8 184
5.7
Exercises
184
Metropolis-Hastings algorithms
191
6.1
Introduction
191
6.2
Definition and properties
193
6.3
Special cases
198
6.3.1
Symmetric chains
198
6.3.2
Random walk chains
198
6.3.3
Independence chains
199
6.3.4
Other forms
204
6.4
Hybrid algorithms
205
6.4.1
Componentwise transition
206
6.4.2
Metropolis within Gibbs
211
6.4.3
Blocking
214
6.4.4
Reparametrization
216
6.5
Applications
217
6.5.1
Generalized linear mixed models
217
6.5.2
Dynamic linear models
223
6.5.3
Dynamic generalized linear models
226
6.5.4
Spatial models
231
6.6
Exercises
234
Further topics in MCMC
237
7.1
Introduction
237
7.2
Model adequacy
237
7.2.1
Estimates of the predictive likelihood
238
7.2.2
Uses of the predictive likelihood
248
7.2.3
Deviance information criterion
253
7.3
Model choice: MCMC over model and parameter spaces
257
7.3.1
Markov chain for supermodels
258
7.3.2
Markov chain with jumps
261
7.3.3
Further issues related to RJMCMC algorithms
270
7.4
Convergence acceleration
271
7.4.1
Alterations to the chain
271
7.4.2
Alterations to the equilibrium distribution
278
7.4.3
Auxiliary variables
282
7.5
Exercises
284
References
289
Author index
311
Subject index
316 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Gamerman, Dani Lopes, Hedibert Freitas |
| author_GND | (DE-588)171261372 (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 | BV021690412 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 239 SK 820 |
| classification_tum | MAT 629f MAT 607f MAT 624f |
| ctrlnum | (OCoLC)266086459 (DE-599)BVBBV021690412 |
| dewey-full | 519.282 519.5/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.282 519.5/42 |
| dewey-search | 519.282 519.5/42 |
| dewey-sort | 3519.282 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV021690412 |
| illustrated | Illustrated |
| index_date | 2024-07-02T15:14:11Z |
| indexdate | 2024-07-09T20:41:45Z |
| institution | BVB |
| isbn | 1584885874 9781584885870 |
| language | English |
| lccn | 2006044491 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014904491 |
| oclc_num | 266086459 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-20 DE-473 DE-BY-UBG DE-739 DE-634 DE-355 DE-BY-UBR |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-703 DE-20 DE-473 DE-BY-UBG DE-739 DE-634 DE-355 DE-BY-UBR |
| physical | XVII, 323 S. Illustrationen, Diagramme |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Texts in statistical science series |
| series2 | Texts in statistical science series |
| spelling | Gamerman, Dani Verfasser (DE-588)171261372 aut Markov chain Monte Carlo stochastic simulation for Bayesian inference Dani Gamerman ; Hedibert Freitas Lopes 2. ed. Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2006 XVII, 323 S. Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Texts in statistical science series 68 Bayesian statistical decision theory Markov processes Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd rswk-swf Markov-Kette (DE-588)4037612-6 gnd rswk-swf Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Bayes-Inferenz (DE-588)4648118-7 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 s Markov-Kette (DE-588)4037612-6 s 1\p DE-604 Bayes-Inferenz (DE-588)4648118-7 s Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 s 2\p DE-604 Monte-Carlo-Simulation (DE-588)4240945-7 s 3\p DE-604 Bayes-Entscheidungstheorie (DE-588)4144220-9 s 4\p DE-604 Lopes, Hedibert Freitas Verfasser (DE-588)17123779X aut Texts in statistical science series 68 (DE-604)BV022819715 68 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014904491&sequence=000002&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 4\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 Texts in statistical science series Bayesian statistical decision theory Markov processes Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Markov-Kette (DE-588)4037612-6 gnd Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Bayes-Inferenz (DE-588)4648118-7 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| subject_GND | (DE-588)4240945-7 (DE-588)4037612-6 (DE-588)4508520-1 (DE-588)4077850-2 (DE-588)4648118-7 (DE-588)4144220-9 |
| 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_exact_search_txtP | 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 | Bayesian statistical decision theory Markov processes Monte Carlo method Monte-Carlo-Simulation (DE-588)4240945-7 gnd Markov-Kette (DE-588)4037612-6 gnd Markov-Ketten-Monte-Carlo-Verfahren (DE-588)4508520-1 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Bayes-Inferenz (DE-588)4648118-7 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd |
| topic_facet | Bayesian statistical decision theory Markov processes Monte Carlo method Monte-Carlo-Simulation Markov-Kette Markov-Ketten-Monte-Carlo-Verfahren Statistische Entscheidungstheorie Bayes-Inferenz Bayes-Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014904491&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022819715 |
| work_keys_str_mv | AT gamermandani markovchainmontecarlostochasticsimulationforbayesianinference AT lopeshedibertfreitas markovchainmontecarlostochasticsimulationforbayesianinference |