Introducing Monte Carlo methods with R:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Springer
2010
|
| Series: | Use R!
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIX, 283 S. graph. Darst. |
| ISBN: | 9781441915757 |
Staff View
MARC
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| 100 | 1 | |a Robert, Christian P. |d 1961- |e Verfasser |0 (DE-588)115436448 |4 aut | |
| 245 | 1 | 0 | |a Introducing Monte Carlo methods with R |c Christian P. Robert ; George Casella |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2010 | |
| 300 | |a XIX, 283 S. |b graph. Darst. | ||
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Record in the Search Index
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| _version_ | 1824553891438526464 |
| adam_text | Contents
Preface
........................................................
vii
List of Figures
................................................. xiii
List of Examples
...............................................xvii
1
Basic
R
Programming
..................................... 1
1.1
Introduction
............................................ 2
1.2
Getting started
.......................................... 3
1.3
R
objects
............................................... 5
1.3.1
The vector class
................................... 6
1.3.2
The matrix, array, and factor classes
.................. 9
1.3.3
The list and data.frame classes
...................... 12
1.4
Probability distributions in
R
............................. 14
1.5
Basic and not-so-basic statistics
........................... 14
1.6
Graphical facilities
....................................... 26
1.7
Writing new
R
functions
.................................. 31
1.8
Input and output in
R
.................................... 35
1.9
Administration of
R
objects
............................... 36
1.10
The mcsm package
....................................... 36
1.11
Additional exercises
...................................... 37
2
Random Variable Generation
.............................. 41
2.1
Introduction
............................................ 42
2.1.1
Uniform simulation
................................ 42
2.1.2
The inverse transform
.............................. 44
2.2
General transformation methods
........................... 46
2.2.1
A normal generator
................................ 47
2.2.2
Discrete distributions
.............................. 48
2.2.3
Mixture representations
............................ 50
2.3
Accept-reject methods
................................... 51
x
Contents
2.4
Additional exercises
...................................... 57
3
Monte Carlo Integration
................................... 61
3.1
Introduction
............................................ 62
3.2
Classical Monte Carlo integration
.......................... 65
3.3
Importance sampling
..................................... 69
3.3.1
An arbitrary change of reference measure
............. 69
3.3.2
Sampling importance resampling
.................... 75
3.3.3
Selection of the importance function
................. 78
3.4
Additional exercises
......................................
S6
4
Controlling and Accelerating Convergence
................. 89
4.1
Introduction
............................................ 90
4.2
Monitoring variation
..................................... 91
4.3
Asymptotic variance of importance sampling estimators
...... 92
4.4
Effective sample size and perplexity
........................ 98
4.5
Simultaneous monitoring
.................................100
4.6
Rao-Blackwellization and deconditioning
...................107
4.7
Acceleration methods
....................................
Ш
4.7.1
Correlated simulations
.............................
Ill
4.7.2
Antithetic variables
................................113
4.7.3
Control
variâtes
...................................116
4.8
Additional exercises
......................................122
5
Monte Carlo Optimization
.................................125
5.1
Introduction
............................................126
5.2
Numerical optimization methods
..........................127
5.3
Stochastic search
........................................130
5.3.1
A basic solution
...................................130
5.3.2
Stochastic gradient methods
........................136
5.3.3
Simulated annealing
...............................140
5.4
Stochastic approximation
.................................146
5.4.1
Optimizing Monte Carlo approximations
.............146
5.4.2
Missing-data models and deniarginalizatiou
...........150
5.4.3
The EM algorithm
................................152
5.4.4
Monte Carlo EM
..................................157
5.5
Additional exercises
......................................163
6
Metropolis—Hastings Algorithms
...........................167
6.1
Introduction
............................................168
6.2
A peek at Markov chain theory
............................168
6.3
Basic Metropolis-Hastings algorithms
......................170
6.3.1
A generic Markov chain Monte Carlo algorithm
.......171
6.3.2
The independent Metropolis-Hastings algorithm
......175
6.4
A selection of candidates
.................................182
Contents xi
0.4.1
Random walks
....................................182
6.4.2
Alternative candidates
.............................185
6.5
Acceptance rates
........................................192
6.6
Additional exercises
......................................195
7
Gibbs Samplers
............................................199
7.1
Introduction
............................................200
7.2
The two-stage Gibbs sampler
.............................200
7.3
The multistage Gibbs sampler
.............................206
7.4
Missing data and latent variables
..........................209
7.5
Hierarchical structures
...................................221
7.6
Other considerations
.....................................224
7.6.1
Reparameterization
................................224
7.6.2
Rao-Blackwellization
..............................227
7.6.3
Metropolis within Gibbs and hybrid strategies
........230
7.6.4
Improper priors
...................................232
7.7
Additional exercises
......................................234
8
Monitoring and Adaptation for MCMC Algorithms
........237
8.1
Introduction
............................................238
8.2
Monitoring what and why
................................238
8.2.1
Convergence to the stationary distribution
............238
8.2.2
Convergence of averages
............................240
8.2.3
Approximating iid
sampling
........................240
8.2.4
The coda package
.................................241
8.3
Monitoring convergence to stationarity
.....................242
8.3.1
Graphical diagnoses
...............................242
8.3.2
Nonparametric tests of stationarity
..................243
8.3.3
Spectral analysis
..................................247
8.4
Monitoring convergence of averages
........................250
8.4.1
Graphical diagnoses
...............................250
8.4.2
Within and between variances
......................253
8.4.3
Effective sample size
...............................255
8.4.4
Fixed-width batch means
...........................257
8.5
Adaptive MCMC
........................................258
8.5.1
Cautions about adaptation
.........................258
8.5.2
The amcmc package
................................264
8.6
Additional exercises
......................................267
References
.....................................................269
Index of
R
Terms
..............................................275
Index of Subjects
..............................................279
|
| any_adam_object | 1 |
| author | Robert, Christian P. 1961- Casella, George 1951-2012 |
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| classification_tum | MAT 629f DAT 307f |
| ctrlnum | (OCoLC)462920377 (DE-599)DNB997866349 |
| dewey-full | 518.282 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
| dewey-raw | 518.282 |
| dewey-search | 518.282 |
| dewey-sort | 3518.282 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Soziologie Mathematik Wirtschaftswissenschaften |
| format | Book |
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| isbn | 9781441915757 |
| language | English |
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| physical | XIX, 283 S. graph. Darst. |
| publishDate | 2010 |
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| publisher | Springer |
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| series2 | Use R! |
| spellingShingle | Robert, Christian P. 1961- Casella, George 1951-2012 Introducing Monte Carlo methods with R R Programm (DE-588)4705956-4 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| subject_GND | (DE-588)4705956-4 (DE-588)4240945-7 |
| title | Introducing Monte Carlo methods with R |
| title_auth | Introducing Monte Carlo methods with R |
| title_exact_search | Introducing Monte Carlo methods with R |
| title_full | Introducing Monte Carlo methods with R Christian P. Robert ; George Casella |
| title_fullStr | Introducing Monte Carlo methods with R Christian P. Robert ; George Casella |
| title_full_unstemmed | Introducing Monte Carlo methods with R Christian P. Robert ; George Casella |
| title_short | Introducing Monte Carlo methods with R |
| title_sort | introducing monte carlo methods with r |
| topic | R Programm (DE-588)4705956-4 gnd Monte-Carlo-Simulation (DE-588)4240945-7 gnd |
| topic_facet | R Programm Monte-Carlo-Simulation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018695020&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 SK 820 R639 |
|---|---|
| Copy 1 | ausleihbar Available Place a Hold |