Bayesian modeling using WinBUGS:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Hoboken, NJ
Wiley
2009
|
| Series: | Wiley series in computational statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXIII, 492 S. Ill., graph. Darst. |
| ISBN: | 9780470141144 |
Staff View
MARC
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| 020 | |a 9780470141144 |9 978-0-470-14114-4 | ||
| 035 | |a (OCoLC)237048398 | ||
| 035 | |a (DE-599)GBV573648093 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
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| 100 | 1 | |a Ntzoufras, Ioannis |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Bayesian modeling using WinBUGS |c Ioannis Ntzoufras |
| 264 | 1 | |a Hoboken, NJ |b Wiley |c 2009 | |
| 300 | |a XXIII, 492 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in computational statistics | |
| 500 | |a Includes bibliographical references and index | ||
| 630 | 0 | 4 | |a WinBUGS |
| 650 | 0 | |a WinBUGS | |
| 650 | 7 | |a Methode van Bayes |2 gtt | |
| 650 | 7 | |a WinBUGS |2 gtt | |
| 650 | 4 | |a Bayesian statistical decision theory | |
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Record in the Search Index
| _version_ | 1804138711686840320 |
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| adam_text | CONTENTS
Preface
xvii
Acknowledgments
xix
Acronyms
xxi
1
Introduction to Bayesian Inference
1
1.1
Introduction: Bayesian modeling in the
21
st century
1
1.2
Definition of statistical models
3
1.3
Bayes
theorem
3
1.4
Model-based Bayesian inference
4
1.5
Inference using conjugate prior distributions
7
1.5.1
Inference for the
Poisson
rate of count data
7
1.5.2
Inference for the success probability of binomial data
8
1.5.3
Inference for the mean of normal data with known variance
9
1.5.4
Inference for the mean and variance of normal data
11
1.5.5
Inference for normal regression models
12
1.5.6
Other conjugate prior distributions
14
1.5.7
Illustrative examples
14
1.6
Nonconjugate analysis
24
Problems
27
vii
VÍM
CONTENTS
2
Markov Chain Monte Carlo Algorithms in Bayesian Inference
31
2.1
Simulation, Monte Carlo integration, and their implementation in
Bayesian inference
31
2.2
Markov chain Monte Carlo methods
35
2.2.1
The algorithm
36
2.2.2
Terminology and implementation details
37
2.3
Popular MCMC algorithms
42
2.3.1
The Metropolis-Hastings algorithm
42
2.3.2
Componentwise Metropolis-Hastings
45
2.3.3
The Gibbs sampler
71
2.3.4
Metropolis within Gibbs
76
2.3.5
The slice Gibbs sampler
76
2.3.6
A simple example using the slice sampler
77
2.4
Summary and closing remarks
81
Problems
81
3
WinBUGS Software: Introduction, Setup, and Basic Analysis
83
3.1
Introduction and historical background
83
3.2
The WinBUGS environment
84
3.2.1
Downloading and installing WinBUGS
84
3.2.2
A short description of the menus
85
3.3
Preliminaries on using WinBUGS
88
3.3.1
Code structure and type of parameters/nodes
88
3.3.2
Scalar, vector, matrix, and array nodes
89
3.4
Building Bayesian models in WinBUGS
93
3.4.1
Function description
93
3.4.2
Using the for syntax and array, matrix, and vector calculations
97
3.4.3
Use of parentheses, brackets and curly braces in WinBUGS
98
3.4.4
Differences between WinBUGS and R/Splus syntax
98
3.4.5
Model specification in WinBUGS
99
3.4.6
Data and initial value specification
100
3.4.7
An example of a complete model specification
107
3.4.8
Data transformations
108
3.5
Compiling the model and simulating values
108
3.6
Basic output analysis using the sample monitor tool
117
3.7
Summarizing the procedure
120
3.8
Chapter summary and concluding comments
121
Problems
121
4
WinBUGS Software: Illustration, Results, and Further Analysis
125
4.1
A complete example of running MCMC in WinBUGS for a simple model
125
CONTENTS
IX
4.1.1
The model
125
4.1.2
Data and initial values
127
4.1.3
Compiling and running the model
127
4.1.4
MCMC output analysis and results
129
4.2
Further output analysis using the inference menu
132
4.2.1
Comparison of nodes
133
4.2.2
Calculation of correlations
136
4.2.3
Using the summary tool
137
4.2.4
Evaluation and ranking of individuals
138
4.2.5
Calculation of deviance information criterion
140
4.3
Multiple chains
141
4.3.1
Generation of multiple chains
141
4.3.2
Output analysis
142
4.3.3
The Gelman-Rubin convergence diagnostic
143
4.4
Changing the properties of a figure
145
4.4.1
General graphical options
145
4.4.2
Special graphical options
145
4.5
Other tools and menus
148
4.5.1
Thenode info tool
148
4.5.2
Monitoring the acceptance rate of the Metropolis-Hastings
algorithm
148
4.5.3
Saving the current state of the chain
149
4.5.4
Setting the starting seed number
149
4.5.5
Running the model as a script
149
4.6
Summary and concluding remarks
149
Problems
150
5
Introduction to Bayesian Models: Normal Models
151
5.1
General modeling principles
151
5.2
Model specification in normal regression models
152
5.2.1
Specifying the likelihood
153
5.2.2
Specifying a simple independent prior distribution
154
5.2.3
Interpretation of the regression coefficients
154
5.2.4
A regression example using WinBUGS
157
5.3
Using vectors and multivariate priors in normal regression models
161
5.3.1
Defining the model using matrices
161
5.3.2
Prior distributions for normal regression models
162
5.3.3
Multivariate normal priors in WinBUGS
163
5.3.4
Continuation of Example
5.1 164
5.4
Analysis of variance models
167
5.4.1
The one-way ANOVA model
167
5.4.2
Parametrization and parameter interpretation
168
CONTENTS
5.4.3
One-way
ANOVA
model
in WinBUGS 169
5.4.4
A one-way
ANOVA
example using WinBUGS
171
5.4.5
Two-way
ANOVA
models
173
5.4.6
Multifactor analysis of variance
184
Problems
184
Incorporating Categorical Variables in Normal Models and Further
Modeling Issues
189
6.
1 Analysis of variance models using dummy variables
191
6.2
Analysis of covariance models
195
6.2.1
Models using one quantitative variable and one qualitative variable
197
6.2.2
The parallel lines model
197
6.2.3
The separate lines model
201
6.3
A bioassay example
203
6.3.1
Parallel lines analysis
204
6.3.2
Slope ratio analysis: Models with common intercept and different
slope
212
6.3.3
Comparison of the two approaches
217
6.4
Further modeling issues
218
6.4.1
Extending the simple ANCOVA model
218
6.4.2
Using binary indicators to specify models in multiple regression
219
6.4.3
Selection of variables using the deviance information criterion
(DIC)
219
6.5
Closing remarks
226
Problems
226
Introduction to Generalized Linear Models: Binomial and
Poisson
Data
229
7.1
Introduction
229
7.1.1
The exponential family
230
7.1.2
Common distributions as members of the exponential family
231
7.1.3
Link functions
234
7.1.4
Common generalized linear models
236
7.1.5
Interpretation of GLM coefficients
238
7.2
Prior distributions
239
7.3
Posterior inference
241
7.3.1
The posterior distribution of a generalized linear model
241
7.3.2
GLM specification in WinBUGS
242
7.4
Poisson
regression models
242
7.4.1
Interpretation of
Poisson
log-linear parameters
242
7.4.2
A simple
Poisson
regression example
245
CONTENTS
XI
7.4.3
A Poisson
regression model for modeling football data
249
7.5
binomial response models
255
7.5.1
Interpretation of model parameters in binomial response models
257
7.5.2
A simple example
263
7.6
Models for contingency tables
269
Problems
270
8
Models for Positive Continuous Data, Count Data, and Other GLM-
Based Extensions
275
8.1
Models with
nonstandard
distributions
275
8.1.1
Specification of arbitrary likelihood using the zeros-ones trick
276
8.1.2
The inverse Gaussian model
277
8.2
Models for positive continuous response variables
279
8.2.1
The gamma model
279
8.2.2
Other models
280
8.2.3
An example
281
8.3
Additional models for count data
282
8.3.1
The negative binomial model
283
8.3.2
The generalized
Poisson
model
286
8.3.3
Zero inflated models
288
8.3.4
The bivariate
Poisson
model
291
8.3.5
The
Poisson
difference model
293
8.4
Further GLM-based models and extensions
296
8.4.1
Survival analysis models
297
8.4.2
Multinomial models
298
8.4.3
Additional models and further reading
300
Problems
301
9
Bayesian Hierarchical Models
305
9.1
Introduction
305
9.1.1
A simple motivating example
306
9.1.2
Why use a hierarchical model?
307
9.1.3
Other advantages and characteristics
308
9.2
Some simple examples
308
9.2.1
Repeated measures data
308
9.2.2
Introducing random effects in performance parameters
ЗІЗ
9.2.3
Poisson
mixture models for count data
315
9.2.4
The use of hierarchical models in meta-analysis
318
9.3
The generalized linear mixed model formulation
320
9.3.1
A hierarchical normal model: A simple crossover trial
321
9.3.2
Logit GLMM for correlated binary responses
325
XU CONTENTS
9.3.3
Poisson
log-linear GLMMs for correlated count data
333
9.4
Discussion, closing remarks, and further reading
338
Problems
340
10
The Predictive Distribution and Model Checking
341
10.1
Introduction
341
10.1.1
Prediction within Bayesian framework
341
10.1.2
Using posterior predictive densities for model evaluation and
checking
342
10.1.3
Cross-validation predictive densities
344
10.2
Estimating the predictive distribution for future or missing observations
using MCMC
344
10.2.1
A simple example: Estimating missing observations
345
10.2.2
An example of Bayesian prediction using a simple model
347
10.3
Using the predictive distribution for model checking
354
10.3.1
Comparison of actual and predictive frequencies for discrete data
354
10.3.2
Comparison of cumulative frequencies for predictive and actual
values for continuous data
357
10.3.3
Comparison of ordered predictive and actual values for continuous
data
358
10.3.4
Estimation of the posterior predictive
ordinate
359
10.3.5
Checking individual observations using residuals
362
10.3.6
Checking structural assumptions of the model
365
10.3.7
Checking the goodness-of-fit of a model
368
10.4
Using cross-validation predictive densities for model checking, evaluation,
and comparison
375
10.4.1
Estimating the conditional predictive
ordinate
375
10.4.2
Generating values from the leave-one-out cross-validatory
predictive distributions
377
10.5
Illustration of a complete predictive analysis: Normal regression models
378
10.5.1
Checking structural assumptions of the model
378
10.5.2
Detailed checks based on residual analysis
379
10.5.3
Overall goodness-of-fit of the model
380
10.5.4
Implementation using WinBUGS
380
10.5.5
An Illustrative example
383
10.5.6
Summary of the model checking procedure
386
10.6
Discussion
387
Problems
387
11
Bayesian Model and Variable Evaluation
389
CONTENTS XIII
11.1 Prior
predictive distributions as measures of model comparison: Posterior
model odds and
Bayes
factors
389
11.2
Sensitivity of the posterior model probabilities: The Lindley-Bartlett
paradox
391
11.3
Computation of the marginal likelihood
392
11.3.1
Approximations based on the normal distribution
392
11.3.2
Sampling from the prior: A naive Monte Carlo estimator
392
11.3.3
Sampling from the posterior: The harmonic mean estimator
393
11.3.4
Importance sampling estimators
394
11.3.5
Bridge sampling estimators
394
11.3.6
Chib s marginal likelihood estimator
395
11.3.7
Additional details and further reading
397
11.4
Computation of the marginal likelihood using WinBUGS
397
11.4.1
A beta-binomial example
399
11.4.2
A normal regression example with conjugate normal-inverse
gamma prior
403
11.5
Bayesian variable selection using Gibbs-based methods
405
11.5.1
Prior distributions for variable selection in GLM
406
11.5.2
Gibbs variable selection
409
11.5.3
Other Gibbs-based methods for variable selection
410
11.6
Posterior inference using the output of Bayesian variable selection samplers
412
11.7
Implementation of Gibbs variable selection in WinBUGS using an
illustrative example
414
11.8
The Carlin-Chib method
419
11.9
Reversible jump MCMC (RJMCMC)
420
11.10
Using posterior predictive densities for model evaluation
421
11.10.1
Estimation from an MCMC output
423
11.10.2
A simple example in WinBUGS
424
11.11
Information criteria
424
11.11.1
The
Bayes
information criterion
(BIC)
425
11.11.2
The
Akaiké
information criterion
(
AIC)
426
11.11.3
Other criteria
427
11.11.4
Calculation of penalized deviance measures from the MCMC
output
428
11.11.5
Implementation in WinBUGS
428
11.11.6
A simple example in WinBUGS
429
11.12
Discussion and further reading
432
Problems
432
Appendix A: Model Specif ication via Directed Acyclic Graphs: The DOODLE
Menu
435
A.I Introduction: Starting with DOODLE
435
XiV
CONTENTS
A.2
Nodes 436
А.З
Edges 438
A.4 Panels 438
A.5 A simple example
439
Appendix B: The Batch Mode: Running a Model in the Background Using
Scripts
443
B.I Introduction
443
B.2 Basic commands: Compiling and running the model
444
Appendix C: Checking Convergence Using CODA/BOA
447
C.I Introduction
447
C.2 A short historical review
448
C.3 Diagnostics implemented by CODA/BOA
448
C.3.1 The Geweke diagnostic
448
C.3.
2
The Gelman-Rubin diagnostic
449
C.3.3 The Raftery-Lewis diagnostic
449
C.3.4 The
Heidelberger-
Welch diagnostic
449
C.3.5 Final remarks
450
C.4 A first look at CODA/BOA
450
C.4.1 CODA
450
C.4.2 BOA
451
С
5
A simple example
453
C.5.1 Illustration in CODA
453
C.5.2 Illustration in BOA
457
Appendix D: Notation Summary
461
D.I MCMC
461
D.2 Subscripts and indices
462
D.3 Parameters
462
D.4 Random variables and data
463
D.5 Sample estimates
463
D.6 Special functions, vectors, and matrices
464
D.7 Distributions
464
D.8 Distribution-related notation
465
D.9 Notation used in ANOVA and ANCOVA
466
D.10 Variable and model specification
466
D.
11
Deviance information criterion (DIC)
466
D.I
2
Predictive measures
467
CONTENTS
XV
References
469
Index 485
|
| any_adam_object | 1 |
| author | Ntzoufras, Ioannis |
| author_facet | Ntzoufras, Ioannis |
| author_role | aut |
| author_sort | Ntzoufras, Ioannis |
| author_variant | i n in |
| building | Verbundindex |
| bvnumber | BV035381821 |
| callnumber-first | Q - Science |
| callnumber-label | QA279 |
| callnumber-raw | QA279.5 |
| callnumber-search | QA279.5 |
| callnumber-sort | QA 3279.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 233 WC 7000 WI 1500 |
| classification_tum | MAT 624f DAT 357f |
| ctrlnum | (OCoLC)237048398 (DE-599)GBV573648093 |
| dewey-full | 519.5/42 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.5/42 |
| dewey-search | 519.5/42 |
| dewey-sort | 3519.5 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Biologie Informatik Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV035381821 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:32:32Z |
| institution | BVB |
| isbn | 9780470141144 |
| language | English |
| lccn | 2008033316 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017186068 |
| oclc_num | 237048398 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-578 DE-703 DE-355 DE-BY-UBR |
| owner_facet | DE-91G DE-BY-TUM DE-19 DE-BY-UBM DE-578 DE-703 DE-355 DE-BY-UBR |
| physical | XXIII, 492 S. Ill., graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in computational statistics |
| spelling | Ntzoufras, Ioannis Verfasser aut Bayesian modeling using WinBUGS Ioannis Ntzoufras Hoboken, NJ Wiley 2009 XXIII, 492 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in computational statistics Includes bibliographical references and index WinBUGS Methode van Bayes gtt WinBUGS gtt Bayesian statistical decision theory Datenanalyse (DE-588)4123037-1 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s Populationsbiologie (DE-588)4046800-8 s Datenanalyse (DE-588)4123037-1 s DE-604 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017186068&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ntzoufras, Ioannis Bayesian modeling using WinBUGS WinBUGS Methode van Bayes gtt WinBUGS gtt Bayesian statistical decision theory Datenanalyse (DE-588)4123037-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| subject_GND | (DE-588)4123037-1 (DE-588)4144220-9 (DE-588)4046800-8 |
| title | Bayesian modeling using WinBUGS |
| title_auth | Bayesian modeling using WinBUGS |
| title_exact_search | Bayesian modeling using WinBUGS |
| title_full | Bayesian modeling using WinBUGS Ioannis Ntzoufras |
| title_fullStr | Bayesian modeling using WinBUGS Ioannis Ntzoufras |
| title_full_unstemmed | Bayesian modeling using WinBUGS Ioannis Ntzoufras |
| title_short | Bayesian modeling using WinBUGS |
| title_sort | bayesian modeling using winbugs |
| topic | WinBUGS Methode van Bayes gtt WinBUGS gtt Bayesian statistical decision theory Datenanalyse (DE-588)4123037-1 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Populationsbiologie (DE-588)4046800-8 gnd |
| topic_facet | WinBUGS Methode van Bayes Bayesian statistical decision theory Datenanalyse Bayes-Entscheidungstheorie Populationsbiologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017186068&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT ntzoufrasioannis bayesianmodelingusingwinbugs |