Bayesian methods for data analysis:
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| Previous Title: | Carlin, Bradley P. Bayes and empirical Bayes methods for data analysis |
|---|---|
| Main Authors: | , |
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2009
|
| Edition: | 3. ed. |
| Series: | Texts in statistical science
78 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XV, 535 S. graph. Darst. |
| ISBN: | 9781584886976 1584886978 |
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MARC
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| 100 | 1 | |a Carlin, Bradley P. |e Verfasser |0 (DE-588)134074505 |4 aut | |
| 245 | 1 | 0 | |a Bayesian methods for data analysis |c Bradley P. Carlin ; Thomas A. Louis |
| 250 | |a 3. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2009 | |
| 300 | |a XV, 535 S. |b graph. Darst. | ||
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Record in the Search Index
| _version_ | 1804138108934946819 |
|---|---|
| adam_text | Contents
Preface
to the Third Edition
xiii
1
Approaches for statistical inference
1
1.1
Introduction
1
1.2
Motivating vignettes
2
1.2.1
Personal probability
2
1.2.2
Missing data
2
1.2.3
Bioassay
3
1.2.4
Attenuation adjustment
4
1.3
Defining the approaches
4
1.4
The
Bayes-
frequentisi
controversy
6
1.5
Some basic Bayesian models
10
1.5.1
A Gaussian/Gaussian (normal/normal) model
11
1.5.2
A beta/binomial model
11
1.6
Exercises
13
2
The
Bayes
approach
15
2.1
Introduction
15
2.2
Prior distributions
27
2.2.1
Elicited priors
28
2.2.2
Conjugate priors
32
2.2.3
Noninformative
priors
36
2.2.4
Other prior construction methods
40
2.3
Bayesian inference
41
2.3.1
Point estimation
41
2.3.2
Interval estimation
48
2.3.3
Hypothesis testing and
Bayes
factors
50
2.4
Hierarchical modeling
59
2.4.1
Normal linear models
59
2.4.2
Effective model size and the DIC criterion
70
2.5
Model assessment
79
2.5.1
Diagnostic measures
79
viii CONTENTS
2.5.2
Model
averaging
89
2.6
Nonparametric methods
93
2.7
Exercises
98
3
Bayesian computation
105
3.1
Introduction
105
3.2
Asymptotic methods
108
3.2.1
Normal approximation
108
3.2.2
Laplace s method
110
3.3
Noniterative
Monte Carlo methods
112
3.3.1
Direct sampling
112
3.3.2
Indirect methods
115
3.4
Markov chain Monte Carlo methods
120
3.4.1
Gibbs sampler
121
3.4.2
Metropolis-Hastings algorithm
130
3.4.3
Slice sampler
139
3.4.4
Hybrid forms, adaptive MCMC, and other algorithms
140
3.4.5
Variance estimation
150
3.4.6
Convergence monitoring and diagnosis
152
3.5
Exercises
159
4
Model criticism and selection
167
4.1
Bayesian modeling
168
4.1.1
Linear models
168
4.1.2
Nonlinear models
174
4.1.3
Binary data models
176
4.2
Bayesian robustness
181
4.2.1
Sensitivity analysis
181
4.2.2
Prior partitioning
188
4.3
Model assessment
194
4.4
Bayes
factors via marginal density estimation
196
4.4.1
Direct methods
197
4.4.2
Using Gibbs sampler output
198
4.4.3
Using Metropolis-Hastings output
200
4.5
Bayes
factors via sampling over the model space
201
4.5.1
Product space search
203
4.5.2
Metropolized product space search
205
4.5.3
Reversible jump MCMC
206
4.5.4
Using partial analytic structure
208
4.6
Other model selection methods
210
4.6.1
Penalized likelihood criteria: AIC,
BIC,
and DIC
210
4.6.2
Predictive model selection
215
4.7
Exercises
217
CONTENTS ix
5
The empirical
Bayes
approach
225
5.1
Introduction
225
5.2
Parametric
ЕВ (РЕВ)
point estimation
226
5.2.1
Gaussian/Gaussian models
227
5.2.2
Computation via the EM algorithm
228
5.2.3
EB performance of the
РЕВ
234
5.2.4
Stein estimation
236
5.3
Nonparametric EB (NPEB) point estimation
240
5.3.1
Compound sampling models
240
5.3.2
Simple NPEB (Robbins method)
240
5.4
Interval estimation
244
5.4.1
Morris approach
245
5.4.2
Marginal posterior approach
246
5.4.3
Bias correction approach
248
5.5
Bayesian processing and performance
251
5.5.1
Univariate stretching with a two-point prior
251
5.5.2
Multivariate Gaussian model
252
5.6
Frequentist performance
253
5.6.1
Gaussian/Gaussian model
254
5.6.2
Beta/binomial model
255
5.7
Empirical
Bayes
performance
258
5.7.1
Point estimation
259
5.7.2
Interval estimation
262
5.8
Exercises
265
6
Bayesian design
269
6.1
Principles of design
269
6.1.1
Bayesian design for frequentist analysis
269
6.1.2
Bayesian design for Bayesian analysis
271
6.2
Bayesian clinical trial design
274
6.2.1
Classical versus Bayesian trial design
275
6.2.2
Bayesian assurance
277
6.2.3
Bayesian indifference zone methods
279
6.2.4
Other Bayesian approaches
282
6.2.5
Extensions
286
6.3
Applications in drug and medical device trials
287
6.3.1
Binary endpoint drug trial
287
6.3.2
Cox regression device trial with interim analysis
297
6.4
Exercises
308
7
Special methods and models
311
7.1
Estimating histograms and ranks
311
7.1.1
Bayesian ranking
311
7.1.2
Histogram and triple goal estimates
324
χ
CONTENTS
7.1.3 Robust
prior distributions
328
7.2
Order restricted inference
333
7.3
Longitudinal data models
334
7.4
Continuous and categorical time series
341
7.5
Survival analysis and frailty models
343
7.5.1
Statistical models
343
7.5.2
Treatment effect prior determination
344
7.5.3
Computation and advanced models
345
7.6
Sequential analysis
346
7.6.1
Model and loss structure
347
7.6.2
Backward induction
348
7.6.3
Forward sampling
349
7.7
Spatial and spatio-temporal models
352
7.7.1
Point source data models
353
7.7.2
Regional summary data models
356
7.8
Exercises
361
8
Case studies
373
8.1
Analysis of longitudinal AIDS data
374
8.1.1
Introduction and background
374
8.1.2
Modeling of longitudinal CD4 counts
375
8.1.3
CD4 response to treatment at two months
384
8.1.4
Survival analysis
385
8.1.5
Discussion
386
8.2
Robust analysis of clinical trials
387
8.2.1
Clinical background
387
8.2.2
Interim monitoring
388
8.2.3
Prior robustness and prior scoping
393
8.2.4
Sequential decision analysis
398
8.2.5
Discussion
401
8.3
Modeling of infectious diseases
402
8.3.1
Introduction and data
402
8.3.2
Stochastic compartmental model
403
8.3.3
Parameter estimation and model building
406
8.3.4
Results
409
8.3.5
Discussion
414
Appendices
417
A Distributional catalog
419
A.I Discrete
420
A.
1.1
Univariate
420
A.
1.2
Multivariate
421
A.
2
Continuous
421
CONTENTS
A.2.1
Univariate
A.2.2
Multivariate
В
Decision theory
B.I
Introduction
B.I.I
Risk and admissibility
B.1.2
Unbiased rules
B.1.3
Bayes
rules
B.1.4
Minimax rules
B.2
Procedure evaluation and other unifying concepts
B.2.1
Mean squared error
(MSE)
B.2.2
The variance-bias tradeoff
B.3
Other
loss functions
B.3.1
Generalized absolute loss
B.3.
2
Testing with a distance penalty
B.3.3
A threshold loss function
B.4
Multiplicity
B.5
Multiple testing
B.5.1
Additive loss
B.5.
2
Non-additive loss
B.6
Exercises
421
425
429
429
430
431
433
434
435
435
435
436
437
437
437
438
439
439
440
441
С
Answers to selected exercises
445
References
487
Author index
521
Subject index
529
|
| adam_txt |
Contents
Preface
to the Third Edition
xiii
1
Approaches for statistical inference
1
1.1
Introduction
1
1.2
Motivating vignettes
2
1.2.1
Personal probability
2
1.2.2
Missing data
2
1.2.3
Bioassay
3
1.2.4
Attenuation adjustment
4
1.3
Defining the approaches
4
1.4
The
Bayes-
frequentisi
controversy
6
1.5
Some basic Bayesian models
10
1.5.1
A Gaussian/Gaussian (normal/normal) model
11
1.5.2
A beta/binomial model
11
1.6
Exercises
13
2
The
Bayes
approach
15
2.1
Introduction
15
2.2
Prior distributions
27
2.2.1
Elicited priors
28
2.2.2
Conjugate priors
32
2.2.3
Noninformative
priors
36
2.2.4
Other prior construction methods
40
2.3
Bayesian inference
41
2.3.1
Point estimation
41
2.3.2
Interval estimation
48
2.3.3
Hypothesis testing and
Bayes
factors
50
2.4
Hierarchical modeling
59
2.4.1
Normal linear models
59
2.4.2
Effective model size and the DIC criterion
70
2.5
Model assessment
79
2.5.1
Diagnostic measures
79
viii CONTENTS
2.5.2
Model
averaging
89
2.6
Nonparametric methods
93
2.7
Exercises
98
3
Bayesian computation
105
3.1
Introduction
105
3.2
Asymptotic methods
108
3.2.1
Normal approximation
108
3.2.2
Laplace's method
110
3.3
Noniterative
Monte Carlo methods
112
3.3.1
Direct sampling
112
3.3.2
Indirect methods
115
3.4
Markov chain Monte Carlo methods
120
3.4.1
Gibbs sampler
121
3.4.2
Metropolis-Hastings algorithm
130
3.4.3
Slice sampler
139
3.4.4
Hybrid forms, adaptive MCMC, and other algorithms
140
3.4.5
Variance estimation
150
3.4.6
Convergence monitoring and diagnosis
152
3.5
Exercises
159
4
Model criticism and selection
167
4.1
Bayesian modeling
168
4.1.1
Linear models
168
4.1.2
Nonlinear models
174
4.1.3
Binary data models
176
4.2
Bayesian robustness
181
4.2.1
Sensitivity analysis
181
4.2.2
Prior partitioning
188
4.3
Model assessment
194
4.4
Bayes
factors via marginal density estimation
196
4.4.1
Direct methods
197
4.4.2
Using Gibbs sampler output
198
4.4.3
Using Metropolis-Hastings output
200
4.5
Bayes
factors via sampling over the model space
201
4.5.1
Product space search
203
4.5.2
"Metropolized" product space search
205
4.5.3
Reversible jump MCMC
206
4.5.4
Using partial analytic structure
208
4.6
Other model selection methods
210
4.6.1
Penalized likelihood criteria: AIC,
BIC,
and DIC
210
4.6.2
Predictive model selection
215
4.7
Exercises
217
CONTENTS ix
5
The empirical
Bayes
approach
225
5.1
Introduction
225
5.2
Parametric
ЕВ (РЕВ)
point estimation
226
5.2.1
Gaussian/Gaussian models
227
5.2.2
Computation via the EM algorithm
228
5.2.3
EB performance of the
РЕВ
234
5.2.4
Stein estimation
236
5.3
Nonparametric EB (NPEB) point estimation
240
5.3.1
Compound sampling models
240
5.3.2
Simple NPEB (Robbins' method)
240
5.4
Interval estimation
244
5.4.1
Morris' approach
245
5.4.2
Marginal posterior approach
246
5.4.3
Bias correction approach
248
5.5
Bayesian processing and performance
251
5.5.1
Univariate stretching with a two-point prior
251
5.5.2
Multivariate Gaussian model
252
5.6
Frequentist performance
253
5.6.1
Gaussian/Gaussian model
254
5.6.2
Beta/binomial model
255
5.7
Empirical
Bayes
performance
258
5.7.1
Point estimation
259
5.7.2
Interval estimation
262
5.8
Exercises
265
6
Bayesian design
269
6.1
Principles of design
269
6.1.1
Bayesian design for frequentist analysis
269
6.1.2
Bayesian design for Bayesian analysis
271
6.2
Bayesian clinical trial design
274
6.2.1
Classical versus Bayesian trial design
275
6.2.2
Bayesian assurance
277
6.2.3
Bayesian indifference zone methods
279
6.2.4
Other Bayesian approaches
282
6.2.5
Extensions
286
6.3
Applications in drug and medical device trials
287
6.3.1
Binary endpoint drug trial
287
6.3.2
Cox regression device trial with interim analysis
297
6.4
Exercises
308
7
Special methods and models
311
7.1
Estimating histograms and ranks
311
7.1.1
Bayesian ranking
311
7.1.2
Histogram and triple goal estimates
324
χ
CONTENTS
7.1.3 Robust
prior distributions
328
7.2
Order restricted inference
333
7.3
Longitudinal data models
334
7.4
Continuous and categorical time series
341
7.5
Survival analysis and frailty models
343
7.5.1
Statistical models
343
7.5.2
Treatment effect prior determination
344
7.5.3
Computation and advanced models
345
7.6
Sequential analysis
346
7.6.1
Model and loss structure
347
7.6.2
Backward induction
348
7.6.3
Forward sampling
349
7.7
Spatial and spatio-temporal models
352
7.7.1
Point source data models
353
7.7.2
Regional summary data models
356
7.8
Exercises
361
8
Case studies
373
8.1
Analysis of longitudinal AIDS data
374
8.1.1
Introduction and background
374
8.1.2
Modeling of longitudinal CD4 counts
375
8.1.3
CD4 response to treatment at two months
384
8.1.4
Survival analysis
385
8.1.5
Discussion
386
8.2
Robust analysis of clinical trials
387
8.2.1
Clinical background
387
8.2.2
Interim monitoring
388
8.2.3
Prior robustness and prior scoping
393
8.2.4
Sequential decision analysis
398
8.2.5
Discussion
401
8.3
Modeling of infectious diseases
402
8.3.1
Introduction and data
402
8.3.2
Stochastic compartmental model
403
8.3.3
Parameter estimation and model building
406
8.3.4
Results
409
8.3.5
Discussion
414
Appendices
417
A Distributional catalog
419
A.I Discrete
420
A.
1.1
Univariate
420
A.
1.2
Multivariate
421
A.
2
Continuous
421
CONTENTS
A.2.1
Univariate
A.2.2
Multivariate
В
Decision theory
B.I
Introduction
B.I.I
Risk and admissibility
B.1.2
Unbiased rules
B.1.3
Bayes
rules
B.1.4
Minimax rules
B.2
Procedure evaluation and other unifying concepts
B.2.1
Mean squared error
(MSE)
B.2.2
The variance-bias tradeoff
B.3
Other
loss functions
B.3.1
Generalized absolute loss
B.3.
2
Testing with a distance penalty
B.3.3
A threshold loss function
B.4
Multiplicity
B.5
Multiple testing
B.5.1
Additive loss
B.5.
2
Non-additive loss
B.6
Exercises
421
425
429
429
430
431
433
434
435
435
435
436
437
437
437
438
439
439
440
441
С
Answers to selected exercises
445
References
487
Author index
521
Subject index
529 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Carlin, Bradley P. Louis, Thomas A. 1944- |
| author_GND | (DE-588)134074505 (DE-588)112468853 |
| author_facet | Carlin, Bradley P. Louis, Thomas A. 1944- |
| author_role | aut aut |
| author_sort | Carlin, Bradley P. |
| author_variant | b p c bp bpc t a l ta tal |
| building | Verbundindex |
| bvnumber | BV035127639 |
| callnumber-first | Q - Science |
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| callnumber-raw | QA279.5 |
| callnumber-search | QA279.5 |
| callnumber-sort | QA 3279.5 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | QH 233 SK 830 SK 850 |
| classification_tum | MAT 622f |
| ctrlnum | (OCoLC)255716684 (DE-599)BSZ283315490 |
| 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 |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 3. ed. |
| format | Book |
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| id | DE-604.BV035127639 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:23:30Z |
| indexdate | 2024-07-09T21:22:57Z |
| institution | BVB |
| isbn | 9781584886976 1584886978 |
| language | English |
| lccn | 2008019143 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016795194 |
| oclc_num | 255716684 |
| open_access_boolean | |
| owner | DE-19 DE-BY-UBM DE-473 DE-BY-UBG DE-91G DE-BY-TUM DE-706 DE-M347 DE-355 DE-BY-UBR DE-578 DE-824 DE-384 DE-20 DE-2070s |
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| physical | XV, 535 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Texts in statistical science |
| series2 | Texts in statistical science A Chapman & Hall book |
| spelling | Carlin, Bradley P. Verfasser (DE-588)134074505 aut Bayesian methods for data analysis Bradley P. Carlin ; Thomas A. Louis 3. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2009 XV, 535 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science 78 A Chapman & Hall book Bayesian statistical decision theory Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Datenanalyse (DE-588)4123037-1 gnd rswk-swf Datenanalyse (DE-588)4123037-1 s Bayes-Verfahren (DE-588)4204326-8 s DE-604 Louis, Thomas A. 1944- Verfasser (DE-588)112468853 aut Bis 2. Auflage Carlin, Bradley P. Bayes and empirical Bayes methods for data analysis (DE-604)BV013567089 Texts in statistical science 78 (DE-604)BV022819715 78 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016795194&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Carlin, Bradley P. Louis, Thomas A. 1944- Bayesian methods for data analysis Texts in statistical science Bayesian statistical decision theory Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4123037-1 |
| title | Bayesian methods for data analysis |
| title_auth | Bayesian methods for data analysis |
| title_exact_search | Bayesian methods for data analysis |
| title_exact_search_txtP | Bayesian methods for data analysis |
| title_full | Bayesian methods for data analysis Bradley P. Carlin ; Thomas A. Louis |
| title_fullStr | Bayesian methods for data analysis Bradley P. Carlin ; Thomas A. Louis |
| title_full_unstemmed | Bayesian methods for data analysis Bradley P. Carlin ; Thomas A. Louis |
| title_old | Carlin, Bradley P. Bayes and empirical Bayes methods for data analysis |
| title_short | Bayesian methods for data analysis |
| title_sort | bayesian methods for data analysis |
| topic | Bayesian statistical decision theory Bayes-Verfahren (DE-588)4204326-8 gnd Datenanalyse (DE-588)4123037-1 gnd |
| topic_facet | Bayesian statistical decision theory Bayes-Verfahren Datenanalyse |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016795194&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022819715 |
| work_keys_str_mv | AT carlinbradleyp bayesianmethodsfordataanalysis AT louisthomasa bayesianmethodsfordataanalysis |