Bayesian ideas and data analysis: an introduction for scientists and statisticians
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2011
|
| Series: | Texts in statistical science
A Chapman & Hall book |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVII, 498 S. graph. Darst. |
| ISBN: | 9781439803547 |
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MARC
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| 245 | 1 | 0 | |a Bayesian ideas and data analysis |b an introduction for scientists and statisticians |c Ronald Christensen ... |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2011 | |
| 300 | |a XVII, 498 S. |b graph. Darst. | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Texts in statistical science | |
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Record in the Search Index
| _version_ | 1804143155483770880 |
|---|---|
| adam_text | Contents
Preface
xv
1
Prologue
1
1.1
Probability of a Defective: Binomial Data
2
1.2
Brass Alloy Zinc Content: Normal Data
3
1.3
Armadillo Hunting:
Poisson Data
4
1.4
Abortion in Dairy Cattle: Survival Data
5
1.5
Ache Hunting with Age Trends
6
1.6
Lung Cancer Treatment: Log-Normal Regression
7
1.7
Survival with Random Effects: Ache Hunting
8
2
Fundamental Ideas I
13
2.1
Simple Probability Computations
14
2.2
Science, Priors, and Prediction
18
2.3
Statistical Models
22
2.4
Posterior Analysis
30
2.5
Commonly Used Distributions
33
3
Integration Versus Simulation
37
3.1
Introduction
37
3.2
WinBUGS I: Getting Started
41
3.3
Method of Composition
48
3.4
Monte Carlo Integration*
49
3.5
Posterior Computations in
R
51
4
Fundamental Ideas II
53
4.1
Statistical Testing
53
4.1.1
Checking Bayesian Models
57
4.1.2
Predictive P- Values
59
4.1.3
Lindley-Jeffreys Paradox
60
4.2
Exchangeability
61
4.3
Likelihood Functions
63
4.4
Sufficient Statistics
66
4.5
Analysis Using Predictive Distributions
67
4.6
Flat Priors
69
4.6.1
Data Translated Likelihoods
71
4.7
Jeffreys Priors
72
4.7.1
Multiple Parameter Jeffreys Prior*
73
4.8
Bayes
Factors*
74
4.8.1
General Parametric Testing
74
4.8.2
Nested Models
75
4.8.3
Simulating
Bayes
Factors
75
CONTHNTS
4.9
Other Model Selection Criteria
78
4.9.1
Bayesian Information Criterion
79
4.9.2
LPML HI
4.9.3
Deviance Information Criterion H2
4.9.4
Final Comments
83
4.10
Normal Approximations to Posteriors* K4
4.11
Bayesian Consistency and Inconsistency
88
4.12
Hierarchical Models
89
4.13
Some Final Comments on Likelihoods*
93
4.14
Identifiability and
Noninformative
Data
94
Comparing Populations
97
5.1
Inference for Proportions
97
5.1.1
Prior Distributions
99
5.1.1.1
Reference Priors
99
5.1.1.2
Informative Beta Priors
99
5.1.1.3
Rare Events
100
5.1.1.4
Non-Beta Priors
102
5.1.2
Effect Measures
103
5.1.3
Independent Binomials
105
5.1.4
Case-Control Sampling
107
5.2
Inference for Normal Populations 111
5.2.1
Reference Priors 111
5.2.2
Conjugate Priors
114
5.2.3
Independence Priors
115
5.2.4
Some Curious Distributional Results*
120
5.2.5
Two-Sample Normal Model
121
5.3
Inference for Rates
128
5.3.1
One-Sample
Poisson
Data
129
5.3.2
Informative Priors
131
5.3.3
Reference Priors
133
5.3.4
Two-Sample
Poisson
Data
134
5.4
Sample Size Determination*
136
Simulations
139
6.1
Generating Random Samples
139
6.2
Traditional Monte Carlo Methods
142
6.2.1
Acceptance-Rejection Sampling
142
6.2.2
Importance Sampling
143
6.3
Markov Chain Monte Carlo
145
6.3.1
Markov Chains
147
6.3.2
Gibbs Sampling
150
6.3.2.1
Proof that
ρ(θ)
is the Stationary Distribution in the Two-Block
Case*
154
6.3.3
Metropolis Algorithm
154
6.3.3.1
Proof that
ρ(θ)
is the Stationary Distribution*
156
6.3.4
Slice Sampling
158
6.3.5
Checking MCMC Samples
159
CONTENTS xi
7 Basic
Concepts
of
Regression 161
7.1
Introduction
161
7.2 Data Notation and Format 162
7.3
Predictive
Models: An
Overview
164
7.4
Modeling with
Linear
Structures
166
7.4.1
Continuous Predictors
166
7.4.2
Binary Predictors
166
7.4.3
Multi-Category Predictors
167
7.4.4
Predictor Selection
169
7.4.5
Several Categorical Covariates
171
7.4.6
Confounding
172
7.4.7
Effect Modification/Interaction
174
7.4.7.1
Two Categorical Predictors
175
7.4.7.2
One Continuous and One Categorical Predictor
176
7.4.7.3
Two Continuous Predictors
177
7.5
Illustration: FEV Data
178
8
Binomial Regression
181
8.1
The Sampling Model
181
8.2
Binomial Regression Analysis
186
8.2.1
Predictive Probabilities
188
8.2.2
Inference for Regression Coefficients
190
8.2.3
Inference for LDa
195
8.3
Model Checking
195
8.3.1
Box s Method
195
8.3.2
Link Selection
196
8.4
Prior Distributions
197
8.4.1
Simple Regression
197
8.4.2
General Regression
199
8.4.2.1
Prior Elicitation
203
8.4.2.2
Data Augmentation Priors
203
8.4.2.3
Standardized Variables
204
8.4.3
Reference Priors
207
8.4.4
Partial Prior Information
209
8.4.5
Partial Priors: Theoretical Considerations*
212
8.5
Mixed Models
213
8.5.1
Prior Elicitation
217
8.5.2
Mixed Model Likelihood
219
8.5.3
Gibbs Sampling and Centering*
219
9
Linear Regression
223
9.1
The Sampling Model
223
9.2
Reference Priors
226
9.2.1
Least Squares Estimation
227
9.2.2
Posterior Analysis
229
9.2.3
A Proper Reference Prior
230
9.3
Conjugate Priors
231
9.4
Independence Priors
233
9.4.1
Prior on
β
234
9.4.2
Prior on
τ
236
9.4.3
Partial Prior Information
237
9.4.4
Inference and Displays
238
xii CONTENTS
9.4.5
Gibbs Sampling*
239
9.4.6
WinBUGS and
R
Code
241
9.5
ANOVA
243
9.5.1
Independence Prior
243
9.5.1.1
Allocation and Diagnosis
248
9.5.2
Hierarchical Priors and Models
251
9.6
Model Diagnostics
252
9.7
Model Selection
257
9.8
Nonlinear Regression*
259
10
Correlated Data
263
10.1
Introduction
263
10.2
Mixed Models
265
10.2.1
Random Intercept Model
267
10.2.2
Random Slopes and Random Intercepts
275
10.3
Multivariate Normal Models
278
10.3.1
Parameterized Covariance Matrices
279
10.3.1.1
Analytic Formulas for CS and AR(1) Precision Matrices
283
10.4
Multivariate Normal Regression
283
10.5
Posterior Sampling and Missing Data
285
11
Count Data
287
11.1
Poisson
Regression
287
11.1.1
Poisson
Regression for Rates
289
11.2
Over-Dispersion and Mixtures of
Poissons
294
11.2.1
Zero-Inflated
Poisson Data
298
11.2.2
SAS
Analysis of Foot-and-Mouth Disease Data
298
11.3
Longitudinal Data
300
12
Time to Event Data
301
12.1
Introduction
301
12.1.1
Survival and Hazard Functions
302
12.1.2
Censoring
303
12.1.3
The Likelihood
304
12.2
One-Sample Models
305
12.2.1
Distributional Models
306
12.2.2
Posterior Analysis
307
12.2.3
Log-Normal Data
307
12.2.4
Exponential Data
307
12.2.5
WinBUGS for Censored Data
308
12.2.6
WeibullData
309
12.2.7
Prediction
311
12.2.8
Interval Censoring
312
12.3
Two-Sample Data
314
12.3.1
Two-Sample Exponential Model
314
12.3.2
Two-Sample Weibull Model
319
12.3.3
Two-Sample Log-Normal Model
320
12.4
Plotting Survival and Hazard Functions
322
CONTENTS
xiii
13
Time to Event Regression
325
13.1
Accelerated Failure Time Models
325
13.1.1
Abortion Data
333
13.1.2
Prior El ¡citation for AFTs
334
13.1.2.1
Specifying the Marginal Prior for
β
335
13.1.2.2
Partial Prior Information for
β
338
13.1.2.3
Uncertainty About
τ
339
13.1.3
Case Deletion Diagnostics for AFT Models
340
13.1.3.1
Predictive Influence
342
13.1.4
Bayes
Factor Model Selection
343
13.1.5
Sensitivity Analysis
343
13.1.6
Final Comments
344
13.2
Proportional Hazards Modeling
345
13.2.1
The Proportional Hazards (PH) Model
345
13.2.2
A Baseline Hazard Model
347
13.2.3
The Likelihood
347
13.2.3.1
Noninformative
Data*
349
13.2.4
Priors for
β
349
13.2.5
Priors for
Я
351
13.2.6
Our Data Model
352
13.2.7
WinBUGSCode
353
13.2.8
Posterior Analysis for Leukemia Data
355
13.2.9
SAS
Analysis of Leukemia Data
356
13.2.10
Another Example
358
13.3
Survival with Random Effects
363
14
Binary Diagnostic Tests
365
14.1
Basic Ideas
366
14.2
One Test, One Population
368
14.2.1
Gold-Standard Data
369
14.2.2
No Gold-Standard Data
371
14.3
Two Tests, Two Populations
374
14.3.1
Methods for Conditionally Independent Tests
374
14.4
Prevalence Distributions
379
15
Nonparametric Models
385
15.1
Flexible Density Shapes
386
15.1.1
Finite Mixtures
386
15.1.1.1
Identifiability Issues*
391
15.1.2
Dirichlet Process Mixtures: Infinite Mixtures
392
15.1.3
Mixtures of Polya Trees
396
15.2
Flexible Regression Functions
402
15.3
Proportional Hazards Modeling
414
Appendix A: Matrices and Vectors
419
A.I Matrix Addition and Subtraction
420
A.2 Scalar Multiplication
420
A.3 Matrix Multiplication
420
A.
4
Special Matrices
422
A.5 Linear Dependence and Rank
423
A.6 Inverse Matrices
424
A.7 A List of Useful Properties
426
xiv CONTENTS
A.8
Eigenvalues and Eigenvectors
426
A.
9
Properties of Determinants
428
A.
10
Calculus and Taylor s Theorem
428
A.
11
Partitioned Matrices
428
Appendix B: Probability
431
B.I Univariate Probability
431
B.2 Multivariate Probability
432
B.2.1 Joint Distribution of Two Vectors
434
B.2.2 Conditional Distributions
434
B.2.3 Independence
436
B.2.4 Moment Generating Functions
437
B.2.5 Change of Variables
437
B.3 Models and Conditional Independence
438
Appendix C: Getting Started in
R
443
C.I Getting
R
443
C.2 Some
R
Basics
443
C.3 User-Contributed Packages
446
C.4 Reading Data
447
C.5 Graphing
447
C.6 Interface Between
R
and WinBUGS
456
C.7 Writing New
R
Functions
456
References
459
Author Index
467
Subject Index
473
|
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| id | DE-604.BV036572722 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:43:10Z |
| institution | BVB |
| isbn | 9781439803547 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020493804 |
| oclc_num | 700637552 |
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| physical | XVII, 498 S. graph. Darst. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Texts in statistical science A Chapman & Hall book |
| spelling | Bayesian ideas and data analysis an introduction for scientists and statisticians Ronald Christensen ... Boca Raton, Fla. [u.a.] CRC Press 2011 XVII, 498 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science A Chapman & Hall book Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 s DE-604 Bayes-Verfahren (DE-588)4204326-8 s Bayes-Entscheidungstheorie (DE-588)4144220-9 s Christensen, Ronald 1951- Sonstige (DE-588)111351820 oth Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020493804&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bayesian ideas and data analysis an introduction for scientists and statisticians Bayes-Verfahren (DE-588)4204326-8 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4144220-9 (DE-588)4077850-2 |
| title | Bayesian ideas and data analysis an introduction for scientists and statisticians |
| title_auth | Bayesian ideas and data analysis an introduction for scientists and statisticians |
| title_exact_search | Bayesian ideas and data analysis an introduction for scientists and statisticians |
| title_full | Bayesian ideas and data analysis an introduction for scientists and statisticians Ronald Christensen ... |
| title_fullStr | Bayesian ideas and data analysis an introduction for scientists and statisticians Ronald Christensen ... |
| title_full_unstemmed | Bayesian ideas and data analysis an introduction for scientists and statisticians Ronald Christensen ... |
| title_short | Bayesian ideas and data analysis |
| title_sort | bayesian ideas and data analysis an introduction for scientists and statisticians |
| title_sub | an introduction for scientists and statisticians |
| topic | Bayes-Verfahren (DE-588)4204326-8 gnd Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Statistische Entscheidungstheorie (DE-588)4077850-2 gnd |
| topic_facet | Bayes-Verfahren Bayes-Entscheidungstheorie Statistische Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020493804&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT christensenronald bayesianideasanddataanalysisanintroductionforscientistsandstatisticians |