Bayesian analysis for the social sciences:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester
Wiley
2009
|
| Edition: | 1. publ. |
| Series: | Wiley series in probability and statistics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXXIV, 564 S. graph. Darst. |
| ISBN: | 9780470011546 0470011548 |
Staff View
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| 245 | 1 | 0 | |a Bayesian analysis for the social sciences |c Simon Jackman |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Chichester |b Wiley |c 2009 | |
| 300 | |a XXXIV, 564 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Wiley series in probability and statistics | |
| 650 | 4 | |a Sozialwissenschaften | |
| 650 | 4 | |a Bayesian statistical decision theory | |
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Record in the Search Index
| _version_ | 1804138005525430273 |
|---|---|
| adam_text | Contents
List of Figures
xiii
List of Tables
xix
Preface
xxi
Acknowledgments
xxv
Introduction
xxvii
Part I Introducing Bayesian Analysis
1
1
The foundations of Bayesian inference
3
1.1
What is probability?
3
1.1.1
Probability in classical statistics
4
1.1.2
Subjective probability
5
1.2
Subjective probability in Bayesian statistics
7
1.3
Bayes
theorem, discrete case
8
1.4
Bayes
theorem, continuous parameter
13
1.4.1
Conjugate priors
15
1.4.2
Bayesian updating with irregular priors
16
1.4.3
Cromwell s Rule
18
1.4.4
Bayesian updating as information accumulation
19
1.5
Parameters as random variables, beliefs as distributions
21
1.6
Communicating the results of a Bayesian analysis
22
1.6.1
Bayesian point estimation
23
1.6.2
Credible regions
26
1.7
Asymptotic properties of posterior distributions
29
1.8
Bayesian hypothesis testing
31
1.8.1
Model choice
36
1.8.2
Bayes
factors
37
viii CONTENTS
1.9
From subjective beliefs to parameters and models
38
1.9.1
Exchangeability
39
1.9.2
Implications and extensions of
de Finetti s
Representation
Theorem
42
1.9.3
Finite exchangeability
43
1.9.4
Exchangeability and prediction
43
1.9.5
Conditional exchangeability and multiparameter models
44
1.9.6
Exchangeability of parameters: hierarchical modeling
45
1.10
Historical note
46
2
Getting started: Bayesian analysis for simple models
49
2.1
Learning about probabilities, rates and proportions
49
2.1.1
Conjugate priors for probabilities, rates and proportions
51
2.1.2
Bayes
estimates as weighted averages of priors and data
58
2.1.3
Parameterizations and priors
61
2.1.4
The variance of the posterior density
64
2.2
Associations between binary variables
67
2.3
Learning from counts
73
2.3.1
Predictive inference with count data
78
2.4
Learning about a normal mean and variance
80
2.4.1
Variance known
80
2.4.2
Mean and variance unknown
83
2.4.3
Conditionally conjugate prior
92
2.4.4
An improper, reference prior
93
2.4.5
Conflict between likelihood and prior
98
2.4.6
Non-conjugate priors
98
2.5
Regression models
99
2.5.1
Bayesian regression analysis
102
2.5.2
Likelihood function
103
2.5.3
Conjugate prior
104
2.5.4
Improper, reference prior
107
2.6
Further reading
124
Part II Simulation Based Bayesian Analysis
129
3
Monte Carlo methods
133
3.1
Simulation consistency
134
3.2
Inference for functions of parameters
140
3.3
Marginalization via Monte Carlo integration
142
3.4
Sampling algorithms
153
3.4.1
Inverse-CDF method
153
3.4.2
Importance sampling
156
CONTENTS ix
3.4.3 Accept-reject
sampling
159
3.4.4
Adaptive rejection sampling
163
3.5
Further reading
167
4
Markov chains
171
4.1
Notation and definitions
172
4.1.1
State space
173
4.1.2
Transition kernel
173
4.2
Properties of Markov chains
176
4.2.1
Existence of a stationary distribution, discrete case
177
4.2.2
Existence of a stationary distribution, continuous case
178
4.2.3
breducibility
179
4.2.4
Recurrence
182
4.2.5
Invariant measure
184
4.2.6
Reversibility
185
4.2.7
Aperiodicity
186
4.3
Convergence of Markov chains
187
4.3.1
Speed of convergence
189
4.4
Limit theorems for Markov chains
191
4.4.1
Simulation inefficiency
191
4.4.2
Central limit theorems for Markov chains
195
4.5
Further reading
196
5
Markov chain Monte Carlo
201
5.1
Metropolis-Hastings algorithm
201
5.1.1
Theory for the Metropolis-Hastings algorithm
202
5.1.2
Choosing the proposal density
204
5.2
Gibbs sampling
214
5.2.1
Theory for the Gibbs sampler
218
5.2.2
Connection to the Metropolis algorithm
221
5.2.3
Deriving conditional densities for the Gibbs sampler: statistical
models as conditional independence graphs
225
5.2.4
Pathologies
229
5.2.5
Data augmentation
236
5.2.6
Missing data problems
237
5.2.7
The slice sampler
244
6
Implementing Markov chain Monte Carlo
251
6.1
Software for Markov chain Monte Carlo
251
6.2
Assessing convergence and run-length
252
6.3
Working with BUGS/JAGS from
R
256
6.4 Trieb
of the trade
261
6.4.1
Thinning
261
CONTENTS
6.4.2
Blocking
264
6.4.3 Reparameterization 270
6.5
Other examples
272
6.6
Further reading
292
Part III Advanced Applications in the Social Sciences
299
7
Hierarchical Statistical Models
301
7.1
Data and parameters that vary by groups: the case for hierarchical
modeling
301
7.1.1
Exchangeable parameters generate hierarchical models
305
7.1.2
Borrowing strength via exchangeability
307
7.1.3
Hierarchical modeling as a semi-pooling estimator
307
7.1.4
Hierarchical modeling as a shrinkage estimator
308
7.1.5
Computation via Markov chain Monte Carlo
310
7.2
ANO
VA as a
hierarchical model
317
7.2.1
One-way analysis of variance
317
7.2.2
Two-way ANOVA
329
7.3
Hierarchical models for longitudinal data
345
7.4
Hierarchical models for non-normal data
354
7.5
Multi-level models
362
8
Bayesian analysis of choice making
379
8.1
Regression models for binary responses
379
8.1.1
Probit
model via data augmentation
380
8.1.2
Probit
model via marginal data augmentation
389
8.1.3
Logit model
393
8.1.4
Binomial model for grouped binary data
395
8.2
Ordered outcomes
397
8.2.1
Identification
399
8.3
Multinomial outcomes
415
8.3.1
Multinomial logit (MNL)
415
8.3.2
Independence of irrelevant alternatives
423
8.4
Multinomial
probit
424
8.4.1
Bayesian analysis via MCMC
426
9
Bayesian approaches to measurement
435
9.1
Bayesian inference for latent states
435
9.1.1
A formal role for prior information
436
9.1.2
Inference for many parameters
436
9.2
Factor analysis
438
9.2.1
Likelihood and prior densities
439
9.2.2
Identification
440
9.2.3
Posterior density
442
9.2.4
Inference over rank
orderings
of the latent variable
448
9.2.5
Incorporating additional information via hierarchical modeling
449
CONTENTS xi
9.3
Item-response models
454
9.4
Dynamic measurement models
471
9.4.1
State-space models for pooling the polls
473
9.4.2
Bayesian inference
474
Part IV Appendices
489
Appendix A: Working with vectors and matrices
491
Appendix B: Probability review
497
B.I Foundations of probability
497
B.2 Probability densities and mass functions
498
B.2.1 Probability mass functions for discrete random quantities
501
B.2.2 Probability density functions for continuous random
quantities
503
B.3 Convergence of sequences of random variables
511
Appendix C: Proofs of selected propositions
513
C.
1
Products of normal densities
513
C.2 Conjugate analysis of normal data
516
C.3 Asymptotic normality of the posterior density
533
References
535
Topic index
553
Author index
559
|
| adam_txt |
Contents
List of Figures
xiii
List of Tables
xix
Preface
xxi
Acknowledgments
xxv
Introduction
xxvii
Part I Introducing Bayesian Analysis
1
1
The foundations of Bayesian inference
3
1.1
What is probability?
3
1.1.1
Probability in classical statistics
4
1.1.2
Subjective probability
5
1.2
Subjective probability in Bayesian statistics
7
1.3
Bayes
theorem, discrete case
8
1.4
Bayes
theorem, continuous parameter
13
1.4.1
Conjugate priors
15
1.4.2
Bayesian updating with irregular priors
16
1.4.3
Cromwell's Rule
18
1.4.4
Bayesian updating as information accumulation
19
1.5
Parameters as random variables, beliefs as distributions
21
1.6
Communicating the results of a Bayesian analysis
22
1.6.1
Bayesian point estimation
23
1.6.2
Credible regions
26
1.7
Asymptotic properties of posterior distributions
29
1.8
Bayesian hypothesis testing
31
1.8.1
Model choice
36
1.8.2
Bayes
factors
37
viii CONTENTS
1.9
From subjective beliefs to parameters and models
38
1.9.1
Exchangeability
39
1.9.2
Implications and extensions of
de Finetti's
Representation
Theorem
42
1.9.3
Finite exchangeability
43
1.9.4
Exchangeability and prediction
43
1.9.5
Conditional exchangeability and multiparameter models
44
1.9.6
Exchangeability of parameters: hierarchical modeling
45
1.10
Historical note
46
2
Getting started: Bayesian analysis for simple models
49
2.1
Learning about probabilities, rates and proportions
49
2.1.1
Conjugate priors for probabilities, rates and proportions
51
2.1.2
Bayes
estimates as weighted averages of priors and data
58
2.1.3
Parameterizations and priors
61
2.1.4
The variance of the posterior density
64
2.2
Associations between binary variables
67
2.3
Learning from counts
73
2.3.1
Predictive inference with count data
78
2.4
Learning about a normal mean and variance
80
2.4.1
Variance known
80
2.4.2
Mean and variance unknown
83
2.4.3
Conditionally conjugate prior
92
2.4.4
An improper, reference prior
93
2.4.5
Conflict between likelihood and prior
98
2.4.6
Non-conjugate priors
98
2.5
Regression models
99
2.5.1
Bayesian regression analysis
102
2.5.2
Likelihood function
103
2.5.3
Conjugate prior
104
2.5.4
Improper, reference prior
107
2.6
Further reading
124
Part II Simulation Based Bayesian Analysis
129
3
Monte Carlo methods
133
3.1
Simulation consistency
134
3.2
Inference for functions of parameters
140
3.3
Marginalization via Monte Carlo integration
142
3.4
Sampling algorithms
153
3.4.1
Inverse-CDF method
153
3.4.2
Importance sampling
156
CONTENTS ix
3.4.3 Accept-reject
sampling
159
3.4.4
Adaptive rejection sampling
163
3.5
Further reading
167
4
Markov chains
171
4.1
Notation and definitions
172
4.1.1
State space
173
4.1.2
Transition kernel
173
4.2
Properties of Markov chains
176
4.2.1
Existence of a stationary distribution, discrete case
177
4.2.2
Existence of a stationary distribution, continuous case
178
4.2.3
breducibility
179
4.2.4
Recurrence
182
4.2.5
Invariant measure
184
4.2.6
Reversibility
185
4.2.7
Aperiodicity
186
4.3
Convergence of Markov chains
187
4.3.1
Speed of convergence
189
4.4
Limit theorems for Markov chains
191
4.4.1
Simulation inefficiency
191
4.4.2
Central limit theorems for Markov chains
195
4.5
Further reading
196
5
Markov chain Monte Carlo
201
5.1
Metropolis-Hastings algorithm
201
5.1.1
Theory for the Metropolis-Hastings algorithm
202
5.1.2
Choosing the proposal density
204
5.2
Gibbs sampling
214
5.2.1
Theory for the Gibbs sampler
218
5.2.2
Connection to the Metropolis algorithm
221
5.2.3
Deriving conditional densities for the Gibbs sampler: statistical
models as conditional independence graphs
225
5.2.4
Pathologies
229
5.2.5
Data augmentation
236
5.2.6
Missing data problems
237
5.2.7
The slice sampler
244
6
Implementing Markov chain Monte Carlo
251
6.1
Software for Markov chain Monte Carlo
251
6.2
Assessing convergence and run-length
252
6.3
Working with BUGS/JAGS from
R
256
6.4 Trieb
of the trade
261
6.4.1
Thinning
261
CONTENTS
6.4.2
Blocking
264
6.4.3 Reparameterization 270
6.5
Other examples
272
6.6
Further reading
292
Part III Advanced Applications in the Social Sciences
299
7
Hierarchical Statistical Models
301
7.1
Data and parameters that vary by groups: the case for hierarchical
modeling
301
7.1.1
Exchangeable parameters generate hierarchical models
305
7.1.2
'Borrowing strength' via exchangeability
307
7.1.3
Hierarchical modeling as a 'semi-pooling' estimator
307
7.1.4
Hierarchical modeling as a 'shrinkage' estimator
308
7.1.5
Computation via Markov chain Monte Carlo
310
7.2
ANO
VA as a
hierarchical model
317
7.2.1
One-way analysis of variance
317
7.2.2
Two-way ANOVA
329
7.3
Hierarchical models for longitudinal data
345
7.4
Hierarchical models for non-normal data
354
7.5
Multi-level models
362
8
Bayesian analysis of choice making
379
8.1
Regression models for binary responses
379
8.1.1
Probit
model via data augmentation
380
8.1.2
Probit
model via marginal data augmentation
389
8.1.3
Logit model
393
8.1.4
Binomial model for grouped binary data
395
8.2
Ordered outcomes
397
8.2.1
Identification
399
8.3
Multinomial outcomes
415
8.3.1
Multinomial logit (MNL)
415
8.3.2
Independence of irrelevant alternatives
423
8.4
Multinomial
probit
424
8.4.1
Bayesian analysis via MCMC
426
9
Bayesian approaches to measurement
435
9.1
Bayesian inference for latent states
435
9.1.1
A formal role for prior information
436
9.1.2
Inference for many parameters
436
9.2
Factor analysis
438
9.2.1
Likelihood and prior densities
439
9.2.2
Identification
440
9.2.3
Posterior density
442
9.2.4
Inference over rank
orderings
of the latent variable
448
9.2.5
Incorporating additional information via hierarchical modeling
449
CONTENTS xi
9.3
Item-response models
454
9.4
Dynamic measurement models
471
9.4.1
State-space models for 'pooling the polls'
473
9.4.2
Bayesian inference
474
Part IV Appendices
489
Appendix A: Working with vectors and matrices
491
Appendix B: Probability review
497
B.I Foundations of probability
497
B.2 Probability densities and mass functions
498
B.2.1 Probability mass functions for discrete random quantities
501
B.2.2 Probability density functions for continuous random
quantities
503
B.3 Convergence of sequences of random variables
511
Appendix C: Proofs of selected propositions
513
C.
1
Products of normal densities
513
C.2 Conjugate analysis of normal data
516
C.3 Asymptotic normality of the posterior density
533
References
535
Topic index
553
Author index
559 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Jackman, Simon 1966- |
| author_GND | (DE-588)139959548 |
| author_facet | Jackman, Simon 1966- |
| author_role | aut |
| author_sort | Jackman, Simon 1966- |
| author_variant | s j sj |
| building | Verbundindex |
| bvnumber | BV035061146 |
| callnumber-first | H - Social Science |
| callnumber-label | HA29 |
| callnumber-raw | HA29 |
| callnumber-search | HA29 |
| callnumber-sort | HA 229 |
| callnumber-subject | HA - Statistics |
| classification_rvk | MR 2100 QH 233 SK 830 |
| ctrlnum | (OCoLC)150384763 (DE-599)BVBBV035061146 |
| 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 | Soziologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Mathematik Wirtschaftswissenschaften |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035061146 |
| illustrated | Illustrated |
| index_date | 2024-07-02T22:00:37Z |
| indexdate | 2024-07-09T21:21:19Z |
| institution | BVB |
| isbn | 9780470011546 0470011548 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016729656 |
| oclc_num | 150384763 |
| open_access_boolean | |
| owner | DE-945 DE-473 DE-BY-UBG DE-355 DE-BY-UBR DE-M382 DE-11 DE-703 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-188 |
| owner_facet | DE-945 DE-473 DE-BY-UBG DE-355 DE-BY-UBR DE-M382 DE-11 DE-703 DE-91 DE-BY-TUM DE-19 DE-BY-UBM DE-188 |
| physical | XXXIV, 564 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley series in probability and statistics |
| spelling | Jackman, Simon 1966- Verfasser (DE-588)139959548 aut Bayesian analysis for the social sciences Simon Jackman 1. publ. Chichester Wiley 2009 XXXIV, 564 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley series in probability and statistics Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 s b DE-604 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016729656&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Jackman, Simon 1966- Bayesian analysis for the social sciences Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4204326-8 |
| title | Bayesian analysis for the social sciences |
| title_auth | Bayesian analysis for the social sciences |
| title_exact_search | Bayesian analysis for the social sciences |
| title_exact_search_txtP | Bayesian analysis for the social sciences |
| title_full | Bayesian analysis for the social sciences Simon Jackman |
| title_fullStr | Bayesian analysis for the social sciences Simon Jackman |
| title_full_unstemmed | Bayesian analysis for the social sciences Simon Jackman |
| title_short | Bayesian analysis for the social sciences |
| title_sort | bayesian analysis for the social sciences |
| topic | Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Verfahren |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016729656&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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