Bayesian statistics for the social sciences:
" Bridging the gap between traditional classical statistics and a Bayesian approach, David Kaplan provides readers with the concepts and practical skills they need to apply Bayesian methodologies to their data analysis problems. Part I addresses the elements of Bayesian inference, including exc...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; London
The Guilford Press
[2014]
|
| Series: | Methodology in the social sciences
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Summary: | " Bridging the gap between traditional classical statistics and a Bayesian approach, David Kaplan provides readers with the concepts and practical skills they need to apply Bayesian methodologies to their data analysis problems. Part I addresses the elements of Bayesian inference, including exchangeability, likelihood, prior/posterior distributions, and the Bayesian central limit theorem. Part II covers Bayesian hypothesis testing, model building, and linear regression analysis, carefully explaining the differences between the Bayesian and frequentist approaches. Part III extends Bayesian statistics to multilevel modeling and modeling for continuous and categorical latent variables. Kaplan closes with a discussion of philosophical issues and argues for an "evidence-based" framework for the practice of Bayesian statistics. Useful features for teaching or self-study: *Includes worked-through, substantive examples, using large-scale educational and social science databases. *Utilizes open-source R software programs available on the CRAN (such as MCMCpack and rjags); readers do not have to master the R language and can easily adapt the example programs to fit individual needs. *Shows readers how to carefully warrant priors on the basis of empirical data. *Companion website features data and code for the book's examples, plus other resources. "-- |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | xviii, 318 Seiten Diagramme |
| ISBN: | 9781462516513 |
Staff View
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| adam_text | Titel: Bayesian statistics for the social sciences
Autor: Kaplan, David
Jahr: 2014
Contents
PART I. FOUNDATIONS OF BAYESIAN STATISTICS
1 • Probability Concepts and Bayes7 Theorem 3
1.1. Relevant Probability Axioms 3
1.1.1. Probability as Long-Run Frequency 4
1.1.2. The Kolmogorov Axioms of Probability 4
1.1.3. The Rényi Axioms of Probability 6
1.1.4. Bayes Theorem 7
1.1.5. Epistemic Probability 8
1.1.6. Coherence 9
1.2. Summary 11
1.3. Suggested Readings 11
2 • Statistical Elements of Bayes Theorem 13
2.1. The Assumption of Exchangeability 15
2.2. The Prior Distribution 17
2.2.1. Noninformative Priors 18
2.2.2. Informative Priors 20
2.3. Likelihood 22
2.3.1. The Law of Likelihood 22
2.4. The Posterior Distribution 24
2.5. The Bayesian Central Limit Theorem
and Bayesian Shrinkage 26
2.6. Summary 30
2.7. Suggested Readings 31
APPENDIX 2.1. DERIVATION OF JEFFREYS PRIOR 32
3 • Common Probability Distributions 33
3.1. The Normal Distribution 34
3.1.1. The Conjugate Prior for the Normal Distribution 35
3.2. The Uniform Distribution 37
3.2.1. The Uniform Distribution as a Noninformative Prior 38
XV
xvi Contents
3.3. The Poisson Distribution 39
3.3.1. The Gamma Density: Conjugate Prior
for the Poisson Distribution 40
3.4. The Binomial Distribution 40
3.4.1. The Beta Distribution: Conjugate Prior
for the Binomial Distribution 41
3.5. The Multinomial Distribution 42
3.5.1. The Dirichlet Distribution: Conjugate Prior
for the Multinomial Distribution 44
3.6. The Wishart Distribution 44
3.6.1. The Inverse-Wishart Distribution: Conjugate Prior
for the Wishart Distribution 46
3.7. Summary 46
3.8. Suggested Readings 46
APPENDIX 3.1. R CODE FOR CHAPTER 3 48
4 • Markov Chain Monte Carlo Sampling 65
4.1. Basic Ideas of MCMC Sampling 66
4.2. The Metropolis-Hastings Algorithm 67
4.3. The Gibbs Sampler 69
4.4. Convergence Diagnostics 71
4.5. Summary 79
4.6. Suggested Readings 79
APPENDIX 4.1. R CODE FOR CHAPTER 4 81
PART II. TOPICS IN BAYESIAN MODELING
5 • Bayesian Hypothesis Testing 91
5.1. Setting the Stage: The Classical Approach to Hypothesis
Testing and Its Limitations 91
5.2. Point Estimates of the Posterior Distribution 93
5.2.1. Interval Summaries of the Posterior Distribution 95
5.3. Bayesian Model Evaluation and Comparison 98
5.3.1. Posterior Predictive Checks 99
5.3.2. Bayes Factors 101
5.3.3. The Bayesian Information Criterion 103
5.3.4. The Deviance Information Criterion 105
5.4. Bayesian Model Averaging 106
5.4.1. Occam s Window 107
5.4.2. Markov Chain Monte Carlo Model Composition 109
5.5. Summary 110
5.6. Suggested Readings 110
Contents xvii
6 • Bayesian Linear and Generalized Linear Models 113
6.1. A Motivating Example 113
6.2. The Normal Linear Regression Model 115
6.3. The Bayesian Linear Regression Model 116
6.3.1. Noninformative Priors in the Linear Regression Model 117
6.3.2. Informative Conjugate Priors 123
6.4. Bayesian Generalized Linear Models 130
6.4.1. The Link Function 131
6.4.2. The Logit-Link Function for Logistic
and Multinomial Models 132
6.5. Summary 136
6.6. Suggested Readings 136
APPENDIX 6.1. R CODE FOR CHAPTER 6 138
7 • Missing Data from a Bayesian Perspective 149
7.1. A Nomenclature for Missing Data 149
7.2. Ad Hoc Deletion Methods for Handling
Missing Data 151
7.2.1. Listwise Deletion 151
7.2.2. Pairwise Deletion 152
7.3. Single Imputation Methods 152
7.3.1. Mean Imputation 153
7.3.2. Regression Imputation 153
7.3.3. Stochastic Regression Imputation 154
7.3.4. Hot-Deck Imputation 155
7.3.5. Predictive Mean Matching 156
7.4. Bayesian Methods of Multiple Imputation 156
7.4.1. Data Augmentation 158
7.4.2. Chained Equations 159
7.4.3. EM Bootstrap: A Hybrid Bayesian/Frequentist
Method 160
7.4.4. Bayesian Bootstrap Predictive Mean Matching 163
7.5. Summary 164
7.6. Suggested Readings 165
APPENDIX 7.1. R CODE FOR CHAPTER 7 167
PART III. ADVANCED BAYESIAN MODELING METHODS
8 • Bayesian Multilevel Modeling 179
8.1. Bayesian Random Effects Analysis ofVariance 181
8.2. Revisiting Exchangeability 184
8.3. Bayesian Multilevel Regression 185
8.4. Summary 190
8.5. Suggested Readings 191
APPENDIX 8.1. R CODE FOR CHAPTER 8
192
xv¡¡¡ , Contents
9 • Bayesian Modeling for Continuous
and Categorical Latent Variables 199
9.1. Bayesian Estimation of the CFA Model 201
9. 1. /. Conjugate Priors for CFA Model Parameters 201
9.2. Bayesian SEM 207
9.2.1. Conjugate Priors for SEM Parameters 208
9.2.2. MC MC Sampling for Bayesian SEM 209
9.3. Bayesian Multilevel SEM 213
9.4. Bayesian Growth Curve Modeling 219
9.5. Bayesian Models for Categorical Latent Variables 226
9.5.1. Mixture Model Specification 226
9.5.2. Bayesian Mixture Models 228
9.6. Summary 232
9.7. Suggested Readings 232
APPENDIX 9.1. rjags CODE FOR CHAPTER 9 233
10 • Philosophical Debates in Bayesian
Statistical Inference 283
10.1. A Summary of the Bayesian versus Frequentist Schools
of Statistics 285
10.1.1. Conditioning on Data 285
10.1.2. Inferences Based on Data Actually Observed 286
10.1.3. Quantifying Evidence 287
10.1.4. Summarizing the Bayesian Advantage 287
10.2. Subjective Bayes 290
10.3. Objective Bayes 291
10.4. Final Thoughts: A Call for Evidence-Based
Subjective Bayes 294
References 297
Author Index 307
Subject Index 310
About the Author 318
|
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| isbn | 9781462516513 |
| language | English |
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| spelling | Kaplan, David 1955- Verfasser (DE-588)130554995 aut Bayesian statistics for the social sciences David Kaplan ; series editor's note by Todd D. Little New York ; London The Guilford Press [2014] © 2014 xviii, 318 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Methodology in the social sciences Includes bibliographical references and index " Bridging the gap between traditional classical statistics and a Bayesian approach, David Kaplan provides readers with the concepts and practical skills they need to apply Bayesian methodologies to their data analysis problems. Part I addresses the elements of Bayesian inference, including exchangeability, likelihood, prior/posterior distributions, and the Bayesian central limit theorem. Part II covers Bayesian hypothesis testing, model building, and linear regression analysis, carefully explaining the differences between the Bayesian and frequentist approaches. Part III extends Bayesian statistics to multilevel modeling and modeling for continuous and categorical latent variables. Kaplan closes with a discussion of philosophical issues and argues for an "evidence-based" framework for the practice of Bayesian statistics. Useful features for teaching or self-study: *Includes worked-through, substantive examples, using large-scale educational and social science databases. *Utilizes open-source R software programs available on the CRAN (such as MCMCpack and rjags); readers do not have to master the R language and can easily adapt the example programs to fit individual needs. *Shows readers how to carefully warrant priors on the basis of empirical data. *Companion website features data and code for the book's examples, plus other resources. "-- Social sciences / Statistical methods Bayesian statistical decision theory PSYCHOLOGY / Statistics bisacsh MEDICAL / Nursing / Research & Theory bisacsh EDUCATION / Statistics bisacsh SOCIAL SCIENCE / Statistics bisacsh BUSINESS & ECONOMICS / Statistics bisacsh Medizin Sozialwissenschaften Statistik Wirtschaft Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 s Statistik (DE-588)4056995-0 s Bayes-Verfahren (DE-588)4204326-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027491332&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kaplan, David 1955- Bayesian statistics for the social sciences Social sciences / Statistical methods Bayesian statistical decision theory PSYCHOLOGY / Statistics bisacsh MEDICAL / Nursing / Research & Theory bisacsh EDUCATION / Statistics bisacsh SOCIAL SCIENCE / Statistics bisacsh BUSINESS & ECONOMICS / Statistics bisacsh Medizin Sozialwissenschaften Statistik Wirtschaft Sozialwissenschaften (DE-588)4055916-6 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4055916-6 (DE-588)4204326-8 (DE-588)4056995-0 |
| title | Bayesian statistics for the social sciences |
| title_auth | Bayesian statistics for the social sciences |
| title_exact_search | Bayesian statistics for the social sciences |
| title_full | Bayesian statistics for the social sciences David Kaplan ; series editor's note by Todd D. Little |
| title_fullStr | Bayesian statistics for the social sciences David Kaplan ; series editor's note by Todd D. Little |
| title_full_unstemmed | Bayesian statistics for the social sciences David Kaplan ; series editor's note by Todd D. Little |
| title_short | Bayesian statistics for the social sciences |
| title_sort | bayesian statistics for the social sciences |
| topic | Social sciences / Statistical methods Bayesian statistical decision theory PSYCHOLOGY / Statistics bisacsh MEDICAL / Nursing / Research & Theory bisacsh EDUCATION / Statistics bisacsh SOCIAL SCIENCE / Statistics bisacsh BUSINESS & ECONOMICS / Statistics bisacsh Medizin Sozialwissenschaften Statistik Wirtschaft Sozialwissenschaften (DE-588)4055916-6 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Social sciences / Statistical methods Bayesian statistical decision theory PSYCHOLOGY / Statistics MEDICAL / Nursing / Research & Theory EDUCATION / Statistics SOCIAL SCIENCE / Statistics BUSINESS & ECONOMICS / Statistics Medizin Sozialwissenschaften Statistik Wirtschaft Bayes-Verfahren |
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