Bayesian methods: a social and behavioral sciences approach
Requiring only a background in introductory statistics, calculus, and matrix algebra, Bayesian Methods: A Social and Behavioral Sciences Approach provides detailed explanations of derivations and theories using a computationally oriented approach. This second edition features new updates on topics s...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
Chapman & Hall/CRC
2008
|
| Ausgabe: | 2. ed. |
| Schriftenreihe: | Statistics in the social and behavioral sciences series
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Inhaltsverzeichnis |
| Zusammenfassung: | Requiring only a background in introductory statistics, calculus, and matrix algebra, Bayesian Methods: A Social and Behavioral Sciences Approach provides detailed explanations of derivations and theories using a computationally oriented approach. This second edition features new updates on topics such as Markov chain Monte Carlo (MCMC) algorithms, perfect sampling, and Bayesian nonparametrics. The author emphasizes the R computing environment as well as the Bugs simulation program. With various examples and exercise problems, this text remains an ideal resource for statisticians and is especially designed to help political and social scientists develop a tool chest for statistical analysis. |
| Beschreibung: | Literaturverz.: S. 591 - 656 |
| Beschreibung: | XXXVII, 711 S. graph. Darst. |
| ISBN: | 9781584885627 1584885629 |
Internformat
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| 245 | 1 | 0 | |a Bayesian methods |b a social and behavioral sciences approach |c Jeff Gill |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton [u.a.] |b Chapman & Hall/CRC |c 2008 | |
| 300 | |a XXXVII, 711 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Statistics in the social and behavioral sciences series | |
| 500 | |a Literaturverz.: S. 591 - 656 | ||
| 520 | 3 | |a Requiring only a background in introductory statistics, calculus, and matrix algebra, Bayesian Methods: A Social and Behavioral Sciences Approach provides detailed explanations of derivations and theories using a computationally oriented approach. This second edition features new updates on topics such as Markov chain Monte Carlo (MCMC) algorithms, perfect sampling, and Bayesian nonparametrics. The author emphasizes the R computing environment as well as the Bugs simulation program. With various examples and exercise problems, this text remains an ideal resource for statisticians and is especially designed to help political and social scientists develop a tool chest for statistical analysis. | |
| 650 | 4 | |a Decisión estadística | |
| 650 | 7 | |a Methode van Bayes |2 gtt | |
| 650 | 4 | |a Teorías bayesian | |
| 650 | 4 | |a Sozialwissenschaften | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Social sciences |x Statistical methods | |
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| 650 | 0 | 7 | |a Statistik |0 (DE-588)4056995-0 |2 gnd |9 rswk-swf |
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Datensatz im Suchindex
| _version_ | 1804137192562360320 |
|---|---|
| adam_text | Contents
Preface
xix
Preface
to the First Edition
xxix
1
Background and Introduction
1
1.1
Introduction
............................ 1
1.2
Motivation and Justification
................... 4
1.3
Why Are We Uncertain about Probability?
.......... 6
1.3.1
Required Probability Principles
............. 8
1.4
Bayes
Law
............................ 10
1.4.1
Bayes
Law for Multiple Events
............. 12
1.5
Conditional Inference with
Bayes
Law
............. 16
1.5.1
Statistical Models with
Bayes
Law
........... 18
1.6
Historical Comments
....................... 21
1.7
The Scientific Process in Our Social Sciences
......... 23
1.7.1
Bayesian Statistics as a Scientific Approach to Social
and Behavioral Data Analysis
.............. 26
1.8
Introducing Markov Chain Monte Carlo Techniques
...... 29
1.8.1
Simple Gibbs Sampling
................. 30
1.8.2
Simple Metropolis Sampling
............... 33
1.9
Exercises
.............................. 37
2
Specifying Bayesian Models
39
2.1
Purpose
.............................. 39
2.2
Likelihood Theory and Estimation
............... 40
2.3
The Basic Bayesian Framework
................. 43
2.3.1
Developing the Bayesian Inference Engine
....... 43
2.3.2
Summarizing Posterior Distributions with Intervals
. . 45
2.3.3
Beta-Binomial Model
................... 52
vu
vin
2.4
Bayesian Learning
....................... 56
2.5
Comments on Prior Distributions
................ 60
2.6
Bayesian Versus Non-Bayesian Approaches
........... 62
2.7
Exercises
.............................. 66
2.8
Computational Addendum:
R
for Basic Analysis
....... 70
3
The Normal and Student s-t Models
73
3.1
Why Be Normal?
......................... 73
3.2
The Normal Model with Variance Known
........... 74
3.3
The Normal Model with Mean Known
............. 77
3.4
The Normal Model with Both Mean and Variance Unknown
. 79
3.5
Multivariate Normal Model,
μ
and
Σ
Both Unknown
..... 81
3.6
Simulated Effects of Differing Priors
.............. 87
3.7
Some Normal Comments
..................... 89
3.8
The Student s-t Model
...................... 90
3.9
Normal Mixture Models
........·............. 95
3.10
Exercises
.............................. 98
3.11
Computational Addendum: Normal Examples
.........100
3.11.1
Normal Example with Variance Known
........100
3.11.2
Divariate
Normal Simulation Example
.........101
3.11.3
Multivariate Normal Example, Health Data
......102
4
The Bayesian Linear Model
105
4.1
The Basic Regression Model
...................105
4.1.1 Uninformative
Priors for the Linear Model
.......107
4.1.2
Conjugate Priors for the Linear Model
.........
Ill
4.1.3
Conjugate Caveats for the Cautious and Careful
. . . 114
4.2
Posterior Predictive Distribution for the Data
.........116
4.3
Linear Regression with Heteroscedasticity
...........123
4.4
Exercises
..............................128
4.5
Computational Addendum
....................130
4.5.1
Palm Beach County Normal Model
...........130
4.5.2
Educational Outcomes Model
..............132
4.5.3
Ancient China Conflict Model
..............133
їх
5
The Bayesian Prior
135
5.1
A Prior Discussion of Priors
...................135
5.2
A Plethora of Priors
.......................136
5.3
Conjugate Prior Forms
......................138
5.3.1
Example: Conjugacy in Exponential Specifications
. . 139
5.3.2
The Exponential Family Form
..............140
5.3.3
Limitations of Conjugacy
................144
5.4 Uninformative
Prior Distributions
...............144
5.4.1
Uniform Priors
......................145
5.4.2
Jeffreys Prior
.......................148
5.4.3
Reference Priors
.....................153
5.4.4
Improper Priors
......................155
5.5
Informative Prior Distributions
.................156
5.5.1
Power Priors
.......................157
5.5.2
Elicited Priors
......................159
5.6
Hybrid Prior Forms
........................175
5.6.1
Spike and Slab Priors for Linear Models
........175
5.6.2
Maximum Entropy Priors
................177
5.6.3
Histogram Priors
.....................179
5.7
Nonparametric Priors
......................180
5.8
Bayesian Shrinkage
........................183
5.9
Exercises
..............................185
6
Assessing Model Quality
191
6.1
Motivation
.............................191
6.1.1
Posterior Data Replication
................193
6.1.2
Likelihood Function Robustness
.............196
6.2
Basic Sensitivity Analysis
....................198
6.2.1
Global Sensitivity Analysis
...............198
6.2.2
Local Sensitivity Analysis
................202
6.2.3
Global and Local Sensitivity Analysis with Recidivism
Data
............................205
6.3
Robustness Evaluation
......................207
6.3.1
Global Robustness
....................209
6.3.2
Local Robustness
.....................212
6.3.3
Bayesian Specification Robustness
...........216
χ
6.4
Comparing Data to the Posterior Predictive Distribution
. . . 216
6.5
Simple Bayesian Model Averaging
...............219
6.6
Concluding Comments on Model Quality
............220
6.7
Exercises
..............................223
6.8
Computational Addendum
....................225
6.8.1
R
Code for the Linear Model
..............225
6.8.2
JAGS Code for the Attitudes Model
...........226
7
Bayesian Hypothesis Testing and the
Bayes
Factor
229
7.1
Motivation
.............................229
7.2
Bayesian Inference and Hypothesis Testing
...........231
7.2.1
Problems with Conventional Hypothesis Testing in the
Social Sciences: Quasi-Frequentism
...........231
7.2.2
Attempting a Bayesian Approximation to
Frequentisi
Hypothesis Testing
....................238
7.2.3
Bayesian Decision Theory
................239
7.3
The
Bayes
Factor as Evidence
..................241
7.3.1
Bayes
Factors for Difference of Means Test
.......247
7.3.2
Bayes
Factors and Improper Priors
...........248
7.3.3
Two-Sided Hypothesis Tests and
Bayes
Factors
.... 255
7.3.4
Challenging Aspects of
Bayes
Factors
.........257
7.4
The Bayesian Information Criterion
(BIC)
...........258
7.5
The Deviance Information Criterion (DIC)
...........260
7.5.1
Some Qualifications
...................264
7.6
Comparing Posterior Distributions with the Kullback-Leibler
Distance
..............................265
7.7
Laplace Approximation of Bayesian Posterior Densities
.... 266
7.8
Exercises
..............................271
8
Monte Carlo and Related Methods
275
8.1
Background
............................275
8.2
Basic Monte Carlo Integration
..................277
8.3
Rejection Sampling
........................282
8.3.1
Continuous Form with Bounded Support
........283
8.3.2
Continuous Form with Unbounded Support
......286
8.4
Classical Numerical Integration
.................291
Xl
8.4.1
Newton-Cotes
.......................292
8.5
Gaussian
Quadrature
.......................296
8.5.1
Redux
...........................300
8.6
Importance
Sampling and Sampling Importance Resampling
. 301
8.6.1
Importance Sampling for Producing HPD Intervals
. . 307
8.7
Mode Finding and the EM Algorithm
.............309
8.7.1
Deriving the EM Algorithm
...............310
8.7.2
Convergence of the EM Algorithm
...........314
8.7.3
Extensions to the EM Algorithm
............322
8.7.4
Additional Comments on EM
..............324
8.7.5
EM for Exponential Families
..............325
8.8
Survey of Random Number Generation
.............330
8.9
Concluding Remarks
.......................333
8.10
Exercises
..............................334
8.11
Computational Addendum:
R
Code for Importance Sampling
337
Basics of Markov Chain Monte Carlo
343
9.1
Who Is Markov and What Is He Doing with Chains?
.....343
9.1.1
What Is a Markov Chain?
................344
9.1.2
A Markov Chain Illustration
..............346
9.1.3
The Chapman-Kolrnogorov Equations
.........349
9.1.4
Marginal Distributions
..................350
9.2
General Properties of Markov Chains
..............351
9.2.1
Homogeneity
.......................351
9.2.2
Irreducibility
.......................352
9.2.3
Recurrence
........................352
9.2.4
Stationarity
........................353
9.2.5
Ergodicity
.........................354
9.3
The Gibbs Sampler
........................356
9.3.1
Description of the Algorithm
..............356
9.3.2
Handling Missing Dichotomous Data with the Gibbs
Sampler
..........................358
9.3.3
Summary of Properties of the Gibbs Sampler
.....367
9.4
The Metropolis-Hastings Algorithm
...............368
9.4.1
Background
........................368
9.4.2
Description of the Algorithm
..............368
хгі
9.4.3
Metropolis-Hastings Properties
.............370
9.4.4
Metropolis-Hastings Derivation
.............371
9.4.5
The Transition Kernel
..................373
9.4.6
Example: Estimating
a Divariate
Normal Density
. . . 374
9.5
The Hit-and-Run Algorithm
...................376
9.6
The Data Augmentation Algorithm
...............379
9.7
Historical Comments
.......................384
9.7.1
Pull Circle?
........................386
9.8
Exercises
..............................387
9.9
Computational Addendum: Simple
R
Graphing Routines for
MCMC
..............................391
10
Bayesian Hierarchical Models
395
10.1
Introduction to Multilevel Models
................395
10.2
Standard Multilevel Linear Models
...............396
10.2.1
Basic Structure of the Bayesian Hierarchical Model
. . 400
10.3
A Poisson-Gamma
Hierarchical Model
.............404
10.4
The General Role of Priors and Hyperpriors
..........412
10.5
Exchangeability
..........................417
10.5.1
The General Bayesian Hierarchical Linear Model
. . . 422
10.6
Empirical
Bayes
..........................425
10.7
Exercises
..............................428
10.8
Computational Addendum: Instructions for Running JAGS,
Trade Data Model
........................431
11
Some Markov Chain Monte Carlo Theory
433
11.1
Motivation
......,......................433
11.2
Measure and Probability Preliminaries
.............433
11.3
Specific Markov Chain Properties
................435
11.3.1
^-Irreducibility
......................435
11.3.2
Closed and Absorbing Sets
...............436
11.3.3
Homogeneity and Periodicity
..............436
11.3.4
Null and Positive Recurrence
..............437
11.3.5
Transience
.........................437
11.3.6
Markov Chain Stability
.................
438
11.3.7
Ergodicity
.........................439
хш
11.4
Defining and Reaching Convergence
..............440
11.5
Rates of Convergence
.......................442
11.6
Implementation Concerns
....................447
11.6.1
Mixing
...........................450
11.6.2
Partial Convergence for Metropolis-Hastings
......451
11.6.3
Partial Convergence for the Gibbs Sampler
......453
11.7
Exercises
..............................456
12
Utilitarian Markov Chain Monte Carlo
459
12.1
Practical Considerations and Admonitions
...........460
12.1.1
Starting Points
......................460
12.1.2
Thinning the Chain
...................461
12.1.3
The Burn-In Period
...................462
12.2
Assessing Convergence of Markov Chains
...........463
12.2.1
Autocorrelation
......................469
12.2.2
Graphical Diagnostics
..................472
12.2.3
Standard Empirical Diagnostics
.............475
12.2.4
Other Empirical Diagnostics
...............489
12.2.5
Why Not to Worry Too Much About Stationarity
... 492
12.3
Mixing and Acceleration
.....................493
12.3.1
Reparameterization
....................494
12.,3..2
Grouping and Collapsing the Gibbs Sampler
......496
12.3.3
Adding Auxiliary Variables
...............497
12.3.4
The Slice Sampler
....................498
12.4
Producing the Marginal Likelihood Integral from Metropolis-
Hastings Output
.........................499
12.5
Rao-Blackwellizing for Improved Variance Estimation
.... 502
12.6
Exercises
..............................505
12.7
Computational Addendum: Code for Chapter Examples
. . . 507
12.7.1
R
Code for the Death Penalty Support Model
.....507
12.7.2
Bugs Code for the Military Personnel Model
......508
13
Advanced Markov Chain Monte Carlo
511
13.1
Simulated Annealing
.......................511
13.1.1
General Points on Simulated Annealing
........516
13.1.2
Metropolis-Coupling
...................517
XIV
13.1.3
Simulated Tempering and Tempered Transitions
... 518
13.1.4
Dynamic Tempered Transitions
.............523
13.2
Reversible Jump Algorithms
...................525
13.3
Perfect Sampling
.........................527
13.4
Exercises
..............................531
Appendix A Generalized Linear Model Review
535
A.I Terms
...............................535
A.
1.1
The Linear Regression Model
..............538
A.2 The Generalized Linear Model
.................541
A.2.1 Defining the Link Function
...............541
A.2.2 Deviance Residuals
....................544
A.3 Numerical Maximum Likelihood
.................545
A.3.1 Newton-Raphson and Root Finding
...........545
A.4 Quasi-Likelihood
.........................553
A.5 Exercises
..............................557
A.6
R
for Generalized Linear Models
.................562
Appendix
В
Common Probability Distributions
567
Appendix
С
Introduction to the BUGS Language
573
C.I General Process
..........................573
C.2 Technical Background on the Algorithm
............574
C.3 WinBUGS Features
.........................583
C.3.1 BUGS and WinBUGS Code for the Marriage Rates Model
586
C.4 JAGS Programming
........................588
References
591
Author Index
657
Subject Index
687
|
| adam_txt |
Contents
Preface
xix
Preface
to the First Edition
xxix
1
Background and Introduction
1
1.1
Introduction
. 1
1.2
Motivation and Justification
. 4
1.3
Why Are We Uncertain about Probability?
. 6
1.3.1
Required Probability Principles
. 8
1.4
Bayes'
Law
. 10
1.4.1
Bayes'
Law for Multiple Events
. 12
1.5
Conditional Inference with
Bayes'
Law
. 16
1.5.1
Statistical Models with
Bayes'
Law
. 18
1.6
Historical Comments
. 21
1.7
The Scientific Process in Our Social Sciences
. 23
1.7.1
Bayesian Statistics as a Scientific Approach to Social
and Behavioral Data Analysis
. 26
1.8
Introducing Markov Chain Monte Carlo Techniques
. 29
1.8.1
Simple Gibbs Sampling
. 30
1.8.2
Simple Metropolis Sampling
. 33
1.9
Exercises
. 37
2
Specifying Bayesian Models
39
2.1
Purpose
. 39
2.2
Likelihood Theory and Estimation
. 40
2.3
The Basic Bayesian Framework
. 43
2.3.1
Developing the Bayesian Inference Engine
. 43
2.3.2
Summarizing Posterior Distributions with Intervals
. . 45
2.3.3
Beta-Binomial Model
. 52
vu
vin
2.4
Bayesian "Learning"
. 56
2.5
Comments on Prior Distributions
. 60
2.6
Bayesian Versus Non-Bayesian Approaches
. 62
2.7
Exercises
. 66
2.8
Computational Addendum:
R
for Basic Analysis
. 70
3
The Normal and Student's-t Models
73
3.1
Why Be Normal?
. 73
3.2
The Normal Model with Variance Known
. 74
3.3
The Normal Model with Mean Known
. 77
3.4
The Normal Model with Both Mean and Variance Unknown
. 79
3.5
Multivariate Normal Model,
μ
and
Σ
Both Unknown
. 81
3.6
Simulated Effects of Differing Priors
. 87
3.7
Some Normal Comments
. 89
3.8
The Student's-t Model
. 90
3.9
Normal Mixture Models
.·. 95
3.10
Exercises
. 98
3.11
Computational Addendum: Normal Examples
.100
3.11.1
Normal Example with Variance Known
.100
3.11.2
Divariate
Normal Simulation Example
.101
3.11.3
Multivariate Normal Example, Health Data
.102
4
The Bayesian Linear Model
105
4.1
The Basic Regression Model
.105
4.1.1 Uninformative
Priors for the Linear Model
.107
4.1.2
Conjugate Priors for the Linear Model
.
Ill
4.1.3
Conjugate Caveats for the Cautious and Careful
. . . 114
4.2
Posterior Predictive Distribution for the Data
.116
4.3
Linear Regression with Heteroscedasticity
.123
4.4
Exercises
.128
4.5
Computational Addendum
.130
4.5.1
Palm Beach County Normal Model
.130
4.5.2
Educational Outcomes Model
.132
4.5.3
Ancient China Conflict Model
.133
їх
5
The Bayesian Prior
135
5.1
A Prior Discussion of Priors
.135
5.2
A Plethora of Priors
.136
5.3
Conjugate Prior Forms
.138
5.3.1
Example: Conjugacy in Exponential Specifications
. . 139
5.3.2
The Exponential Family Form
.140
5.3.3
Limitations of Conjugacy
.144
5.4 Uninformative
Prior Distributions
.144
5.4.1
Uniform Priors
.145
5.4.2
Jeffreys Prior
.148
5.4.3
Reference Priors
.153
5.4.4
Improper Priors
.155
5.5
Informative Prior Distributions
.156
5.5.1
Power Priors
.157
5.5.2
Elicited Priors
.159
5.6
Hybrid Prior Forms
.175
5.6.1
Spike and Slab Priors for Linear Models
.175
5.6.2
Maximum Entropy Priors
.177
5.6.3
Histogram Priors
.179
5.7
Nonparametric Priors
.180
5.8
Bayesian Shrinkage
.183
5.9
Exercises
.185
6
Assessing Model Quality
191
6.1
Motivation
.191
6.1.1
Posterior Data Replication
.193
6.1.2
Likelihood Function Robustness
.196
6.2
Basic Sensitivity Analysis
.198
6.2.1
Global Sensitivity Analysis
.198
6.2.2
Local Sensitivity Analysis
.202
6.2.3
Global and Local Sensitivity Analysis with Recidivism
Data
.205
6.3
Robustness Evaluation
.207
6.3.1
Global Robustness
.209
6.3.2
Local Robustness
.212
6.3.3
Bayesian Specification Robustness
.216
χ
6.4
Comparing Data to the Posterior Predictive Distribution
. . . 216
6.5
Simple Bayesian Model Averaging
.219
6.6
Concluding Comments on Model Quality
.220
6.7
Exercises
.223
6.8
Computational Addendum
.225
6.8.1
R
Code for the Linear Model
.225
6.8.2
JAGS Code for the Attitudes Model
.226
7
Bayesian Hypothesis Testing and the
Bayes
Factor
229
7.1
Motivation
.229
7.2
Bayesian Inference and Hypothesis Testing
.231
7.2.1
Problems with Conventional Hypothesis Testing in the
Social Sciences: Quasi-Frequentism
.231
7.2.2
Attempting a Bayesian Approximation to
Frequentisi
Hypothesis Testing
.238
7.2.3
Bayesian Decision Theory
.239
7.3
The
Bayes
Factor as Evidence
.241
7.3.1
Bayes
Factors for Difference of Means Test
.247
7.3.2
Bayes
Factors and Improper Priors
.248
7.3.3
Two-Sided Hypothesis Tests and
Bayes
Factors
. 255
7.3.4
Challenging Aspects of
Bayes
Factors
.257
7.4
The Bayesian Information Criterion
(BIC)
.258
7.5
The Deviance Information Criterion (DIC)
.260
7.5.1
Some Qualifications
.264
7.6
Comparing Posterior Distributions with the Kullback-Leibler
Distance
.265
7.7
Laplace Approximation of Bayesian Posterior Densities
. 266
7.8
Exercises
.271
8
Monte Carlo and Related Methods
275
8.1
Background
.275
8.2
Basic Monte Carlo Integration
.277
8.3
Rejection Sampling
.282
8.3.1
Continuous Form with Bounded Support
.283
8.3.2
Continuous Form with Unbounded Support
.286
8.4
Classical Numerical Integration
.291
Xl
8.4.1
Newton-Cotes
.292
8.5
Gaussian
Quadrature
.296
8.5.1
Redux
.300
8.6
Importance
Sampling and Sampling Importance Resampling
. 301
8.6.1
Importance Sampling for Producing HPD Intervals
. . 307
8.7
Mode Finding and the EM Algorithm
.309
8.7.1
Deriving the EM Algorithm
.310
8.7.2
Convergence of the EM Algorithm
.314
8.7.3
Extensions to the EM Algorithm
.322
8.7.4
Additional Comments on EM
.324
8.7.5
EM for Exponential Families
.325
8.8
Survey of Random Number Generation
.330
8.9
Concluding Remarks
.333
8.10
Exercises
.334
8.11
Computational Addendum:
R
Code for Importance Sampling
337
Basics of Markov Chain Monte Carlo
343
9.1
Who Is Markov and What Is He Doing with Chains?
.343
9.1.1
What Is a Markov Chain?
.344
9.1.2
A Markov Chain Illustration
.346
9.1.3
The Chapman-Kolrnogorov Equations
.349
9.1.4
Marginal Distributions
.350
9.2
General Properties of Markov Chains
.351
9.2.1
Homogeneity
.351
9.2.2
Irreducibility
.352
9.2.3
Recurrence
.352
9.2.4
Stationarity
.353
9.2.5
Ergodicity
.354
9.3
The Gibbs Sampler
.356
9.3.1
Description of the Algorithm
.356
9.3.2
Handling Missing Dichotomous Data with the Gibbs
Sampler
.358
9.3.3
Summary of Properties of the Gibbs Sampler
.367
9.4
The Metropolis-Hastings Algorithm
.368
9.4.1
Background
.368
9.4.2
Description of the Algorithm
.368
хгі
9.4.3
Metropolis-Hastings Properties
.370
9.4.4
Metropolis-Hastings Derivation
.371
9.4.5
The Transition Kernel
.373
9.4.6
Example: Estimating
a Divariate
Normal Density
. . . 374
9.5
The Hit-and-Run Algorithm
.376
9.6
The Data Augmentation Algorithm
.379
9.7
Historical Comments
.384
9.7.1
Pull Circle?
.386
9.8
Exercises
.387
9.9
Computational Addendum: Simple
R
Graphing Routines for
MCMC
.391
10
Bayesian Hierarchical Models
395
10.1
Introduction to Multilevel Models
.395
10.2
Standard Multilevel Linear Models
.396
10.2.1
Basic Structure of the Bayesian Hierarchical Model
. . 400
10.3
A Poisson-Gamma
Hierarchical Model
.404
10.4
The General Role of Priors and Hyperpriors
.412
10.5
Exchangeability
.417
10.5.1
The General Bayesian Hierarchical Linear Model
. . . 422
10.6
Empirical
Bayes
.425
10.7
Exercises
.428
10.8
Computational Addendum: Instructions for Running JAGS,
Trade Data Model
.431
11
Some Markov Chain Monte Carlo Theory
433
11.1
Motivation
.,.433
11.2
Measure and Probability Preliminaries
.433
11.3
Specific Markov Chain Properties
.435
11.3.1
^-Irreducibility
.435
11.3.2
Closed and Absorbing Sets
.436
11.3.3
Homogeneity and Periodicity
.436
11.3.4
Null and Positive Recurrence
.437
11.3.5
Transience
.437
11.3.6
Markov Chain Stability
.
438
11.3.7
Ergodicity
.439
хш
11.4
Defining and Reaching Convergence
.440
11.5
Rates of Convergence
.442
11.6
Implementation Concerns
.447
11.6.1
Mixing
.450
11.6.2
Partial Convergence for Metropolis-Hastings
.451
11.6.3
Partial Convergence for the Gibbs Sampler
.453
11.7
Exercises
.456
12
Utilitarian Markov Chain Monte Carlo
459
12.1
Practical Considerations and Admonitions
.460
12.1.1
Starting Points
.460
12.1.2
Thinning the Chain
.461
12.1.3
The Burn-In Period
.462
12.2
Assessing Convergence of Markov Chains
.463
12.2.1
Autocorrelation
.469
12.2.2
Graphical Diagnostics
.472
12.2.3
Standard Empirical Diagnostics
.475
12.2.4
Other Empirical Diagnostics
.489
12.2.5
Why Not to Worry Too Much About Stationarity
. 492
12.3
Mixing and Acceleration
.493
12.3.1
Reparameterization
.494
12.,3.2
Grouping and Collapsing the Gibbs Sampler
.496
12.3.3
Adding Auxiliary Variables
.497
12.3.4
The Slice Sampler
.498
12.4
Producing the Marginal Likelihood Integral from Metropolis-
Hastings Output
.499
12.5
Rao-Blackwellizing for Improved Variance Estimation
. 502
12.6
Exercises
.505
12.7
Computational Addendum: Code for Chapter Examples
. . . 507
12.7.1
R
Code for the Death Penalty Support Model
.507
12.7.2
Bugs Code for the Military Personnel Model
.508
13
Advanced Markov Chain Monte Carlo
511
13.1
Simulated Annealing
.511
13.1.1
General Points on Simulated Annealing
.516
13.1.2
Metropolis-Coupling
.517
XIV
13.1.3
Simulated Tempering and Tempered Transitions
. 518
13.1.4
Dynamic Tempered Transitions
.523
13.2
Reversible Jump Algorithms
.525
13.3
Perfect Sampling
.527
13.4
Exercises
.531
Appendix A Generalized Linear Model Review
535
A.I Terms
.535
A.
1.1
The Linear Regression Model
.538
A.2 The Generalized Linear Model
.541
A.2.1 Defining the Link Function
.541
A.2.2 Deviance Residuals
.544
A.3 Numerical Maximum Likelihood
.545
A.3.1 Newton-Raphson and Root Finding
.545
A.4 Quasi-Likelihood
.553
A.5 Exercises
.557
A.6
R
for Generalized Linear Models
.562
Appendix
В
Common Probability Distributions
567
Appendix
С
Introduction to the BUGS Language
573
C.I General Process
.573
C.2 Technical Background on the Algorithm
.574
C.3 WinBUGS Features
.583
C.3.1 BUGS and WinBUGS Code for the Marriage Rates Model
586
C.4 JAGS Programming
.588
References
591
Author Index
657
Subject Index
687 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Gill, Jeff |
| author_facet | Gill, Jeff |
| author_role | aut |
| author_sort | Gill, Jeff |
| author_variant | j g jg |
| building | Verbundindex |
| bvnumber | BV022949801 |
| 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 | CM 4000 QH 233 |
| classification_tum | SOZ 720f MAT 624f SOZ 260f |
| ctrlnum | (OCoLC)144774105 (DE-599)DNB 2007025535 |
| 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 Psychologie Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Soziologie Psychologie Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV022949801 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:01:45Z |
| indexdate | 2024-07-09T21:08:23Z |
| institution | BVB |
| isbn | 9781584885627 1584885629 |
| language | English |
| lccn | 2007025535 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016154289 |
| oclc_num | 144774105 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-20 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-188 DE-83 |
| owner_facet | DE-91G DE-BY-TUM DE-473 DE-BY-UBG DE-20 DE-355 DE-BY-UBR DE-19 DE-BY-UBM DE-188 DE-83 |
| physical | XXXVII, 711 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Statistics in the social and behavioral sciences series |
| spelling | Gill, Jeff Verfasser aut Bayesian methods a social and behavioral sciences approach Jeff Gill 2. ed. Boca Raton [u.a.] Chapman & Hall/CRC 2008 XXXVII, 711 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Statistics in the social and behavioral sciences series Literaturverz.: S. 591 - 656 Requiring only a background in introductory statistics, calculus, and matrix algebra, Bayesian Methods: A Social and Behavioral Sciences Approach provides detailed explanations of derivations and theories using a computationally oriented approach. This second edition features new updates on topics such as Markov chain Monte Carlo (MCMC) algorithms, perfect sampling, and Bayesian nonparametrics. The author emphasizes the R computing environment as well as the Bugs simulation program. With various examples and exercise problems, this text remains an ideal resource for statisticians and is especially designed to help political and social scientists develop a tool chest for statistical analysis. Decisión estadística Methode van Bayes gtt Teorías bayesian Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Sozialwissenschaften (DE-588)4055916-6 gnd rswk-swf Bayes-Entscheidungstheorie (DE-588)4144220-9 s DE-604 Sozialwissenschaften (DE-588)4055916-6 s Statistik (DE-588)4056995-0 s Bayes-Verfahren (DE-588)4204326-8 s DE-188 http://www.loc.gov/catdir/enhancements/fy0728/2007025535-d.html Publisher description Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016154289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gill, Jeff Bayesian methods a social and behavioral sciences approach Decisión estadística Methode van Bayes gtt Teorías bayesian Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Statistik (DE-588)4056995-0 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Sozialwissenschaften (DE-588)4055916-6 gnd |
| subject_GND | (DE-588)4144220-9 (DE-588)4056995-0 (DE-588)4204326-8 (DE-588)4055916-6 |
| title | Bayesian methods a social and behavioral sciences approach |
| title_auth | Bayesian methods a social and behavioral sciences approach |
| title_exact_search | Bayesian methods a social and behavioral sciences approach |
| title_exact_search_txtP | Bayesian methods a social and behavioral sciences approach |
| title_full | Bayesian methods a social and behavioral sciences approach Jeff Gill |
| title_fullStr | Bayesian methods a social and behavioral sciences approach Jeff Gill |
| title_full_unstemmed | Bayesian methods a social and behavioral sciences approach Jeff Gill |
| title_short | Bayesian methods |
| title_sort | bayesian methods a social and behavioral sciences approach |
| title_sub | a social and behavioral sciences approach |
| topic | Decisión estadística Methode van Bayes gtt Teorías bayesian Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Entscheidungstheorie (DE-588)4144220-9 gnd Statistik (DE-588)4056995-0 gnd Bayes-Verfahren (DE-588)4204326-8 gnd Sozialwissenschaften (DE-588)4055916-6 gnd |
| topic_facet | Decisión estadística Methode van Bayes Teorías bayesian Sozialwissenschaften Bayesian statistical decision theory Social sciences Statistical methods Bayes-Entscheidungstheorie Statistik Bayes-Verfahren |
| url | http://www.loc.gov/catdir/enhancements/fy0728/2007025535-d.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016154289&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT gilljeff bayesianmethodsasocialandbehavioralsciencesapproach |