Applied Bayesian hierarchical methods:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
CRC Press
2010
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XIII, 590 S. graph. Darst., Kt. |
| ISBN: | 9781584887201 1584887206 |
Staff View
MARC
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| 245 | 1 | 0 | |a Applied Bayesian hierarchical methods |c Peter D. Congdon |
| 264 | 1 | |a Boca Raton, Fla. [u.a.] |b CRC Press |c 2010 | |
| 300 | |a XIII, 590 S. |b graph. Darst., Kt. | ||
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| 500 | |a Includes bibliographical references and index | ||
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| 650 | 4 | |a Bayesian statistical decision theory | |
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Record in the Search Index
| _version_ | 1804143849157689344 |
|---|---|
| adam_text | Contents
Preface
xi
Author
xiii
Bayesian Methods for Complex Data: Estimation
and Inference
1
1.1
Introduction
........................... 1
1.2
Posterior Inference from
Bayes
Formula
............ 3
1.3
Markov Chain Monte Carlo Sampling in Relation to
Monte Carlo Methods: Obtaining Posterior Inferences
.... 4
1.4
Hierarchical
Bayes
Applications
................ 6
1.5
Metropolis Sampling
....................... 9
1.6
Choice of Proposal Density
................... 11
1.7
Obtaining Full Conditional Densities
............. 12
1.8
Metropolis-Hastings Sampling
................. 15
1.9
Gibbs Sampling
......................... 19
1.10
Assessing Efficiency and Convergence:
Ways of Improving Convergence
................ 20
1.10.1
Hierarchical model parameterization
to improve convergence
................. 23
1.10.2
Multiple chain methods
................. 24
1.11
Choice of Prior Density
..................... 26
1.11.1
Including evidence
.................... 27
1.11.2
Assessing posterior sensitivity: Robust priors
..... 28
1.11.3
Problems in prior selection in hierarchical
Bayes
models
....................... 31
Appendix: Computational Notes
................... 34
Model Fit, Comparison, and Checking
43
2.1
Introduction
........................... 43
2.2
Formal Methods: Approximating Marginal Likelihoods
... 45
2.2.1
Importance and bridge sampling estimates
....... 47
2.2.2
Path sampling
...................... 49
2.2.3
Marginal likelihood for hierarchical models
...... 50
2.3
Effective Model Dimension and Deviance
Information Criterion
...................... 54
2.4
Variance Component Choice and Model Averaging
...... 60
vi
Contents
2.5
Predictive Methods for Model Choice and Checking
..... 67
2.5.1
Predictive model checking and choice
.......... 67
2.5.2
Posterior predictive model checks
............ 70
2.5.3
Mixed predictive checks
................. 72
2.6
Estimating Posterior Model Probabilities
........... 76
2.6.1
Random effects models
.................. 80
Appendix: Computational Notes
................... 81
3
Hierarchical Estimation for Exchangeable Units:
Continuous and Discrete Mixture Approaches
89
3.1
Introduction
........................... 89
3.2
Hierarchical Priors for Ensemble Estimation using
Continuous Mixtures
...................... 91
3.3
The Normal-Normal Hierarchical Model and Its
Applications
........................... 93
3.4
Prior for Second Stage Variance
................ 97
3.4.1
Nonconjugate priors
................... 99
3.5
Multivariate Meta-Analysis
................... 100
3.6
Heterogeneity in Count Data: Hierarchical
Poisson
Models
.......................... 104
3.6.1
Nonconjugate
Poisson
mixing
.............. 107
3.7
Binomial and Multinomial Heterogeneity
........... 109
3.7.1
Nonconjugate priors for binomial mixing
........
Ill
3.7.2
Multinomial mixtures
.................. 113
3.7.3
Ecological inference using mixture models
....... 114
3.8
Discrete Mixtures and Nonparametric
Smoothing Methods
....................... 116
3.8.1
Finite mixtures of parametric densities
......... 117
3.8.2
Finite mixtures of standard densities
.......... 118
3.8.3
Inference in mixture models
............... 119
3.8.4
Particular types of discrete mixture model
....... 121
3.8.5
The logistic-normal alternative to the
Dirichlet prior
...................... 123
3.9
Nonparametric Mixing via Dirichlet Process
and Polya Tree Priors
...................... 124
3.9.1
Specifying the baseline density
............. 127
3.9.2
Truncated Dirichlet processes and
stick-breaking priors
................... 128
3.9.3
Polya Tree priors
..................... 129
Appendix: Computational Notes
................... 133
4
Structured Priors Recognizing Similarity
over Time and Space
141
4.1
Introduction
........................... 141
4.2
Modeling Temporal Structure:
Autoregressive
Models
.... 144
Contents
vii
4.2.1
Random coefficient
autoregressive
models
....... 145
4.2.2
Low order
autoregressive
models
............ 146
4.2.3
Antedependence models
................. 148
4.3
State-Space Priors for Metric Data
.............. 149
4.3.1
Simple signal models
................... 150
4.3.2
Sampling schemes
.................... 152
4.3.3
Basic structural model
.................. 154
4.3.4
Identification questions
................. 155
4.4
Time Series for Discrete Responses: State-Space Priors
and Alternatives
......................... 160
4.4.1
Other approaches
..................... 163
4.5
Stochastic Variances
....................... 167
4.6
Modeling Discontinuities in Time
............... 171
4.7
Spatial Smoothing and Prediction for Area Data
....... 176
4.8
Conditional
Autoregressive
Priors
............... 179
4.8.1
Linking conditional and joint specifications
...... 180
4.8.2
Alternative conditional priors
.............. 181
4.8.3
ICAR(l) and convolution priors
............. 183
4.9
Priors on Variances in Conditional Spatial Models
...... 185
4.10
Spatial Discontinuity and Robust Smoothing
......... 187
4.11
Models for Point Processes
................... 192
4.11.1
Discrete convolution models
............... 195
Appendix: Computational Notes
................... 200
5
Regression Techniques Using Hierarchical Priors
207
5.1
Introduction
........................... 207
5.2
Regression for Overdispersed Discrete Data
.......... 209
5.2.1
Overdispersed binomial and
multinomial regression
.................. 211
5.3
Latent Scales for Binary and Categorical Data
........ 215
5.3.1
Augmentation for ordinal responses
.......... 219
5.4
Nonconstant
Regression Relationships and
Variance Heterogeneity
..................... 221
5.5
Heterogenous Regression and Discrete Mixture
Regressions
............................ 222
5.5.1
Discrete mixture regressions
............... 223
5.5.2
Zero-inflated mixture regression
............. 226
5.6
Time Series Regression: Correlated Errors and
Time-Varying Regression Effects
................ 231
5.7
Time-Varying Regression Effects
................ 234
5.8
Spatial Correlation in Regression Residuals
.......... 240
5.8.1
Spatial lag and spatial error models
.......... 241
5.9
Spatially Varying Regression Effects: Geographically
Weighted Linear Regression and Bayesian Spatially
Varying Coefficient Models
................... 244
viii Contents
5.9.1
Bayesian spatially varying coefficient models
..... 246
Appendix: Computational Notes
................... 250
6
Bayesian Multilevel Models
257
6.1
Introduction
........................... 257
6.2
The Normal Linear Mixed Model for Hierarchical Data
. . . 258
6.2.1
The Lindley-Smith model format
............ 261
6.3
Discrete Responses: General Linear Mixed Model,
Conjugate, and Augmented Data Models
........... 262
6.3.1
Augmented data multilevel models
........... 264
6.3.2
Conjugate cluster effects
................. 265
6.4
Crossed and Multiple Membership
Random Effects
......................... 270
6.5
Robust Multilevel Models
.................... 273
Appendix: Computational Notes
................... 277
7
Multi
variate
Priors, with a Focus on Factor
and Structural Equation Models
281
7.1
Introduction
........................... 281
7.2
The Normal Linear
SEM
and Factor Models
......... 283
7.2.1
Forms of model
...................... 284
7.2.2
Marginal and complete data likelihoods, and
Markov Chain Monte Carlo sampling
.......... 285
7.3
Identifiability and Priors on Loadings
............. 287
7.3.1
An illustration of identifiability issues
......... 289
7.4
Multivariate Exponential Family Outcomes
and General Linear Factor Models
............... 292
7.4.1
Multivariate
Poisson data
................ 293
7.4.2
Multivariate binary data and item response models
. . 295
7.4.3
Latent scale binary models
............... 297
7.4.4
Categorical data
..................... 298
7.5
Robust Options in Multivariate and Factor Analysis
..... 303
7.5.1
Discrete mixture multivariate models
.......... 303
7.5.2
Discrete mixtures in
SEM
and factor models
..... 304
7.5.3
Robust density assumptions in factor models
..... 307
7.6
Multivariate Spatial Priors for Discrete Area Frameworks
. . 311
7.7
Spatial Factor Models
...................... 315
7.8
Multivariate Time Series
.................... 318
7.8.1
Multivariate dynamic linear models
.......... 319
7.8.2
Dynamic factor analysis
................. 321
7.8.3
Multivariate stochastic volatility
............ 323
Appendix: Computational Notes
................... 332
8
Hierarchical Models for Panel Data
337
8.1
Introduction
........................... 337
Contents ix
8.2 General Linear
Mixed
Models
for
Panel Data......... 338
8.2.1
Centered or noncentered priors.............
341
8.2.2 Priors
on
permanent
random effects
.......... 343
8.2.3 Priors
for random covariance matrix and random
effect selection
...................... 345
8.2.4
Priors for multiple sources of error variation
...... 348
8.3
Temporal Correlation and Autocorrelated
Residuals
............................. 351
8.3.1
Explicit temporal schemes for errors
.......... 352
8.4
Panel Categorical Choice Data
................. 357
8.5
Observation-Driven Autocorrelation:
Dynamic Panel Models
..................... 362
8.5.1
Dynamic panel models for discrete data
........ 364
8.6
Robust Panel Models: Heteroscedasticity, Generalized
Error Densities, and Discrete Mixtures
............ 370
8.6.1
Robust panel data models:
discrete mixture models
................. 373
8.7
Multilevel, Multivariate, and Multiple Time Scale
Longitudinal Data
........................ 380
8.7.1
Latent trait longitudinal models
............ 384
8.7.2
Multiple scale panel data
................ 386
8.8
Missing Data in Panel Models
................. 393
8.8.1
Forms of missingness regression (selection
approach)
......................... 396
8.8.2
Common factor models
................. 397
8.8.3
Missing predictor data
.................. 399
8.8.4
Pattern mixture models
................. 401
Appendix: Computational Notes
................... 406
9
Survival and Event History Models
413
9.1
Introduction
........................... 413
9.2
Survival Analysis in Continous Time
............. 414
9.2.1
Counting process functions
............... 416
9.2.2
Parametric hazards
.................... 417
9.2.3
Accelerated hazards
................... 419
9.3
Semi-Parametric Hazards
.................... 423
9.3.1
Cumulative hazard specifications
............ 425
9.4
Including Frailty
......................... 428
9.4.1
Cure rate models
..................... 430
9.5
Discrete Time Hazard Models
................. 435
9.5.1
Life tables
......................... 437
9.6
Dependent Survival Times: Multivariate and Nested
Survival Times
.......................... 441
9.7
Competing Risks
......................... 447
9.7.1
Modeling frailty
..................... 449
x
Contents
Appendix:
Computational
Notes .................. 451
10
Hierarchical Methods for Nonlinear Regression
459
10.1
Introduction
.......................... 459
10.2
Nonparametric Basis Function Models
for the Regression Mean
................... 460
10.2.1
Mixed model splines
................. 462
10.2.2
Model selection
.................... 464
10.2.3
Basis functions other than truncated
polynomials
...................... 465
10.3
Multivariate Basis Function Regression
........... 468
10.4
Heteroscedasticity via Adaptive Nonparametric
Regression
........................... 476
10.5
General Additive Methods
.................. 479
10.6
Nonparametric Regression Methods
for Longitudinal Analysis
................... 483
Appendix: Computational Notes
.................. 491
Appendix
1:
Using WinBUGS and BayesX
495
Al.l WinBUGS: Compiling, Initializing,
and Running Programs
................ 495
Al.
2
WinBUGS Steps in Program Checking
and Execution
..................... 495
A1.3 Using BayesX
..................... 498
References
501
Index
565
|
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| dewey-raw | 519.5/42 |
| dewey-search | 519.5/42 |
| dewey-sort | 3519.5 242 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV037239811 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:54:12Z |
| institution | BVB |
| isbn | 9781584887201 1584887206 |
| language | English |
| lccn | 2010008252 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021153315 |
| oclc_num | 845650846 |
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| owner | DE-355 DE-BY-UBR DE-473 DE-BY-UBG |
| owner_facet | DE-355 DE-BY-UBR DE-473 DE-BY-UBG |
| physical | XIII, 590 S. graph. Darst., Kt. |
| publishDate | 2010 |
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| publisher | CRC Press |
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| spelling | Congdon, Peter 1949- Verfasser (DE-588)170438783 aut Applied Bayesian hierarchical methods Peter D. Congdon Boca Raton, Fla. [u.a.] CRC Press 2010 XIII, 590 S. graph. Darst., Kt. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index Multilevel models (Statistics) Bayesian statistical decision theory Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf R Programm (DE-588)4705956-4 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 s R Programm (DE-588)4705956-4 s 1\p DE-604 Digitalisierung UB Bamberg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021153315&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Congdon, Peter 1949- Applied Bayesian hierarchical methods Multilevel models (Statistics) Bayesian statistical decision theory Bayes-Verfahren (DE-588)4204326-8 gnd R Programm (DE-588)4705956-4 gnd |
| subject_GND | (DE-588)4204326-8 (DE-588)4705956-4 |
| title | Applied Bayesian hierarchical methods |
| title_auth | Applied Bayesian hierarchical methods |
| title_exact_search | Applied Bayesian hierarchical methods |
| title_full | Applied Bayesian hierarchical methods Peter D. Congdon |
| title_fullStr | Applied Bayesian hierarchical methods Peter D. Congdon |
| title_full_unstemmed | Applied Bayesian hierarchical methods Peter D. Congdon |
| title_short | Applied Bayesian hierarchical methods |
| title_sort | applied bayesian hierarchical methods |
| topic | Multilevel models (Statistics) Bayesian statistical decision theory Bayes-Verfahren (DE-588)4204326-8 gnd R Programm (DE-588)4705956-4 gnd |
| topic_facet | Multilevel models (Statistics) Bayesian statistical decision theory Bayes-Verfahren R Programm |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021153315&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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