The BUGS book: a practical introduction to Bayesian analysis
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press
2013
|
| Schriftenreihe: | Texts in statistical science
|
| Schlagworte: | |
| Online-Zugang: | Cover image Inhaltsverzeichnis |
| Beschreibung: | "Preface History Markov chain Monte Carlo (MCMC) methods, in which plausible values for unknown quantities are simulated from their appropriate probability distribution, have revolutionised the practice of statistics. For more than 20 years the BUGS project has been at the forefront of this movement. The BUGS project began in Cambridge, UK, in 1989, just as Alan Gelfand and Adrian Smith were working 80 miles away in Nottingham on their classic Gibbs sampler paper (Gelfand and Smith, 1990) that kicked off the revolution. But we never communicated (except through the intermediate node of David Clayton) and whereas the Gelfand-Smith approach used image-processing as inspiration, the philosophy behind BUGS was rooted more in techniques for handling uncertainty in artificial intelligence using directed graphical models and what came to be called Bayesian networks (Pearl, 1988). Lunn et al. (2009b) lay out all this history in greater detail. Some people have accused Markov chain Monte Carlo methods of being slow, but nothing could compare with the time it has taken this book to be written! The first proposal dates from 1995, but things got in the way, as they do, and it needed a vigorous new generation of researchers to finally get it finished. It is slightly galling that much of the current book could have been written in the mid-1990s, since the basic ideas of the software, the language for model description, and indeed some of the examples are unchanged. Nevertheless there have been important developments in the extended gestational period of the book, for example techniques for model criticism and comparison, implementation of differential equations and nonparametric techniques, and the ability to run BUGS code within a range of alternative programs"-- Provided by publisher. Includes bibliographical references and index |
| Beschreibung: | XVII, 381 S. graph. Darst. |
| ISBN: | 9781584888499 |
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| 500 | |a "Preface History Markov chain Monte Carlo (MCMC) methods, in which plausible values for unknown quantities are simulated from their appropriate probability distribution, have revolutionised the practice of statistics. For more than 20 years the BUGS project has been at the forefront of this movement. The BUGS project began in Cambridge, UK, in 1989, just as Alan Gelfand and Adrian Smith were working 80 miles away in Nottingham on their classic Gibbs sampler paper (Gelfand and Smith, 1990) that kicked off the revolution. But we never communicated (except through the intermediate node of David Clayton) and whereas the Gelfand-Smith approach used image-processing as inspiration, the philosophy behind BUGS was rooted more in techniques for handling uncertainty in artificial intelligence using directed graphical models and what came to be called Bayesian networks (Pearl, 1988). Lunn et al. (2009b) lay out all this history in greater detail. Some people have accused Markov chain Monte Carlo methods of being slow, but nothing could compare with the time it has taken this book to be written! The first proposal dates from 1995, but things got in the way, as they do, and it needed a vigorous new generation of researchers to finally get it finished. It is slightly galling that much of the current book could have been written in the mid-1990s, since the basic ideas of the software, the language for model description, and indeed some of the examples are unchanged. Nevertheless there have been important developments in the extended gestational period of the book, for example techniques for model criticism and comparison, implementation of differential equations and nonparametric techniques, and the ability to run BUGS code within a range of alternative programs"-- Provided by publisher. | ||
| 500 | |a Includes bibliographical references and index | ||
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Datensatz im Suchindex
| _version_ | 1804149535881035776 |
|---|---|
| adam_text | Titel: The BUGS book
Autor: Lunn, David
Jahr: 2013
Contents
Preface
xm
1 Introduction: Probability and parameters 1
1.1 Probability ............................ 1
1.2 Probability distributions..................... 5
1.3 Calculating properties of probability distributions....... 7
1.1 Monte Carlo integration ..................... 8
2 Monte Carlo simulations using BUGS 13
2.1 Introduction to BUGS ...................... 13
2.1.1 Background........................ 13
2.1.2 Directed graphical models................ 13
2.1.3 The BUGS language................... 15
2.1.1 Running BUGS models ................. 16
2.1.0 Running VYinBUGS for a simple example....... 17
2.2 DoodleBUGS ........................... 21
2-3 Using BUGS to simulate from distributions .......... 22
2.4 Transformations of random variables .............. 24
2.5 Complex calculations using Monte Carlo............ 26
2.6 Multivariate Monte Carlo analysis ............... 27
2.7 Predictions with unknown parameters ............. 29
3 Introduction to Bayesian inference 33
3.1 Bayesian learning......................... 33
3.1.1 Bayes theorem for observable quant it ies........ 33
3.1.2 Bayesian inference for parameters............ 34
3.2 Posterior predictive distributions ................ 36
3.3 Conjugate Bayesian inference .................. 36
3.3.1 Binomial data....................... 37
3.3.2 Normal data with unknown mean, known variance . . 41
3.4 Inference about a discrete parameter .............. 45
3.5 Combinations of conjugate analyses............... 49
3.6 Bayesian and classical methods ................. 51
3.6.1 Likelihood-based inference................ 52
3.6.2 Exchangeability...................... 52
3.6.3 Long-run properties of Bayesian methods ....... 53
The BUGS Book
3.6.4 Model-based vs procedural methods.......... 54
3.6.5 The - likelihood principle ................ 55
Introduction to Markov chain Monte Carlo methods 57
4.1 Bayesian computation ...................... 57
4.1.1 Single-parameter models................. 57
4.1.2 Multi-parameter models................. 59
4.1.3 Monte Carlo integration for evaluating posterior inte-
grals ............................ 61
4.2 Markov chain Monte Carlo methods .............. 62
4.2.1 Gibbs sampling...................... 63
4.2.2 Gibbs sampling and directed graphical models..... 64
4.2.3 Derivation of full conditional distributions in BUGS . 68
4.2.4 Other MCMC methods ................. 68
4.3 Initial values ........................... 70
4.4 Convergence............................ 71
4.4.1 Detecting convergence/stationarity by eye....... 72
4.4.2 Formal detection of convergence/stationarity..... 73
4.5 Efficiency and accuracy ..................... 77
4.5.1 Monte Carlo standard error of the posterior mean . . 77
4.5.2 Accuracy of the whole posterior............. 78
4.6 Beyond MCMC.......................... 79
Prior distributions 81
?5.1 Different purposes of priors ................... 81
5.2 Vague, objective, and reference priors ........... 82
5.2.1 Introduction........................ 82
5.2.2 Discrete uniform distributions.............. 83
5.2.3 Continuous uniform distributions and Jeffreys prior . . 83
5.2.4 Location parameters................... 84
5.2.5 Proportions........................ 84
5.2.6 Counts and rates..................... 85
5.2.7 Scale parameters..................... 87
5.2.8 Distributions on the positive integers.......... 88
5.2.9 More complex situations................. 89
5.3 Representation of informative priors .............. 89
5.3.1 Elicitation of pure judgement.............. 90
5.3.2 Discounting previous data................ 93
5.4 Mixture of prior distributions .................. 95
5.5 Sensitivity analysis ........................ 97
Contents vii
6 Regression models 103
6.1 Linear regression with normal errors .............. 103
6.2 Linear regression with non-normal errors............ 107
6.3 Non-linear regression with normal errors............ 109
6.4 Multivariate responses ...................... 112
6.5 Generalised linear regression models .............. 114
6.6 Inference on functions of parameters .............. 118
6.7 Further reading.......................... 119
7 Categorical data 121
7.1 2x2 tables............................121
7.1.1 Tables with one margin fixed..............122
7.1.2 Case-control studies...................125
7.1.3 Tables with both margins fixed.............126
7.2 Multinomial models .......................126
7.2.1 Conjugate analysis....................126
7.2.2 Non-conjugate analysis ? parameter constraints . . . 128
7.2.3 Categorical data with covariates ............129
7.2.4 Multinomial and Poisson regression equivalence .... 131
7.2.5 Contingency tables....................132
7.3 Ordinal regression ........................132
7.4 Further reading..........................134
8 Model checking and comparison 137
8.1 Introduction............................137
8.2 Deviance..............................138
8.3 Residuals .............................140
8.3.1 Standardised Pearson residuals.............140
8.3.2 Multivariate residuals..................142
8.3.3 Observed p-values for distributional shape.......143
8.3.4 Deviance residuals and tests of fit............145
8.4 Predictive checks and Bayesian p-values ............147
8.4.1 Interpreting discrepancy statistics ? how big is big? . 147
8.4.2 Out-of-sample prediction.................148
8.4.3 Checking functions based on data alone........148
8.4.4 Checking functions based on data and parameters . . 152
8.4.5 Goodness of fit for grouped data............155
8.5 Model assessment by embedding in larger models.......157
8.6 Model comparison using deviances ...............159
8.6.1 po- The effective number of parameters........159
8.6.2 Issues with pD ......................161
8.6.3 Alternative measures of the effective number of pa-
rameters ..........................164
8.6.4 DIG for model comparison................165
8.6.5 How and why does WinBUGS partition DIG and pp? 167
viii The BUGS Book
8.6.6 Alternatives to DIC ...................168
8.7 Bayes factors ...........................169
8.7.1 Lindley-Bartlett paradox in model selection......171
8.7.2 Computing marginal likelihoods.............172
8.8 Model uncertainty ........................173
8.8.1 Bayesian model averaging................ 173
8.8.2 MCMC sampling over a space of models........ 173
8.8.3 Model averaging when all models are wrong...... 175
8.8.4 Model expansion..................... 176
8.9 Discussion on model comparison ................ 177
8.10 Prior-data conflict ........................ 178
8.10.1 Identification of prior-data conflict...........179
8.10.2 Accommodation of prior-data conflict .........180
9 Issues in Modelling 185
9.1 Missing data ...........................185
9.1.1 Missing response data..................186
9.1.2 Missing covariate data..................189
9.2 Prediction.............................193
9.3 Measurement error ........................195
9.4 Cutting feedback .........................201
9.5 New distributions.........................204
9.5.1 Specifying a new sampling distribution.........204
9.5.2 Specifying a new prior distribution...........205
9.6 Censored, truncated, and grouped observations ........206
9.6.1 Censored observations..................206
9.6.2 Truncated sampling distributions............208
9.6.3 Grouped, rounded, or interval-censored data......209
9.7 Constrained parameters .....................211
9.7.1 Univariate fully specified prior distributions......211
9.7.2 Multivariate fully specified prior distributions.....211
9.7.3 Prior distributions with unknown parameters.....214
9.8 Bootstrapping...........................214
9.9 Ranking ..............................215
10 Hierarchical models 219
10.1 Exchangeability.......................... 219
10.2 Priors ............................... 223
10.2.1 Unit-specific parameters................. 223
10.2.2 Parameter constraints.................. 223
10.2.3 Priors for variance components............. 225
10.3 Hierarchical regression models.................. 227
10.3.1 Data formatting ..................... 230
10.4 Hierarchical models for variances ................ 237
10.5 Redundant parameterisations .................. 240
Contents ix
10.6 More general formulations.................... 242
10.7 Checking of hierarchical models................. 242
10.8 Comparison of hierarchical models ............... 249
10.8.1 Focus : The crucial element of model comparison in
hierarchical models.................... 250
10.9 Further resources......................... 252
11 Specialised models 253
11.1 Time-to-event data........................ 253
11.1.1 Parametric survival regression.............. 254
11.2 Time series models ........................ 257
11.3 Spatial models .......................... 262
11.3.1 Intrinsic conditionally autoregressive (CAR) models . 263
11.3.2 Supplying map polygon data to WinBUGS and creat-
ing adjacency matrices.................. 264
11.3.3 Multivariate CAR models................ 268
11.3.4 Proper CAR model.................... 269
11.3.5 Poisson-gamma moving average models ........ 269
11.3.6 Geostatistical models................... 270
11.4 Evidence synthesis ........................ 273
11.4.1 Meta-analysis....................... 273
11.4.2 Generalised evidence synthesis ............. 274
11.5 Differential equation and pharmacokinetic models....... 278
11.6 Finite mixture and latent class models ............. 280
11.6.1 Mixture models using an explicit likelihood...... 283
11.7 Piecewise parametric models................... 286
11.7.1 Change-point models................... 286
11.7.2 Splines........................... 288
11.7.3 Semiparametric survival models............. 288
11.8 Bayesian nonparametric models................. 291
11.8.1 Dirichlet process mixtures................ 293
11.8.2 Stick-breaking implementation ............. 293
12 Different implementations of BUGS 297
12.1 Introduction ? BUGS engines and interfaces ......... 297
12.2 Expert systems and MCMC methods.............. 298
12.3 Classic BUGS........................... 299
12.4 WinBUGS............................. 300
12.4.1 Using WinBUGS: compound documents........ 301
12.4.2 Formatting data ..................... 301
12.4.3 Using the WinBUGS graphical interface........ 304
12.4.4 Doodles.......................... 308
12.4.5 Scripting.......................... 308
12.4.6 Interfaces with other software.............. 310
12.4.7 R2WinBUGS....................... 311
x The BUGS Book
12.4.8 WBDev..........................313
12.5 OpenBUGS ............................315
12.5.1 Differences from WinBUGS...............317
12.5.2 OpenBUGS on Linux...................317
12.5.3 BRugs...........................318
12.5.4 Parallel computation...................319
12.6 JAGS ...............................320
12.6.1 Extensibility: modules.................. 321
12.6.2 Language differences................... 321
12.6.3 Other differences from WinBUGS............ 324
12.6.4 Running JAGS from the command line......... 325
12.6.5 Running JAGS from R.................. 326
Appendix A BUGS language syntax 329
A.l Introduction............................329
A.2 Distributions ...........................329
A.2.1 Standard distributions..................329
A.2.2 Censoring and truncation................330
A.2.3 Non-standard distributions ...............331
A.3 Deterministic functions......................331
A.3.1 Standard functions....................331
A.3.2 Special functions.....................331
A.3.3 Add-on functions.....................332
A.4 Repetition.............................332
A.5 Multivariate quantities......................333
A.6 Indexing..............................334
A.6.1 Functions as indices ...................334
A.6.2 Implicit indexing.....................334
A.6.3 Nested indexing......................334
A.7 Data transformations.......................335
A.8 Commenting ...........................335
Appendix B Functions in BUGS 337
B.l Standard functions ........................ 337
B.2 Trigonometric functions ..................... 337
B.3 Matrix algebra .......................... 337
B.4 Distribution utilities and model checking............ 340
B.5 Functional and differential equations.............. 341
B.6 Miscellaneous ...........................342
Appendix C Distributions in BUGS 343
C.l Continuous univariate, unrestricted range ...........343
C.2 Continuous univariate, restricted to be positive ........345
C.3 Continuous univariate, restricted to a finite interval......349
C.4 Continuous multivariate distributions..............350
Contents xi
C.5 Discrete univariate distributions.................351
C.6 Discrete multivariate distributions ...............354
Bibliography 357
Index 373
|
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| illustrated | Illustrated |
| indexdate | 2024-07-10T00:24:35Z |
| institution | BVB |
| isbn | 9781584888499 |
| language | English |
| lccn | 2012026280 |
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| physical | XVII, 381 S. graph. Darst. |
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| record_format | marc |
| series2 | Texts in statistical science |
| spelling | The BUGS book a practical introduction to Bayesian analysis David Lunn ... Boca Raton [u.a.] CRC Press 2013 XVII, 381 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Texts in statistical science "Preface History Markov chain Monte Carlo (MCMC) methods, in which plausible values for unknown quantities are simulated from their appropriate probability distribution, have revolutionised the practice of statistics. For more than 20 years the BUGS project has been at the forefront of this movement. The BUGS project began in Cambridge, UK, in 1989, just as Alan Gelfand and Adrian Smith were working 80 miles away in Nottingham on their classic Gibbs sampler paper (Gelfand and Smith, 1990) that kicked off the revolution. But we never communicated (except through the intermediate node of David Clayton) and whereas the Gelfand-Smith approach used image-processing as inspiration, the philosophy behind BUGS was rooted more in techniques for handling uncertainty in artificial intelligence using directed graphical models and what came to be called Bayesian networks (Pearl, 1988). Lunn et al. (2009b) lay out all this history in greater detail. Some people have accused Markov chain Monte Carlo methods of being slow, but nothing could compare with the time it has taken this book to be written! The first proposal dates from 1995, but things got in the way, as they do, and it needed a vigorous new generation of researchers to finally get it finished. It is slightly galling that much of the current book could have been written in the mid-1990s, since the basic ideas of the software, the language for model description, and indeed some of the examples are unchanged. Nevertheless there have been important developments in the extended gestational period of the book, for example techniques for model criticism and comparison, implementation of differential equations and nonparametric techniques, and the ability to run BUGS code within a range of alternative programs"-- Provided by publisher. Includes bibliographical references and index BUGS Bayesian statistical decision theory MATHEMATICS / Probability & Statistics / General bisacsh Bayes-Verfahren (DE-588)4204326-8 gnd rswk-swf Bayes-Verfahren (DE-588)4204326-8 s DE-604 Lunn, David Sonstige oth http://jacketsearch.tandf.co.uk/common/jackets/covers/websmall/978158488/9781584888499.jpg Cover image HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025318072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | The BUGS book a practical introduction to Bayesian analysis BUGS Bayesian statistical decision theory MATHEMATICS / Probability & Statistics / General bisacsh Bayes-Verfahren (DE-588)4204326-8 gnd |
| subject_GND | (DE-588)4204326-8 |
| title | The BUGS book a practical introduction to Bayesian analysis |
| title_auth | The BUGS book a practical introduction to Bayesian analysis |
| title_exact_search | The BUGS book a practical introduction to Bayesian analysis |
| title_full | The BUGS book a practical introduction to Bayesian analysis David Lunn ... |
| title_fullStr | The BUGS book a practical introduction to Bayesian analysis David Lunn ... |
| title_full_unstemmed | The BUGS book a practical introduction to Bayesian analysis David Lunn ... |
| title_short | The BUGS book |
| title_sort | the bugs book a practical introduction to bayesian analysis |
| title_sub | a practical introduction to Bayesian analysis |
| topic | BUGS Bayesian statistical decision theory MATHEMATICS / Probability & Statistics / General bisacsh Bayes-Verfahren (DE-588)4204326-8 gnd |
| topic_facet | BUGS Bayesian statistical decision theory MATHEMATICS / Probability & Statistics / General Bayes-Verfahren |
| url | http://jacketsearch.tandf.co.uk/common/jackets/covers/websmall/978158488/9781584888499.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025318072&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lunndavid thebugsbookapracticalintroductiontobayesiananalysis |