Applied Bayesian Modelling (Wiley Series in Probability and Statistics)

Applied Bayesian Modelling (Wiley Series in Probability and Statistics)

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  • 製本 Hardcover:ハードカバー版/ページ数 457 p.
  • 言語 ENG
  • 商品コード 9780471486954
  • DDC分類 519.542

Full Description


The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author's best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS - a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example - explaining fully the choice of model for each particular problem. The book * Provides a broad and comprehensive account of applied Bayesian modelling. * Describes a variety of model assessment methods and the flexibility of Bayesian prior specifications. * Covers many application areas, including panel data models, structural equation and other multivariate structure models, spatial analysis, survival analysis and epidemiology. * Provides detailed worked examples in WINBUGS to illustrate the practical application of the techniques described. All WINBUGS programs are available from an ftp site. The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.

Table of Contents

Preface                                            xi
Chapter 1 The Basis for, and Advantages of, 1 (30)
Bayesian Model Estimation via Repeated
Sampling
1.1 Introduction 1 (4)
1.2 Gibbs sampling 5 (7)
1.3 Simulating random variables from 12 (6)
standard densities
1.4 Monitoring MCMC chains and assessing 18 (2)
convergence
1.5 Model assessment and sensitivity 20 (7)
1.6 Review 27 (1)
References 28 (3)
Chapter 2 Hierarchical Mixture Models 31 (48)
2.1 Introduction: Smoothing to the 31 (1)
Population
2.2 General issues of model assessment: 32 (9)
marginal likelihood and other approaches
2.2.1 Bayes model selection using 33 (2)
marginal likelihoods
2.2.2 Obtaining marginal likelihoods in 35 (2)
practice
2.2.3 Approximating the posterior 37 (2)
2.2.4 Predictive criteria for model 39 (1)
checking and selection
2.2.5 Replicate sampling 40 (1)
2.3 Ensemble estimates: pooling over 41 (17)
similar units
2.3.1 Mixtures for Poisson and binomial 43 (8)
data
2.3.2 Smoothing methods for continuous 51 (7)
data
2.4 Discrete mixtures and Dirichlet 58 (9)
processes
2.4.1 Discrete parametric mixtures 58 (2)
2.4.2 DPP priors 60 (7)
2.5 General additive and histogram 67 (7)
smoothing priors
2.5.1 Smoothness priors 68 (1)
2.5.2 Histogram smoothing 69 (5)
2.6 Review 74 (1)
References 75 (3)
Exercises 78 (1)
Chapter 3 Regression Models 79 (56)
3.1 Introduction: Bayesian regression 79 (5)
3.1.1 Specifying priors: constraints on 80 (1)
parameters
3.1.2 Prior specification: adopting 81 (1)
robust or informative priors
3.1.3 Regression models for overdispersed 82 (2)
discrete outcomes
3.2 Choice between regression models and 84 (14)
sets of predictors in regression
3.2.1 Predictor selection 85 (1)
3.2.2 Cross-validation regression model 86 (12)
assessment
3.3 Polytomous and ordinal regression 98 (12)
3.3.1 Multinomial logistic choice models 99 (1)
3.3.2 Nested logit specification 100 (1)
3.3.3 Ordinal outcomes 101 (1)
3.3.4 Link functions 102 (8)
3.4 Regressions with latent mixtures 110 (5)
3.5 General additive models for nonlinear 115 (3)
regression effects
3.6 Robust Regression Methods 118 (8)
3.6.1 Binary selection models for 119 (1)
robustness
3.6.2 Diagnostics for discordant 120 (6)
observations
3.7 Review 126 (3)
References 129 (3)
Exercises 132 (3)
Chapter 4 Analysis of Multi-Level Data 135 (36)
4.1 Introduction 135 (2)
4.2 Multi-level models: univariate 137 (8)
continuous and discrete outcomes
4.2.1 Discrete outcomes 139 (6)
4.3 Modelling heteroscedasticity 145 (6)
4.4 Robustness in multi-level modelling 151 (5)
4.5 Multi-level data on multivariate indices 156 (7)
4.6 Small domain estimation 163 (4)
4.7 Review 167 (1)
References 168 (1)
Exercises 169 (2)
Chapter 5 Models for Time Series 171 (56)
5.1 Introduction 171 (1)
5.2 Autoregressive and moving average 172 (19)
models under stationarity and
non-stationarity
5.2.1 Specifying priors 174 (5)
5.2.2 Further types of time dependence 179 (1)
5.2.3 Formal tests of stationarity in the 180 (2)
AR(1) model
5.2.4 Model assessment 182 (9)
5.3 Discrete Outcomes 191 (9)
5.3.1 Auto regression on transformed 193 (1)
outcome
5.3.2 INAR models for counts 193 (2)
5.3.3 Continuity parameter models 195 (1)
5.3.4 Multiple discrete outcomes 195 (5)
5.4 Error correction models 200 (3)
5.5 Dynamic linear models and time varying 203 (7)
coefficients
5.5.1 State space smoothing 205 (5)
5.6 Stochastic variances and stochastic 210 (5)
volatility
5.6.1 ARCH and GARCH models 210 (1)
5.6.2 Stochastic volatility models 211 (4)
5.7 Modelling structural shifts 215 (6)
5.7.1 Binary indicators for mean and 215 (1)
variance shifts
5.7.2 Markov mixtures 216 (1)
5.7.3 Switching regressions 216 (5)
5.8 Review 221 (1)
References 222 (3)
Exercises 225 (2)
Chapter 6 Analysis of Panel Data 227 (46)
6.1 Introduction 227 (4)
6.1.1 Two stage models 228 (2)
6.1.2 Fixed vs. random effects 230 (1)
6.1.3 Time dependent effects 231 (1)
6.2 Normal linear panel models and growth 231 (12)
curves for metric outcomes
6.2.1 Growth Curve Variability 232 (2)
6.2.2 The linear mixed model 234 (1)
6.2.3 Variable autoregressive parameters 235 (8)
6.3 Longitudinal discrete data: binary, 243 (14)
ordinal and multinomial and Poisson panel
data
6.3.1 Beta-binomial mixture for panel data 244 (13)
6.4 Panels for forecasting 257 (7)
6.4.1 Demographic data by age and time 261 (3)
period
6.5 Missing data in longitudinal studies 264 (4)
6.6 Review 268 (1)
References 269 (2)
Exercises 271 (2)
Chapter 7 Models for Spatial Outcomes and 273 (50)
Geographical Association
7.1 Introduction 273 (2)
7.2 Spatial regressions for continuous data 275 (3)
with fixed interaction schemes
7.2.1 Joint vs. conditional priors 276 (2)
7.3 Spatial effects for discrete outcomes: 278 (11)
ecological analysis involving count data
7.3.1 Alternative spatial priors in 279 (2)
disease models
7.3.2 Models recognising discontinuities 281 (1)
7.3.3 Binary Outcomes 282 (7)
7.4 Direct modelling of spatial covariation 289 (9)
in regression and interpolation applications
7.4.1 Covariance modelling in regression 290 (1)
7.4.2 Spatial interpolation 291 (1)
7.4.3 Variogram methods 292 (1)
7.4.4 Conditional specification of 293 (5)
spatial error
7.5 Spatial heterogeneity: spatial 298 (5)
expansion, geographically weighted
regression, and multivariate errors
7.5.1 Spatial expansion model 298 (1)
7.5.2 Geographically weighted regression 299 (1)
7.5.3 Varying regressions effects via 300 (3)
multivariate priors
7.6 Clustering in relation to known centres 303 (7)
7.6.1 Areas vs. case events as data 306 (1)
7.6.2 Multiple sources 306 (4)
7.7 Spatio-temporal models 310 (6)
7.7.1 Space-time interaction effects 312 (1)
7.7.2 Area Level Trends 312 (1)
7.7.3 Predictor effects in 313 (1)
spatio-temporal models
7.7.4 Diffusion processes 314 (2)
7.8 Review 316 (1)
References 317 (3)
Exercises 320 (3)
Chapter 8 Structural Equation and Latent 323 (38)
Variable Models
8.1 Introduction 323 (4)
8.1.1 Extensions to other applications 325 (1)
8.1.2 Benefits of Bayesian approach 326 (1)
8.2 Confirmatory factor analysis with a 327 (7)
single group
8.3 Latent trait and latent class analysis 334 (6)
for discrete outcomes
8.3.1 Latent class models 335 (5)
8.4 Latent variables in panel and clustered 340 (12)
data analysis
8.4.1 Latent trait models for continuous 341 (1)
data
8.4.2 Latent class models through time 341 (2)
8.4.3 Latent trait models for time 343 (1)
varying discrete outcomes
8.4.4 Latent trait models for clustered 343 (1)
metric data
8.4.5 Latent trait models for mixed 344 (8)
outcomes
8.5 Latent structure analysis for missing 352 (5)
data
8.6 Review 357 (1)
References 358 (2)
Exercises 360 (1)
Chapter 9 Survival and Event History Models 361 (36)
9.1 Introduction 361 (2)
9.2 Continuous time functions for survival 363 (7)
9.3 Accelerated hazards 370 (2)
9.4 Discrete time approximations 372 (12)
9.4.1 Discrete time hazards regression 375 (6)
9.4.2 Gamma process priors 381 (3)
9.5 Accounting for frailty in event history 384 (4)
and survival models
9.6 Counting process models 388 (5)
9.7 Review 393 (1)
References 394 (2)
Exercises 396 (1)
Chapter 10 Modelling and Establishing Causal 397
Relations: Epidemiological Methods and Models
10.1 Causal processes and establishing 397 (2)
causality
10.1.1 Specific methodological issues 398 (1)
10.2 Confounding between disease risk 399 (14)
factors
10.2.1 Stratification vs. multivariate 400 (13)
methods
10.3 Dose-response relations 413 (16)
10.3.1 Clustering effects and other 416 (11)
methodological issues
10.3.2 Background mortality 427 (2)
10.4 Meta-analysis: establishing consistent 429 (14)
associations
10.4.1 Priors for study variability 430 (6)
10.4.2 Heterogeneity in patient risk 436 (3)
10.4.3 Multiple treatments 439 (2)
10.4.4 Publication bias 441 (2)
10.5 Review 443 (1)
References 444 (3)
Exercises 447 (2)
Index 449
052182415X
Acknowledgments ix
Preface xiii
1 Rethinking Judicial Policy Making in a 1 (41)
Separation of Powers System
2 False Victories: Labor, Congress, and the 42 (26)
Courts, 1898-1935
3 "As Harmless as an Infant": The Erdman Act 68 (31)
in Congress and the Courts
4 Killing with Kindness: Legislative 99 (62)
Ambiguity, Judicial Policy Making, and the
Clayton Act
5 The Norris-LaGuardia Act, for Once: 161 (56)
Learning What to Learn from the Past
6 Legislative Deferrals and Judicial Policy 217 (35)
Making in the Administrative State: A Brief
Look at the Wagner Act
7 Conclusion 252 (13)
Reference List 265 (5)
References 270 (9)
Index 279