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Gelman A., Carlin J.B., Stern H.S. — Bayesian data analysis
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Название: Bayesian data analysisАвторы: Gelman A., Carlin J.B., Stern H.S.Аннотация: Incorporating new and updated information, this second edition of THE bestselling text in Bayesian data analysis continues to emphasize practice over theory, describing how to conceptualize, perform, and critiques statistical analysis from a Bayesian perspective. Changes in the new edition include: added material on how Bayesian methods are connected to other approaches, stronger focus on MCMC, added chapter on further computation topics, more examples, and additional chapters on current models for Bayesian data analysis such as equation models, generalized linear mixed models, and more. The book is an introductory text and a reference for working scientists throughout their professional life.
Язык: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2nd editionГод издания: 2004Количество страниц: 668Добавлена в каталог: 11.02.2006Операции: Положить на полку |
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Mixture of exponentials, as example of an ill-posed system 506 516 Model see also "Hierarchical models" "Regression Model averaging 191 338 Model checking 157—196 265—271 Model checking, adolescent smoking example 172—174 Model checking, election forecasting example 158 394 Model checking, incumbency example 364 Model checking, power transformation example 267 Model checking, pre-election polling 214 Model checking, psychology examples 165—170 Model checking, residual plots 170 503 513 Model checking, SAT coaching 186—190 Model checking, schizophrenia example 477 479 Model checking, speed of light example 160 164 Model checking, toxicology example 512 Model comparison 179—186 Model complexity 181—182 Model complexity, educational testing example 183 Model expansion 177—179 Model expansion, continuous 186 376 449 Model expansion, continuous, schizophrenia example 478—479 Model selection, why we avoid it 180 185—186 371 405 Model, beta-binomial 447 Model, binomial 33 43 97 163 Model, Cauchy 69 446 Model, exponential 55 71 Model, lognormal 266 Model, multinomial 83 95 430—433 Model, multivariate 481—495 Model, multivariate normal 85 Model, negative binomial 446 458 Model, nonlinear 497—516 Model, normal 46 48 50 70 74—83 Model, overdispersed 445—448 Model, Poisson 51 53 70 71 Model, robit 447 Model, robust or nonrobust 448 Model, space-time 494 Model, spatial 493 494 Model, Student-t 303 446 451—457 Model, time series 491—494 Model, underidentified 108 Molenberghs, G. 494 Mollie, A. 151 494 Monitoring convergence of iterative simulation 294—298 Monotone missing data pattern 522 524—525 530—534 Monte Carlo error 277 278 282 Monte Carlo simulation 276—350 Montomoli, C. 66 Morgan, B. 242 Morgan, J. 31 Moroff, S. 569 Morris, C. 113 150 151 Moskowitz, A. 569 Mosteller, F. 150 190 457 458 Mugglin, A. 494 Muller, R. 480 569 Mulligan, C. 30 Multilevel models see "Hierarchical models" Multimodal posterior distribution 314 337 Multinomial distribution 576 583 Multinomial logistic regression 430 Multinomial model 83 95 Multinomial model for missing data 533—534 Multinomial probit model 440 Multinomial regression 420 430—433 Multinomial regression, parameterization as a Poisson regression 432 Multiparameter models 73—100 Multiple comparisons 152 174 250 253 Multiple imputation 203 519—523 Multiple imputation, combining inferences 522 Multiple imputation, pre-election polling 526—533 Multiple imputation, recoding Census data 261—263 Multiple imputation, Slovenia survey 534—539 Multiple modes 312 319 Multivariate models 481—495 Multivariate models for nonnormal data 488—491 Multivariate models, hierarchical 486—488 Multivariate models, prior distributions 483—486 Multivariate models, prior distributions, noninformative 481 483 529 Multivariate normal distribution 574 578 Multivariate t distribution 315 576 Murray, W. 331 385 Mykland, R. 348 Nachtsheim, C. 385 Nadaram, B. 238 Natural parameter for an exponential family 42 Naylor, J. 348 Neal, R. 308 348 515 Negative binomial distribution 52 150 576 583 Negative binomial distribution as overdispersed alternative to Poisson 446 458 Nelder, J. 191 412 439 514 Neter, J. 385 Neural networks 515 New York population 265—269 Newcomb, S. 77 Newhouse, J. 238 Newman, T. 255 Newton's method for optimization 313 Neyman, J. 237 Nicolae, D. 348 Nisselson, H. 539 No interference between units 201 Nolan, D. 29 66 515 Nolan, T. 238 Non-Bayesian methods 247—252 256 257 Non-Bayesian methods, cross-validation 253 Non-Bayesian methods, difficulties for SAT coaching experiments 139 Nonconjugate prior distributions see "Prior distribution" Nonidentified parameters 108 Nonignorable and known designs 206 Nonignorable and unknown designs 206 Noninformative prior distribution 61—66 252 597 Noninformative prior distribution for hyperparameters 125 127—129 134 136 137 470 Noninformative prior distribution for many parameters 253 Noninformative prior distribution, binomial model 43 63 Noninformative prior distribution, Bugs software 596 Noninformative prior distribution, difficulties 64 Noninformative prior distribution, Jeffreys' rule 62—63 66 69 Noninformative prior distribution, multivariate normal model 88 Noninformative prior distribution, normal model 74 Noninformative prior distribution, pivotal quantities 64 66 Nonlinear models 497—516 Nonlinear models, golf putting 515 Nonlinear models, mixture of exponentials 516 Nonlinear models, serial dilution assay 498—504 Nonlinear models, toxicology 504—514 nonparametric methods 251 Nonrandomized studies 225 Normal approximation 101—106 314—316 Normal approximation for generalized linear models 422 Normal approximation, bioassay experiment 104 Normal approximation, lower-dimensional 104 Normal approximation, meta-analysis example 146—147 Normal approximation, multimodal 314 Normal distribution 574 578 Normal model 46 48 70 74—83 see "Hierarchical Normal model, multivariate 85 483—486 523—533 Normal model, power-transformed 195—196 265—269 Normalizing factors 8 345—349 Normand, S. 151 239 411 Notation for data collection 199 Notation for observed and missing data 200 517 521 Novick, M. 28 151 237 411 Nuisance parameters 73 Numerical integration 340—345 348 Numerical integration, Laplace's method 341—342 348 Numerical posterior predictive checks 172—177 Nychka, D. 494 NYPD stops example 425—428 O'Hagan, A. 29 191 457 O'Muircheartaigh, I. 457 Objective assignment of probability distributions, football example 14—17 Objective assignment of probability distributions, record linkage example 17—21 Objectivity of Bayesian inference 14 271 Observational studies 226—231 Observational studies, difficulties with 228 Observational studies, distinguished from experiments 226 Observational studies, incumbency example 359—367 Observed at random 518 Observed data see "Missing data" Observed information 102 Odds ratio 9 96 145 Offsets for generalized linear models 418 Offsets for generalized linear models, chess example 433 Offsets for generalized linear models, police example 426 Olkin, I. 539 Optimization and the Metropolis algorithm 290 Orchard, T. 331 Ordered logit and probit models 420 430 Ott, J. 349 Oudshoom, C. 539 Outcome variable 353 Outliers, models for 443 Output analysis for iterative simulation 294—299 Overdispersed models 418 439 441 445—448 Overfitting 117 371 421 p-values 162 255 see p-values, Bayesian (posterior predictive) 162 p-values, classical 162 p-values, interpretation of 175 Packages see "Software" Paired comparisons with ties 440 Paired comparisons with ties, multinomial model for 431 Parameter expansion for ANOVA computation 407 Parameter expansion for EM algorithm 324 331 Parameter expansion for hierarchical regression 404 407 Parameter expansion, election forecasting example 404 Parameter expansion, programming in Bugs 597—598 Parameter expansion, programming in R 606—607 Parameters 5 Parameters, effective number of 181 Parameters, frequentist distinction between parameters and predictions 249 411 Park, D. 440 Parmar, M. 255 Parmigiani, G. 152 412 568 Partial pooling 133 Path sampling 344—345 348 Pauker, S. 569 Pauler, D. 28 191 Pearl, J. 151 237 Pedlow, S. 331 Pellom, A. 66 151 Pendleton, B. 348 Perchloroethylene 504 Perfect simulation for MCMC 340 348 Pericchi, L. 195 Permutation tests 251 Personal (subjective) probability 14 567—568 Peto, R. 151 Petrie, T. 331 Pettit, A. 349 Pharmacokinetics 260 Pivotal quantities 64 66 77 Plackett, R. 412 Plummer, M. 609 Point estimation 103 111 256 Poison, N. 309 Poisson distribution 576 582 Poisson model 51 70 71 Poisson model, parameterized in terms of rate and exposure 53 Poisson regression 99 417 441 Poisson regression for multinomial data 431 Poisson regression, hierarchical 425—428 Pole, A. 494 Police stops, example of hierarchical Poisson regression 425—428 Pooling, partial 133 271 Population distribution 117 Posterior distribution 3 8 Posterior distribution as compromise 36—37 47 67 Posterior distribution, calculating marginal 81 Posterior distribution, improper 64 109 154 Posterior distribution, joint 73 Posterior distribution, marginal 73 Posterior distribution, normal approximation see "Normal approximation" Posterior distribution, predictive 8 Posterior distribution, summaries of 37 Posterior distribution, use as prior distribution when new data arrive 11 561 Posterior intervals 4 38 276 Posterior modes 312—314 Posterior modes, approximate conditional posterior density using marginal modes 324 Posterior modes, conditional maximization (stepwise ascent) 312 Posterior modes, EM algorithm for marginal posterior modes 317—324 331 Posterior modes, EM algorithm for marginal posterior modes, ECM and ECME algorithms 321 471 526 Posterior modes, EM algorithm for marginal posterior modes, examples 319 328 379 455 471 537 Posterior modes, EM algorithm for marginal posterior modes, generalized EM algorithm 318 Posterior modes, EM algorithm for marginal posterior modes, marginal posterior density increases at each step 329 Posterior modes, EM algorithm for marginal posterior modes, missing data 521 523 Posterior modes, EM algorithm for marginal posterior modes, SEM algorithm 538 Posterior modes, EM algorithm for marginal posterior modes, SEM and SECM algorithms 322—324 Posterior modes, joint mode, problems with 333 Posterior modes, joint mode, problems with, Newton's method 313 Posterior predictive checks 159—177 253 see Posterior predictive checks, graphical 165—172 Posterior predictive checks, numerical 172—177 Posterior predictive distribution 8 Posterior predictive distribution, hierarchical models 125 137 Posterior predictive distribution, linear regression 358 Posterior predictive distribution, missing data 203 Posterior predictive distribution, mixture model 476 Posterior predictive distribution, multivariate normal model 86 Posterior predictive distribution, normal model 77 Posterior predictive distribution, speed of light example 160 Posterior simulation 25—26 276—350 see Posterior simulation, computation in R and Bugs 591—608 Posterior simulation, direct 283—285 Posterior simulation, grid approximation 91—92 284 Posterior simulation, hierarchical models 130 Posterior simulation, how many draws are needed 277 278 282 Posterior simulation, rejection sampling 284 Posterior simulation, simple problems 93—94 Posterior simulation, two-dimensional 82 92 99 Posterior simulation, using inverse cdf 25—26 Poststratification 228 428—430 Potential scale reduction factor 297 Pourahmadi, M. 494 Power transformations 195—196 265—269 Pratt, J. 28 113 237 Pre-election polling 83 95 242—244 428—430 Pre-election polling in Slovenia 534—539 Pre-election polling, missing data 526—539 Pre-election polling, state-level opinions from national polls 428—430 Pre-election polling, stratified sampling 210—214 Precision (inverse of variance) 47 Precision (inverse of variance), used by Bugs software 592 Prediction see "Posterior predictive distribution" Predictive simulation 31 Predictor variables see "Regression models explanatory Predictors, including even if not 'statistically significant' 263 546—552 Predictors, selecting 254 Pregibon, D. 28 439 Press, W. 331 348 584 Price, P. 66 569 Principal stratification 229—231 Prior distribution 7 Prior distribution for covariance matrices 483—486 Prior distribution for covariance matrices, noninformative 481 483 529 Prior distribution for multivariate models 483—486 Prior distribution, conjugate 40—43 66 Prior distribution, conjugate, binomial model 40—41 45
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