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Ghosh Sujit K., Mallick Bani K., Dey Dipak K. Ч Generalized Linear Models: A Bayesian Perspective
Ghosh Sujit K., Mallick Bani K., Dey Dipak K. Ч Generalized Linear Models: A Bayesian Perspective

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Ќазвание: Generalized Linear Models: A Bayesian Perspective

јвторы: Ghosh Sujit K., Mallick Bani K., Dey Dipak K.

јннотаци€:

Describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation, covering random effects in generalized linear mixed models (GLMMs) with explained examples. Considers parametric and semiparametric approaches to overdispersed GLMs, applies Bayesian GLMs to US mortality data, and presents methods of analyzing correlated binary data using latent variables. Describes and analyzes item response modeling for categorical data, and provides variable selection methods using the Gibbs sampler for Cox models. Dey is professor and head of the department of statistics at the University of Connecticut-Storrs


язык: en

–убрика: ћатематика/¬еро€тность/—татистика и приложени€/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 2000

 оличество страниц: 442

ƒобавлена в каталог: 28.05.2005

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
Ability parameters, conditional distribution, item response modeling      184
Absolute residuals, male flour beetle data set      268t
Acute myocardial infarction practice, guidelinespost      see УPost acute myocardial infarction practice guidelinesФ
Additive Log Ratio (ALR), AitchisonТs transformation      359Ч361
Additive Log Ratio (ALR), function      349Ч350
Adjusted density method (ADM), small area inference      95Ч96
AIDS clinical trials, variable selection, predictive approach      288
AitchisonТs Additive Log Ratio (ALR) transformation      359Ч361
Akaike Information Criteria (AIC)      16
AlbertТs model      7
Alcohol consumption, errors-in-variables      340
Analysis of regression models, censored survival data      287
Analysis of survival data mixture-model approach      255Ч268
Analysis of survival data mixture-model approach, Gibbs sampler      259Ч260
Analysis of survival data mixture-model approach, MCEM      256Ч259
Analysis of survival data mixture-model approach, mixture-model approach example      261Ч268
Analysis of survival data mixture-model approach, mixture-model approach example, EM algorithm      262Ч263
Analysis of survival data mixture-model approach, mixture-model approach example, Gibbs samplers      263Ч265
Analysis of survival data mixture-model approach, mixture-model approach example, numerical results      265Ч268
Analysis of survival data mixture-model approach, model selection      260Ч261
Analysis of survival models, MCMC      287
Asymmetric links, generation      239
Asymptotic theory, MLE      5
Autocorrelated random effects      30
Autoregressive (AR) model of Ord      27
Baseline hazard rate, model      289
Baseline hazard rate, model, cumulative      289Ч290
Baseline hazard rate, prior distribution, Cox variable selection      289Ч292
Basic marginal likelihood identity      124
Basis functions, classification trees      366Ч367
Basis functions, classification trees, example      366f
Bayesian analysis, classification trees      368Ч369
Bayesian analysis, compositional data      349Ч362
Bayesian analysis, compositional data, parametric approach      351Ч352
Bayesian analysis, compositional data, posterior distributions and estimation      355Ч359
Bayesian analysis, compositional data, results      359Ч361 360tЧ361t
Bayesian analysis, compositional data, semiparametric approach      354Ч355
Bayesian analysis, compositional data, simulation based model, determination      352Ч354
Bayesian analysis, correlated ordinal data models      133Ч155
Bayesian analysis, GLM      273Ч284
Bayesian analysis, informative prior elicitation      44Ч46
Bayesian analysis, likelihood analysis      6
Bayesian analysis, logit regression model      243
Bayesian analysis, model choice      15Ч16
Bayesian computations      36Ч37
Bayesian deviance      16
Bayesian fitting, one-parameter model, item response modeling      185
Bayesian generalized linear models, post AMI practice guideline development      209Ч210
Bayesian generalized linear models, small area inference      89Ч105
Bayesian generalized linear models, small area inference, challenges and future directions      102Ч104
Bayesian generalized linear models, small area inference, computational issues      96Ч100
Bayesian generalized linear models, small area inference, Poisson regression models      94Ч96
Bayesian generalized linear models, small area inference, U.S. mortality data      100Ч102
Bayesian graphical models, computation      388Ч389
Bayesian graphical models, conditional independence structures      387Ч389
Bayesian graphical models, constructing software      389
Bayesian graphical models, marginal posterior distribution      388
Bayesian graphical models, Markov chain Monte Carlo, (MCMC) methods      388Ч389
Bayesian graphical models, WinBUGS      389
Bayesian hierarchical logistic regression, coronary angiography appropriateness      202Ч203
Bayesian hierarchical logistic regression, post AMI practice guideline development      209Ч210
Bayesian inferences, hierarchical GLMMs      36Ч37
Bayesian inferences, Markov Chain Monte Carlo, (MCMC)-based approaches      62Ч65
Bayesian MARS (BMARS)      222Ч223
Bayesian MARS (BMARS), generalized linear models      221Ч228
Bayesian MARS (BMARS), generalized linear models, motivating example      224Ч225
Bayesian MARS (BMARS), generalized linear models, Pima Indian example      225Ч228
Bayesian method, correlated binary data      113Ч129
Bayesian method, time series count data      159Ч171
Bayesian model      5Ч8
Bayesian model, adequacy criterion      14Ч15
Bayesian model, based method, post AMI practice guideline development      198Ч199
Bayesian model, diagnostics, correlated binary data      313Ч326
Bayesian model, multivariate exponential power distribution family links (MVEP)      137
Bayesian model, ordinal probit, post AMI practice guideline development      209Ч210
Bayesian model, partition, classification trees      371
Bayesian procedure, Markov Chain Monte Carlo (MCMC) implementation      12
Bayesian residual posterior distribution, box plots      250 250f
Bayesian residuals, item response modeling      186Ч187
Bayesian two-stage prior distribution, small area inference      96Ч97
Bayesian variable selection      48Ч50
Bayesian variable selection, Cox model      287Ч309
Bayesian variable selection, Gibbs sampler      273Ч284
Bayesian view, generalized linear models (GLMS)      3Ч17
BAYESTAT      121 122Ч123
BAYESTAT, correlated binary data      127
BayesТ approach, linear      60Ч61
BayesТ Theorem      59
Berkson measurement error model      332 341
Bernoulli distribution      390
Bernoulli random variables, small area inference      91Ч92
Beta processes      10
Binary regression, data adaptive Bayesian analysis      244Ч248
Binary regression, data adaptive Bayesian analysis, exponential power distribution      246Ч248
Binary regression, data adaptive Bayesian analysis, normal distribution      245
Binary regression, data adaptive robust link functions      243Ч251
Binary regression, data adaptive robust link functions, binary regression model      244Ч248
Binary regression, data adaptive robust link functions, numerical illustration      248Ч250
Binary regression, data adaptive robust link functions, outliers detection      248
Binary regression, nonparametric approach      219
Binary regression, parametric family of link functions      232
Binary response hierarchical model, correlated binary data      122
Binary response regression, application      237Ч239
Binary response regression, Dirichlet process prior      234Ч236
Binary response regression, finite mixture model      233Ч234
Binary response regression, general mixtures      234Ч236
Binary response regression, link function g modeling      218Ч219
Binary response regression, model diagnostic      236Ч237
Binary response regression, normal scale mixture links      231Ч240
Binomial distribution      5 25 390
Binomial logit hierarchical model      8
Binomial logit hierarchical model, small area inference      97
Birth step, classification trees      368
Box-Cox transformation      350Ч351 359Ч361
Boxplots, Bayesian residual posterior distribution      250 251f
Boxplots, kyphosis dataset      226f
Boxplots, posterior, multivariate probit (MVP)      119f
Boxplots, posterior, Probit hierarchical model      123f
Boxplots, posterior, probit normal model      121f
Breast cancer, classification trees      369Ч371 370f 371t
BrooksТs method      8
BrooksТs method, small area inference      97
Bugs      16 (see also УWinBUGSФ)
BUGS, codes      282Ч284)
BUGS, codes, log-linear models for $2^3$ contingency table      282Ч283
BUGS, codes, logistic models with 2 binary explanatory factors      283Ч284
BUGS, small area inference      94
BUGS, small area inference, Markov Chain Monte Carlo (MCMC)      96
Can Evaluate method, graphical model      403
Cancer clinical trials, variable selection, predictive approach      288
Canonical link function      224
Canonical link function, small area inference      98
Canonical parameters      5 12 13
Cargo data analysis, OGLMs      80
Carlin and ChibТs algorithm, conditional distribution sampling      122 129
Carlin and ChibТs method      275
Carlin and ChibТs method, contingency table      278Ч281
Carlin and ChibТs method, example      278Ч281
Carlin and ChibТs method, Gibbs sampler variable selection strategies      275
Carlin and ChibТs method, log-linear model example      280 280t
Carlin and ChibТs method, logistic regression model, example      280Ч281 281t
Carlin and ChibТs method, Stochastic Search Variable Selection (SSVS)      276
Carlin and ChibТs method, unconditional priors      277
CarstairsТ index      333
Categorical data, GLM      365
Censored survival data analysis of regression models      287
Check method, graphical model      403
Chen and Shao method, Monte Carlos posterior estimates      301
Chi-squared discrepancy measure      102
Chib and CarlinТs algorithm, conditional distribution sampling      122 129
Chib and CarlinТs method, Gibbs sampler variable selection strategies      275
ChibТs method, marginal likelihood      127
Classical approach, classification trees      367
Classical estimation procedures GLMs      5
Classical logistic regression model vs. logistic regression estimate      224Ч225 225f
Classical MARS, semiparametric generalized linear models      221Ч222
Classical measurement error, WinBUGS      398Ч399
Classification and regression trees (CART)      221
Classification trees      365Ч371
Classification trees, basis functions      366Ч367
Classification trees, basis functions, example      366f
Classification trees, Bayesian approach      368Ч369
Classification trees, Bayesian partition model      371
Classification trees, birth step      368
Classification trees, breast cancer      369Ч371 370f 371t
Classification trees, classical approach      367
Classification trees, death step      368
Classification trees, example      369Ч371
Classification trees, Poison prior      368
Clinical indications, development      197
Closed forms, small area inference      97
Clustered binary outcome models      123
Common logit      236
Compatible vs. functionally compatible      29
Complementary log-log link      390
Complete hierarchical centering reparameterization technique      48 51
Compositional data, Bayesian analysis      349Ч362
Compositional data, Bayesian analysis, parametric approach      351Ч352
Compositional data, Bayesian analysis, posterior distributions and estimation      355Ч359
Compositional data, Bayesian analysis, results      359Ч361 360tЧ361t
Compositional data, Bayesian analysis, semiparametric approach      354Ч355
Compositional data, Bayesian analysis, simulation based model determination      352Ч354
Conditional autoregressive (CAR) model, Besag      28
Conditional autoregressive (CAR) model, sample paths      32f
Conditional distribution sampling, Chib and Carlin algorithm      122 129
Conditional distribution, ability parameters, item response modeling      184
Conditional distribution, item parameters, item response modeling      185
Conditional distribution, latent variables, item response modeling      184
Conditional independence structures, Bayesian graphical models      387Ч389
Conditional latency distributions      255
Conditional marginal density estimation (CDME), time series count data      167
Conditional models, correlated binary data diagnostics      314Ч315
Conditional models, correlated binary data diagnostics, posterior computations, correlated binary data diagnostics      318
Conditional posterior distributions, small area inference      97 99
Conditional predictive ordinate, OGLMs      81
Consensus panel      196
Contingency table, Gibbs sampler variable selection      278Ч281
Convergence, WinBUGS      401
Convex credible regions      359Ч360
Coronary angiography, post AMI practice guideline development      198Ч199 205Ч208 206fЧ207f
Coronary angiography, post AMI practice guideline development, likelihood      209f
Correlated binary data diagnostics      313Ч326
Correlated binary data diagnostics, model adequacy for data      320Ч324
Correlated binary data diagnostics, model adequacy for data, posterior predictive comparison      322Ч323
Correlated binary data diagnostics, model adequacy for data, simulation based model checking      323Ч324
Correlated binary data diagnostics, models      314Ч316
Correlated binary data diagnostics, models, conditional      314Ч315
Correlated binary data diagnostics, models, MVP      315
Correlated binary data diagnostics, models, MVT      315Ч316
Correlated binary data diagnostics, models, stratified and mixture      314
Correlated binary data diagnostics, posterior computations      317Ч320
Correlated binary data diagnostics, posterior computations, conditional models      318
Correlated binary data diagnostics, posterior computations, MVP      318Ч320
Correlated binary data diagnostics, posterior computations, MVT      320
Correlated binary data diagnostics, posterior computations, stratified and mixture models      317
Correlated binary data diagnostics, prior distributions      316Ч317
Correlated binary data diagnostics, voter behavior data      324Ч325
Correlated binary data, Bayesian method      113Ч129
Correlated binary data, Bayesian method, longitudinal binary data      119Ч123
Correlated binary data, Bayesian method, multivariate probit model      114Ч119
Correlated ordinal data models, Bayesian analysis      133Ч155
Correlated ordinal data models, Bayesian analysis, item response data example      148Ч155
Correlated ordinal data models, Bayesian analysis, model comparisons      143Ч146
Correlated ordinal data models, Bayesian analysis, model determination      142Ч148
Correlated ordinal data models, Bayesian analysis, model diagnostics      146Ч148
Correlated ordinal data models, Bayesian analysis, models      135Ч137
Correlated ordinal data models, Bayesian analysis, posterior computations      138Ч142
Correlated ordinal data models, Bayesian analysis, prior distributions      138
Correlated random effects      26Ч29
Correlated random effects, GLMMs      392Ч393
Correlation matrix, direct specification      26Ч27
Count data, time series, Bayesian methods      159Ч171
Covariance structure, model adequacy      15
Covariate effects, multivariate probit (MVP)      118t
Covariate measurement error, WinBUGS      397Ч400
Cox variable selection      287Ч309
Cox variable selection, computational implementation      299Ч305
Cox variable selection, computational implementation, data marginal distribution      299Ч301
Cox variable selection, computational implementation, posterior distribution sampling      302Ч305
Cox variable selection, method      289Ч299
Cox variable selection, method, baseline hazard rate prior distribution      289Ч292
Cox variable selection, method, likelihood function      292Ч293
Cox variable selection, method, model and notation      289
Cox variable selection, method, model space prior distribution      297Ч299
Cox variable selection, method, regression coefficient prior distribution      293Ч297
Cox variable selection, simulation study      305Ч308
CoxТs partial likelihood, proportional hazards regression models      287
Cross-validation approach, OGLMs      80
Cumulative baseline hazard rate model      289Ч290
Curves and surfaces models      220Ч221
Data adaptive Bayesian analysis, binary regression model      244Ч248
Data adaptive robust link functions, binary regression      243Ч251
Data marginal distribution, Cox variable selection      299Ч301
Death step, classification trees      368
Dependence structures, correlated binary data      116
Dependent variable logit, small area inference      92
Deprivation score, histogram      336f
Deprivation score, spatial variation      335f
Deterministic component      389
Deterministic error model, systemic part h modeling      220
Deviance information criteria (DIG)      16 402
Diabetes, predicted probability      227f
Difficulty parameters, item response modeling      176
Difficulty parameters, posterior scatterplot      188f
Directed acyclic graph (DAG), GLM      387 388f
Directed acyclic graph (DAG), GLM, extensions      393f
Dirichlet Process (DP)      10 11
Dirichlet Process (DP), model determination      83Ч84
Dirichlet Process (DP), OGLMs      81
Dirichlet Process mixed generalized linear models (DPMGLMs)      14
Dirichlet Process mixed generalized linear models (DPMGLMs), OGLMs      81Ч84
Dirichlet Process mixed overdispersed generalized linear models (DPMOGLMs), OGLMs      81Ч84
Dirichlet process prior      219
Dirichlet process prior, binary response regression      234Ч236
Dirichlet process prior, compositional data      349Ч360
Dirichlet process prior, errors-in-variables      341
Discrimination parameters, item response modeling      176 180
Disease mapping      90
Disease mapping, small area inference      94
Dispersion parameter, OGLMs      77
distribution      274
Distribution, system errors      60
Distributional assumptions, GLMs      4
Disturbances, set of      58
DoodleBUGS, GLM      389Ч390
Double-exponential families      12
Double-exponential families, OGLMs      76
Drop-outs, longitudinal binary data      127
Dynamic generalized linear models (DGLMs)      57Ч70
Dynamic generalized linear models (DGLMs), applications      65Ч70
Dynamic generalized linear models (DGLMs), definition      59Ч60
Dynamic linear models (DLM)      58Ч59
EfronТs model      13
EM algorithm      256
EM algorithm, mixture-model approach example      262Ч263
Empirical Bayes (EB) approaches      90
Empirical Bayes (EB) approaches, Bayesian approaches      339Ч341
Empirical Bayes (EB) approaches, Bayesian approaches, framework      339Ч340
Empirical Bayes (EB) approaches, Bayesian approaches, implementation      340
Empirical Bayes (EB) approaches, Bayesian approaches, previous work      340Ч341
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