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出版社:世界圖書出版公司 ISBN:9787519261818 商品編碼:10020133222785 品牌:文軒 出版時間:2020-06-01 代碼:169 作者:安德魯·格爾曼等
" 作 者:(美)安德魯·格爾曼 等 著 定 價:169 出 版 社:世界圖書出版公司 出版日期:2020年06月01日 頁 數:667 裝 幀:平裝 ISBN:9787519261818 ●Preface Part I: Fundamentals of Bayesian Inference 1 Probability and inference I.I The three steps of Bayesian data analysis 1.2 General notation for statistical inference 1.3 Bayesian inference 1.4 Discrete examples: genetics and spell checking 1.5 Probability as a measure of uncertainty 1.6 Example: probabilities from football point spreads 1.7 Example: calibration for record linkage 1.8 Some useful results from probability theory 1.9 Computation and software I.I0 Bayesian inference in applied statistics i.Ii Bibliographic note 1.12 Exercises 2 Single-parameter models 2.1 Estimating a probability from binomial data 2.2 terior as compromise between data and prior information 2.3 Summarizing posterior inference 2.4 Informative prior distributions 2.5 Normal distribution with known variance 2.6 Other standard single-parameter models 2.7 Example: informative prior distribution for cancer rates 2.8 Noninformative prior distributions 2.9 Weakly informative prior distributions 2.10 Bibliographic note 2.11 Exercises 3 Introduction to multiparameter models 3.1 Averaging over 'nuisance parameters' 3.2 Normal data with a noninformative prior distribution 3.3 Normal data with a conjugate prior distribution 3.4 ltinomial model for categorical data 3.5 ltivariate normal model with known variance 3.6 ltivariate normal with unknown mean and variance 3.7 Example: analysis of a bioassay experiment 3.8 Summary of elementary modeling and computation 3.9 Bibliographic note 3.10 Exercises 4 Asymptotics and connections to non-Bayesian approaches 4.1 Normal approximations to the posterior distribution 4.2 Large-sample theory 4.3 Counterexamples to the theorems 4.4 Frequency evaluations of Bayesian inferences 4.5 Bayesian interpretations of other statistical methods 4.6 Bibliographic note 4.7 Exercises 5 Hierarchical models 5.1 Constructing a parameterized prior distribution 5.2 Exchangeability and hierarchical models 5.3 Bayesian analysis of conjugate hierarchical models 5.4 Normal model with exchangeable parameters 5.5 Example: parallel experiments in eight schools 5.6 Hierarchical modeling applied to a meta-analysis 5.7 Weakly informative priors for variance parameters 5.8 Bibliographic note 5.9 Exercises Part II: Fundamentals of Bayesian Data Analysis 6 Model checking 6.1 The place of model checking in applied Bayesian statistics 6.2 Do the inferences from the model make sense? 6.3 terior predictive checking 6.4 Graphical posterior predictive checks 6.5 Model checking for the educational testing example 6.6 Bibliographic note 6.7 Exercises ? Evaluating, comparing, and expanding models 7.1 Measures of predictive accuracy 7.2 Information criteria and cross-validation 7.3 Model comparison based on predictive performance 7.4 Model comparison using Bayes factors 7.5 Continuous model expansion 7.6 Implicit assumptions and model expansion: an example 7.7 Bibliographic note 7.8 Exercises 8 Modeling accounting for data collection 8.1 Bayesian inference requires a model for data collection 8.2 Data-collection models and ignorability 8.3 Sample surveys 8.4 Designed experiments 8.5 Sensitivity and the role of randomization 8.6 Observational studies 8.7 Censoring and truncation 8.8 Discussion 8.9 Bibliographic note 8.10 Exercises 9 Decision analysis 9.1 Bayesian decision theory in different contexts 9.2 Using regression predictions: survey incentives 9.3 ltistage decision making: medical screening 9.4 Hierarchical decision analysis for home radon 9.5 Personal vs. institutional decision analysis 9.6 Bibliographic note 9.7 Exercises Part III: Advanced Computation 10 Introduction to Bayesian computation 10.1 Numerical integration 10.2 Distributional approximations 10.3 Direct simulation and rejection sampling 10.4 Importance sampling 10.5 How many simulation draws are needed? 10.6 Computing environments 10.7 Debugging Bayesian computing 10.8 Bibliographic note 10.9 Exercises 11 Basics of Markov chain simulation 11.1 Gibbs sampler 11.2 Metropolis and Metropolis-Hastings algorithms 11.3 Using Gibbs and Metropolis as building blocks 11.4 Inference and assessing convergence 11.5 Effective number of simulation draws 11.6 Example: hierarchical normal model 11.7 Bibliographic note 11.8 Exercises 12 Computationally efficient Markov chain simulation 12.1 Efficient Gibbs samplers 12.2 Efficient Metropolis jumping rules 12.3 Further extensions to Gibbs and Metropolis 12.4 Hamiltonian Monte Carlo 12.5 Hamiltonian Monte Carlo for a hierarchical model 12.6 Stan: developing a computing environment 12.7 Bibliographic note 12.8 Exercises 13 Modal and distributional approximations 13.1 Finding posterior modes 13.2 Boundary-avoiding priors for modal summaries 13.3 Normal and related mixture approximations 13.4 Finding marginal posterior modes using EM 13.5 Conditional and marginal posterior approximations 13.6 Example: hierarchical normal model (continued) 13.7 Variational inference 13.8 Expectation propagation 13.9 Other approximations 13.10 Unknown normalizing factors 13.11 Bibliographic note 13.12 Exercises Part IV: Regression Models 14 Introduction to regression models 14.1 Conditional modeling 14.2 Bayesian analysis of classical regression 14.3 Regression for causal inference: incumbency and voting 14.4 Goals of regression analysis 14.5 Assembling the matrix of explanatory variables 14.6 Regularization and dimension reduction 14.7 Unequal variances and correlations 14.8 Including numerical prior information 14.9 Bibliographic note 14.10 Exercises 15 Hierarchical linear models 15.1 Regression coefficients exchangeable in batches 15.2 Example: forecasting U.S. presidential elections 15.3 Interpreting a normal prior distribution as extra data 15.4 Varying intercepts and slopes 15.5 Computation: batching and transformation 15.6 Analysis of variance and the batching of coefficients 15.7 Hierarchical models for batches of variance components 15.8 Bibliographic note 15.9 Exercises 16 Generalized linear models 16.1 Standard generalized linear model likelihoods 16.2 Working with generalized linear models 16.3 Weakly informative priors for logistic regression 16.4 Overdispersed Poisson regression for police stops 16.5 State-level opinons from national polls 16.6 Models for multivariate and multinomial responses 16.7 Loglinear models for multivariate discrete data 16.8 Bibliographic note 16.9 Exercises 17 Models for robust inference 17.1 Aspects of robustness 17.2 Overdispersed versions of standard models 17.3 terior inference and computation 17.4 Robust inference for the eight schools 17.5 Robust regression using t-distributed errors 17.6 Bibliographic note 17.7 Exercises 18 Models for missing data 18.1 Notation 18.2 ltiple imputation 18.3 Missing data in the multivariate normal and t models 18.4 Example: multiple imputation for a series of polls 18.5 Missing values with counted data 18.6 Example: an opinion poll in Slovenia 18.7 Bibliographic note 18.8 Exercises Part V: Nonlinear and Nonparametric Models 19 Parametric nonlinear models 19.1 Example: serial dilution assay 19.2 Example: population toxicokinetics 19.3 Bibliographic note 19.4 Exercises 20 Basis function models 20.1 Splines and weighted sums of basis functions 20.2 Basis selection and shrinkage of coefficients 20.3 Non-normal models and regression surfaces 20.4 Bibliographic note 20.5 Exercises 21 Gaussian process models 21.1 Gaussian process regression 21.2 Example: birthdays and birthdates 21.3 Latent Gaussian process models 21.4 Functional data analysis 21.5 Density estimation and regression 21.6 Bibliographic note 21.7 Exercises 22 Finite mixture models 22.1 Setting up and interpreting mixture models 22.2 Example: reaction times and schizophrenia 22.3 Label switching and posterior computation 22.4 Unspecified number of mixture components 22.5 Mixture models for classification and regression 22.6 Bibliographic note 22.7 Exercises 23 Dirichlet process models 23.1 Bayesian histograms 23.2 Dirichlet process prior distributions 23.3 Dirichlet process mixtures 23.4 Beyond density estimation 23.5 Hierarchical dependence 23.6 Density regression 23.7 Bibliographic note 23.8 Exercises Appendixes A Standard probability distributions A.1 Continuous distributions A.2 Discrete distributions A.3 Bibliographic note B Outline of proofs of limit theorems B.1 Bibliographic note C Computation in R and Stan C.1 Getting started with R and Stan C.2 Fitting a hierarchical model in Stan C.3 Direct simulation, Gibbs, and Metropolis in R C.4 Programming Hamiltonian Monte Carlo in R C.5 Further comments on computation C.6 Bibliographic note References Author Index Subject Index 這本書獲得了2016年德格魯特獎(De Groot Prize),兩年一次的統計教科書獎。這是第三版,這部教材已經相當經典了。是一部被廣泛認可的關於貝葉斯方法的最領先的讀本,因為其易於理解、分析數據和解決研究問題的實際操作性強而廣受贊譽。貝葉斯數據分析,第三版應用近期新的貝葉斯方法,繼續采用實用的方法來分析數據。作者均是統計界的領導人物,在呈現更高等的方法之前,從數據分析的觀點引進基本概念。整本書從始至終,從實際應用和研究中提取的大量的練習實例強調了貝葉斯推理在實踐中的應用。
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