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E-raamat: Bayesian Regression Modeling with INLA

4.00/5 (2 hinnangut Goodreads-ist)
(Cleveland Clinic Lerner College of Medicine, Case Western Reserve University, USA), (University of Bath, UK), (Department of Statistics and CIS, Baruch College, NY, USA)
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INLA stands for Integrated Nested Laplace Approximations, which is a new method for fitting a broad class of Bayesian regression models. No samples of the posterior marginal distributions need to be drawn using INLA, so it is a computationally convenient alternative to Markov chain Monte Carlo (MCMC), the standard tool for Bayesian inference.

Bayesian Regression Modeling with INLA covers a wide range of modern regression models and focuses on the INLA technique for building Bayesian models using real-world data and assessing their validity. A key theme throughout the book is that it makes sense to demonstrate the interplay of theory and practice with reproducible studies. Complete R commands are provided for each example, and a supporting website holds all of the data described in the book. An R package including the data and additional functions in the book is available to download.

The book is aimed at readers who have a basic knowledge of statistical theory and Bayesian methodology. It gets readers up to date on the latest in Bayesian inference using INLA and prepares them for sophisticated, real-world work.

Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic.

Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York.

Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.

Arvustused

"The book focuses on regression models with R-INLA and it will be of interest to a wide audience. INLA is becoming a very popular method for approximate Bayesian inference and it is being applied to many problems in many different fields. This book will be of interest not only to statisticians but also to applied researchers in other disciplines interested in Bayesian inference. This book can probably be used as a reference book for research and as a textbook at graduate level." ~Virgilio Gómez-Rubio,University of Castilla-La Mancha

"This is a well-written book on an important subject, for which there is a lack of good introductory material. The tutorial-style works nicely, and they have an excellent set of examples. They manage to do a practical introduction with just the right amount of theory backgroundThe book should be very useful to scientists who want to analyze data using regression models. INLA allows users to fit Bayesian models quickly and without too much programming effort, and it has been used successfully in many applications. The book is written in a tutorial style, while explaining the basics of the needed theory very well, so it could serve both as a reference or textbookThe book is well written and technically correct." ~Egil Ferkingstad, deCode genetics

"The authors have done a great job of not over-doing the technical details, thereby making the presentation accessible to a broader audience beyond the statistics worldIt covers many contemporary parametric, nonparametric, and semiparametric methods that applied scientists from many fields use in modern research." ~Adam Branscum, Oregon State University "The book focuses on regression models with R-INLA and it will be of interest to a wide audience. INLA is becoming a very popular method for approximate Bayesian inference and it is being applied to many problems in many different fields. This book will be of interest not only to statisticians but also to applied researchers in other disciplines interested in Bayesian inference. This book can probably be used as a reference book for research and as a textbook at graduate level." ~Virgilio Gómez-Rubio, University of Castilla-La Mancha

"This is a well-written book on an important subject, for which there is a lack of good introductory material. The tutorial-style works nicely, and they have an excellent set of examples. They manage to do a practical introduction with just the right amount of theory backgroundThe book should be very useful to scientists who want to analyze data using regression models. INLA allows users to fit Bayesian models quickly and without too much programming effort, and it has been used successfully in many applications. The book is written in a tutorial style, while explaining the basics of the needed theory very well, so it could serve both as a reference or textbookThe book is well written and technically correct." ~Egil Ferkingstad, deCode genetics

"The authors have done a great job of not over-doing the technical details, thereby making the presentation accessible to a broader audience beyond the statistics worldIt covers many contemporary parametric, nonparametric, and semiparametric methods that applied scientists from many fields use in modern research." ~Adam Branscum, Oregon State University

1 Introduction
1(18)
1.1 Quick Start
1(7)
1.1.1 Hubble's Law
1(1)
1.1.2 Standard Analysis
2(1)
1.1.3 Bayesian Analysis
3(1)
1.1.4 INLA
4(4)
1.2 Bayes Theory
8(1)
1.3 Prior and Posterior Distributions
9(2)
1.4 Model Checking
11(1)
1.5 Model Selection
12(1)
1.6 Hypothesis Testing
13(2)
1.7 Bayesian Computation
15(4)
1.7.1 Exact
15(1)
1.7.2 Sampling
16(1)
1.7.3 Approximation
17(2)
2 Theory of INLA
19(20)
2.1 Latent Gaussian Models (LGMs)
19(2)
2.2 Gaussian Markov Random Fields (GMRFs)
21(2)
2.3 Laplace Approximation and INLA
23(8)
2.4 INLA Problems
31(4)
2.5 Extensions
35(4)
3 Bayesian Linear Regression
39(32)
3.1 Introduction
39(1)
3.2 Bayesian Inference for Linear Regression
40(7)
3.3 Prediction
47(2)
3.4 Model Selection and Checking
49(7)
3.4.1 Model Selection by DIC
49(1)
3.4.2 Posterior Predictive Model Checking
50(2)
3.4.3 Cross-Validation Model Checking
52(2)
3.4.4 Bayesian Residual Analysis
54(2)
3.5 Robust Regression
56(1)
3.6 Analysis of Variance
57(2)
3.7 Ridge Regression for Multicollinearity
59(4)
3.8 Regression with Autoregressive Errors
63(8)
4 Generalized Linear Models
71(30)
4.1 GLMs
71(2)
4.2 Binary Responses
73(3)
4.3 Count Responses
76(8)
4.3.1 Poisson Regression
77(2)
4.3.2 Negative Binomial Regression
79(5)
4.4 Modeling Rates
84(3)
4.5 Gamma Regression for Skewed Data
87(4)
4.6 Proportional Responses
91(5)
4.7 Modeling Zero-Inflated Data
96(5)
5 Linear Mixed and Generalized Linear Mixed Models
101(40)
5.1 Linear Mixed Models
101(1)
5.2 Single Random Effect
102(9)
5.2.1 Choice of Priors
106(3)
5.2.2 Random Effects
109(2)
5.3 Longitudinal Data
111(8)
5.3.1 Random Intercept
112(1)
5.3.2 Random Slope and Intercept
113(3)
5.3.3 Prediction
116(3)
5.4 Classical Z-Matrix Model
119(5)
5.4.1 Ridge Regression Revisited
121(3)
5.5 Generalized Linear Mixed Models
124(1)
5.6 Poisson GLMM
125(8)
5.7 Binary GLMM
133(8)
5.7.1 Improving the Approximation
139(2)
6 Survival Analysis
141(28)
6.1 Introduction
141(2)
6.2 Semiparametric Models
143(5)
6.2.1 Piecewise Constant Baseline Hazard Models
143(3)
6.2.2 Stratified Proportional Hazards Models
146(2)
6.3 Accelerated Failure Time Models
148(3)
6.4 Model Diagnosis
151(6)
6.5 Interval Censored Data
157(3)
6.6 Frailty Models
160(4)
6.7 Joint Modeling of Longitudinal and Time-to-Event Data
164(5)
7 Random Walk Models for Smoothing Methods
169(42)
7.1 Introduction
169(1)
7.2 Smoothing Splines
170(15)
7.2.1 Random Walk (RW) Priors for Equally-Spaced Locations
170(6)
7.2.2 Choice of Priors on σ2ε and σ2f
176(3)
7.2.3 Random Walk Models for Non-Equally Spaced Locations
179(6)
7.3 Thin-Plate Splines
185(7)
7.3.1 Thin-Plate Splines on Regular Lattices
185(3)
7.3.2 Thin-Plate Splines at Irregularly-Spaced Locations
188(4)
7.4 Besag Spatial Model
192(3)
7.5 Penalized Regression Splines (P-Splines)
195(3)
7.6 Adaptive Spline Smoothing
198(3)
7.7 Generalized Nonparametric Regression Models
201(5)
7.8 Excursion Set with Uncertainty
206(5)
8 Gaussian Process Regression
211(18)
8.1 Introduction
211(5)
8.2 Penalized Complexity Priors
216(1)
8.3 Credible Bands for Smoothness
217(3)
8.4 Non-Stationary Fields
220(2)
8.5 Interpolation with Uncertainty
222(4)
8.6 Survival Response
226(3)
9 Additive and Generalized Additive Models
229(22)
9.1 Additive Models
229(7)
9.2 Generalized Additive Models
236(9)
9.2.1 Binary Response
237(3)
9.2.2 Count Response
240(5)
9.3 Generalized Additive Mixed Models
245(6)
10 Errors-in-Variables Regression
251(16)
10.1 Introduction
251(3)
10.2 Classical Errors-in-Variables Models
254(9)
10.2.1 A Simple Linear Model with Heteroscedastic Errors-in-Variables
254(3)
10.2.2 A General Exposure Model with Replicated Measurements
257(6)
10.3 Berkson Errors-in-Variables Models
263(4)
11 Miscellaneous Topics in INLA
267(22)
11.1 Splines as a Mixed Model
267(5)
11.1.1 Truncated Power Basis Splines
267(1)
11.1.2 O'Sullivan Splines
268(1)
11.1.3 Example: Canadian Income Data
269(3)
11.2 Analysis of Variance for Functional Data
272(6)
11.3 Extreme Values
278(5)
11.4 Density Estimation Using INLA
283(6)
Appendix A Installation 289(2)
Appendix B Uninformative Priors in Linear Regression 291(6)
Bibliography 297(12)
Index 309
Xiaofeng Wang is Professor of Medicine and Biostatistics at the Cleveland Clinic Lerner College of Medicine of Case Western Reserve University and a Full Staff in the Department of Quantitative Health Sciences at Cleveland Clinic.

Yu Ryan Yue is Associate Professor of Statistics in the Paul H. Chook Department of Information Systems and Statistics at Baruch College, The City University of New York.

Julian J. Faraway is Professor of Statistics in the Department of Mathematical Sciences at the University of Bath.
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