Bayesian regression modeling with INLA / Xiaofeng Wang, Yu Yue, Julian J. Faraway.

Format:

Book

Author/Creator:

Wang, Xiaofeng (Professor of medicine), author.

Yue, Yu, 1981- author.

Faraway, Julian James, author.

Contributor:

ProQuest ebook central.

Language:

English

Subjects (All):

Regression analysis.

Bayesian statistical decision theory.

Laplace transformation.

Gaussian processes.

Physical Description:

1 online resource

Other Title:

Bayesian regression modeling with integrated Laplace approximation

Place of Publication:

Boca Raton : CRC Press, 2018.

System Details:

text file

Summary:

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. Book jacket.

Contents:

1 Introduction 1

1.1 Quick Start 1

1.1.1 Hubble's Law 1

1.1.2 Standard Analysis 2

1.1.3 Bayesian Analysis 3

1.1.4 INLA 4

1.2 Bayes Theory 8

1.3 Prior and Posterior Distributions 9

1.4 Model Checking 11

1.5 Model Selection 12

1.6 Hypothesis Testing 13

1.7 Bayesian Computation 15

1.7.1 Exact 15

1.7.2 Sampling 16

1.7.3 Approximation 17

2 Theory of INLA 19

2.1 Latent Gaussian Models (LGMs) 19

2.2 Gaussian Markov Random Fields (GMRFs) 21

2.3 Laplace Approximation and INLA 23

2.4 INLA Problems 31

2.5 Extensions 35

3 Bayesian Linear Regression 39

3.1 Introduction 39

3.2 Bayesian Inference for Linear Regression 40

3.3 Prediction 47

3.4 Model Selection and Checking 49

3.4.1 Model Selection by DIC 49

3.4.2 Posterior Predictive Model Checking 50

3.4.3 Cross-Validation Model Checking 52

3.4.4 Bayesian Residual Analysis 54

3.5 Robust Regression 56

3.6 Analysis of Variance 57

3.7 Ridge Regression for Multicollinearity 59

3.8 Regression with Autoregressive Errors 63

4 Generalized Linear Models 71

4.1 GLMs 71

4.2 Binary Responses 73

4.3 Count Responses 76

4.3.1 Poisson Regression 77

4.3.2 Negative Binomial Regression 79

4.4 Modeling Rates 84

4.5 Gamma Regression for Skewed Data 87

4.6 Proportional Responses 91

4.7 Modeling Zero-Inflated Data 96

5 Linear Mixed and Generalized Linear Mixed Models 101

5.1 Linear Mixed Models 101

5.2 Single Random Effect 102

5.2.1 Choice of Priors 106

5.2.2 Random Effects 109

5.3 Longitudinal Data m

5.3.1 Random Intercept 112

5.3.2 Random Slope and Intercept 113

5.3.3 Prediction 116

5.4 Classical Z-Matrix Model 119

5.4.1 Ridge Regression Revisited 121

5.5 Generalized Linear Mixed Models 124

5.6 Poisson GLMM 125

5.7 Binary GLMM 133

5.7.1 Improving the Approximation 139

6 Survival Analysis 141

6.1 Introduction 141

6.2 Semiparametric Models 143

6.2.1 Piecewise Constant Baseline Hazard Models 143

6.2.2 Stratified Proportional Hazards Models 146

6.3 Accelerated Failure Time Models 148

6.4 Model Diagnosis 151

6.5 Interval Censored Data 157

6.6 Frailty Models 160

6.7 Joint Modeling of Longitudinal and Time-to-Event Data 164

7 Random Walk Models for Smoothing Methods 169

7.1 Introduction 169

7.2 Smoothing Splines 170

7.2.1 Random Walk (RW) Priors for Equally-Spaced Locations 170

7.2.2 Choice of Priors on σ²_ε and σ²_f 176

7.2.3 Random Walk Models for Non-Equally Spaced Locations 179

7.3 Thin-Plate Splines 185

7.3.1 Thin-Plate Splines on Regular Lattices 185

7.3.2 Thin-Plate Splines at Irregularly-Spaced Locations 188

7.4 Besag Spatial Model 192

7.5 Penalized Regression Splines (P-Splines) 195

7.6 Adaptive Spline Smoothing 198

7.7 Generalized Nonparametric Regression Models 201

7.8 Excursion Set with Uncertainty 206

8 Gaussian Process Regression 211

8.1 Introduction 211

8.2 Penalized Complexity Priors 216

8.3 Credible Bands for Smoothness 217

8.4 Non-Stationary Fields 220

8.5 Interpolation with Uncertainty 222

8.6 Survival Response 226

9 Additive and Generalized Additive Models 229

9.1 Additive Models 229

9.2 Generalized Additive Models 236

9.2.1 Binary Response 237

9.2.2 Count Response 240

9.3 Generalized Additive Mixed Models 245

10 Errors-in-Variables Regression 251

10.1 Introduction 251

10.2 Classical Errors-in-Variables Models 254

10.2.1 A Simple Linear Model with Heteroscedastic Errors-in-Variables 254

10.2.2 A General Exposure Model with Replicated Measurements 257

10.3 Berkson Errors-in-Variables Models 263

11 Miscellaneous Topics in INLA 267

11.1 Splines as a Mixed Model 267

11.1.1 Truncated Power Basis Splines 267

11.1.2 O'Sullivan Splines 268

11.1.3 Example: Canadian Income Data 269

11.2 Analysis of Variance for Functional Data 272

11.3 Extreme Values 278

11.4 Density Estimation Using INLA 283.

Notes:

Includes index.

Electronic reproduction. Ann Arbor, MI Available via World Wide Web.

Description based on print version record.

ISBN:

9781351165747

1351165747

Publisher Number:

99976193978

Access Restriction:

Restricted for use by site license.