Wang X., Yue Y.R., Faraway J. Bayesian Regression Modeling with INLA

Boca Raton: CRC Press, 2018. — 313 p.FeaturesCovers a variety of regression models
Discusses real case studies
Includes R code examples
Explains innovative and efficient Bayesian inference
Handles complex dataThis book addresses the applications of extensively used regression models under a Bayesian framework. It emphasizes efficient Bayesian inference through integrated nested Laplace approximations (INLA) and real data analysis using R. The INLA method directly computes very accurate approximations to the posterior marginal distributions and is a promising alternative to Markov chain Monte Carlo (MCMC) algorithms, which come with a range of issues that impede practical use of Bayesian models.Quick Start
Hubble’s Law
Standard Analysis
Bayesian Analysis
INLA
Bayes Theory
Prior and Posterior Distributions
Model Checking
Model Selection
Hypothesis testing
Bayesian Computation
Exact
Sampling
ApproximationTheory of INLA
Latent Gaussian Models (LGMs)
Gaussian Markov Random Fields (GMRFs)
Laplace Approximation and INLA
INLA Problems
ExtensionsBayesian Linear RegressionBayesian Inference for Linear Regression
Prediction
Model Selection and Checking
Model Selection by DIC
Posterior Predictive Model Checking
Cross-validation Model Checking
Bayesian Residual Analysis
Robust Regression
Analysis of Variance
Ridge Regression for Multicollinearity
Regression with Autoregressive ErrorsGeneralized Linear Models
GLMs
Binary Responses
Count Responses
Poisson Regression
Negative binomial regression
Modeling Rates
Gamma Regression for Skewed Data
Proportional Responses
Modeling Zero-inflated DataLinear Mixed and Generalized Linear Mixed Models
Linear Mixed Models
Single Random Effect
Choice of Priors
Random Effects
Longitudinal Data
Random Intercept
Random Slope and Intercept
Prediction
Classical Z-matrix Model
Ridge Regression Revisited
Generalized Linear Mixed Models
Poisson GLMM
Binary GLMM
Improving the ApproximationSurvival AnalysisSemiparametric Models
Piecewise Constant Baseline Hazard Models
Stratified Proportional Hazards Models
Accelerated Failure Time Models
Model Diagnosis
Interval Censored Data
Frailty Models
Joint Modeling of Longitudinal and Time-to-event DataRandom Walk Models for Smoothing MethodsSmoothing Splines
Random Walk (RW) Priors for Equally-spaced Locations
Choice of Priors on s e and sf
Random Walk Models for Non-equally Spaced Locations
Thin-plate Splines
Thin-plate Splines on Regular Lattices
Thin-plate Splines at Irregularly-spaced Locations
Besag Spatial Model
Penalized Regression Splines (P-splines)
Adaptive Spline Smoothing
Generalized Nonparametric Regression Models
Excursion Set with UncertaintyGaussian Process RegressionPenalized Complexity Priors
Credible Bands for Smoothness
Non-stationary Fields
Interpolation with Uncertainty
Survival ResponseAdditive and Generalized Additive Models
Additive Models
Generalized Additive Models
Binary response
Count response
Generalized Additive Mixed ModelsErrors-in-Variables RegressionClassical Errors-in-Variables Models
A simple linear model with heteroscedastic errors-invariables
A general exposure model with replicated measurements
Berkson Errors-in-Variables ModelsMiscellaneous Topics in INLA
Splines as a Mixed Model
Truncated Power Basis Splines
O’Sullivan Splines
Example: Canadian Income Data
Analysis of Variance for Functional Data
Extreme Values
Density Estimation using INLAAppendix A Installation
Appendix B Uninformative Priors in Linear Regression