Bayesian Regression Modeling with Inla

Content: 1.Introduction  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                             Approximation                          2.Theory of INLA  Latent Gaussian Models (LGMs)                    Gaussian Markov Random Fields (GMRFs)               Laplace Approximation and INLA                    INLA Problems                              Extensions                                3.Bayesian Linear Regression  Introduction                                Bayesian 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 Errors                4.Generalized Linear Models  GLMs                                   Binary Responses                             Count Responses                             Poisson Regression                        Negative binomial regression                   Modeling Rates                              Gamma Regression for Skewed Data                  Proportional Responses                         Modeling Zero-inflated Data                       5.Linear 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 Approximation                 6.Survival Analysis  Introduction                                Semiparametric 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 Data        7.Random Walk Models for Smoothing Methods  Introduction                                Smoothing 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 Uncertainty                     8.Gaussian Process Regression  Introduction                                Penalized Complexity Priors                       Credible Bands for Smoothness                     Non-stationary Fields                           Interpolation with Uncertainty                      Survival Response                            9.Additive and Generalized Additive Models  Additive Models                             Generalized Additive Models                      Binary response                          Count response                          Generalized Additive Mixed Models                   10.Errors-in-Variables Regression  Introduction                                Classical Errors-in-Variables Models                  A simple linear model with heteroscedastic errors-invariables A general exposure model with replicated measurements    Berkson Errors-in-Variables Models                  11.Miscellaneous 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 INLA                     Appendix A Installation  Appendix B Uninformative Priors in Linear Regression  Index