Intro
Preface
Contents
Bayesian Latent Gaussian Models
1 Introduction
1.1 Structure of This Chapter and the Book
2 The Class of Bayesian Latent Gaussian Models
2.1 Bayesian Gaussian-Gaussian Models
2.1.1 The Structure of Bayesian Gaussian-Gaussian Models
2.1.2 Posterior Inference for Gaussian-Gaussian Models
2.1.3 Predictions Based on Gaussian-Gaussian Models
2.2 Bayesian LGMs with a Univariate Link Function
2.2.1 The Structure of Bayesian LGMs with a Univariate Link Function
2.2.2 Posterior Inference for LGMs with a Univariate Link Function Using INLA

2.2.3 Predictions Based on LGMs with a Univariate Link Function
2.3 Bayesian LGMs with a Multivariate Link Function
2.3.1 The Structure of Bayesian LGMs with a Multivariate Link Function
2.3.2 Posterior Inference for LGMs with a Multivariate Link Function
2.3.3 Predictions Based on LGMs with a Multivariate Link Function
3 Priors for the Parameters of Bayesian LGMs
3.1 Priors for the Fixed Effects
3.2 Priors for the Random Effects
3.3 Priors for the Hyperparameters
3.3.1 Penalized Complexity Priors

3.3.2 PC Priors for Hyperparameters in Common Temporal and Spatial Models
3.3.3 Priors for Multiple Variance Parameters
4 Application of the Bayesian Gaussian-Gaussian Model-Evaluation of Manning's Formula
4.1 The Application and Data
4.2 Statistical Model
4.3 Inference Scheme
4.4 Results
5 Application of a Bayesian LGM with a Univariate Link Function-Predicting Chances of Precipitation
5.1 The Application and Data
5.2 Statistical Model
5.3 Inference Scheme
5.4 Results
6 Application of Bayesian LGMs with a Multivariate Link Function-Three Examples

6.1 Seasonal Temperature Forecast
6.2 High-dimensional Spatial Extremes
6.3 Monthly Precipitation
Bibliographic Note
Appendix
Posterior Computation for the Gaussian-Gaussian Model
The LGM Split Sampler
References
A Review of Bayesian Modelling in Glaciology
1 Introduction
2 A Synopsis of Bayesian Modelling and Inference in Glaciology
2.1 Gaussian-Gaussian Models
2.2 Bayesian Hierarchical Models
2.3 Bayesian Calibration of Physical Models
3 Spatial Prediction of Langjökull Surface Mass Balance
4 Assessing Antarctica's Contribution to Sea-Level Rise

5 Conclusions and Future Directions
Appendix: Governing Equations
References
Bayesian Discharge Rating Curves Based on the Generalized Power Law
1 Introduction
2 Data
3 Statistical Models
4 Posterior Inference
5 Results and Software
6 Summary
References
Bayesian Modeling in Engineering Seismology: Ground-MotionModels
1 Introduction
2 Ground-Motion Models
3 Methods
3.1 Regression Analysis
3.2 Bayesian Inference
4 Applications
4.1 Site Effect Characterization Using a Bayesian Hierarchical Model for Array Strong Ground Motions