Preface
1 Introduction to Bayesian thinking
2 Introduction to Bayesian science
3 Assigning a prior distribution
4 Assigning a likelihood function
5 Deriving the posterior distribution
6 Sampling from any distribution by MCMC
7 Sampling from the posterior distribution by MCMC
8 Twelve ways to fit a straight line
9 MCMC and complex models
10 Bayesian calibration and MCMC: Frequently asked questions
11 After the calibration: Interpretation, reporting, visualization
2 Model ensembles: BMC and BMA
13 Discrepancy
14 Gaussian Processes and model emulation
15 Graphical Modelling (GM)
16 Bayesian Hierarchical Modelling (BHM)
17 Probabilistic risk analysis and Bayesian decision theory
18 Approximations to Bayes
19 Linear modelling: LM, GLM, GAM and mixed models
20 Machine learning
21 Time series and data assimilation
22 Spatial modelling and scaling error
23 Spatio-temporal modelling and adaptive sampling
24 What next?
Appendix 1: Notation and abbreviations
Appendix 2: Mathematics for modellers
Appendix 3: Probability theory for modellers
Appendix 4: R
Appendix 5: Bayesian software.