Description
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.
