Bayesian Compendium

Marcel van Oijen studied mathematical biology at the University of Utrecht. He completed his PhD in plant disease epidemiology at Wageningen University, where he worked on modelling the impacts of environmental change on crops. He moved to the U.K. in 1999, becoming a Senior Scientist at the Natural Environment Research Council. There he focused on the use of Bayesian methods in the modelling of ecosystem services provided by grasslands, forests and agroforestry systems. He now works as an independent scientist and as such has written two books: Bayesian Compendium (first edition in 2020) and Probabilistic Risk Analysis and Bayesian Decision Theory (2022).

• - 1. Science and Uncertainty.- 2. Bayesian Inference.- 3. Assigning a Prior Distribution.- 4. Assigning a Likelihood Function.- 5. Deriving the Posterior Distribution.- 6. Markov Chain Monte Carlo Sampling (MCMC).- 7. Sampling from the Posterior Distribution by MCMC.- 8. MCMC and Multivariate Models.- 9. Bayesian Calibration and MCMC: Frequently Asked Questions.- 10. After the Calibration: Interpretation, Reporting, Visualisation.- 11. Model Ensembles: BMC and BMA.- 12. Discrepancy.- 13. Approximations to Bayes.- 14.Thirteen Ways to Fit a Straight Line.- 15. Gaussian Processes and Model Emulation.- 16. Graphical Modelling.- 17. Bayesian Hierarchical Modelling.- 18. Probabilistic Risk Analysis.- 19. Bayesian Decision Theory.- 20. Linear Modelling: LM, GLM, GAM and Mixed Models.- 21. Machine Learning.- 22. Time Series and Data Assimilation.- 23. Spatial Modelling and Scaling Error.- 24. Spatio-Temporal Modelling and Adaptive Sampling.- 25. What Next?.