Van Oijen M. Bayesian Compendium

Springer, 2020. — 209 p. — ISBN: 978-3-030-55897-0.This book describes how Bayesian methods work. Its primary aim is to demystify them, and to show readers: Bayesian thinking isn’t difficult and can be used in virtually every kind of research. In addition to revealing the underlying simplicity of statistical methods, the book explains how to parameterise and compare models while accounting for uncertainties in data, model parameters and model structures.
How exactly should data be used in modelling? The literature offers a bewildering variety of techniques and approaches (Bayesian calibration, data assimilation, Kalman filtering, model-data fusion, etc). This book provides a short and easy guide to all of these and more. It was written from a unifying Bayesian perspective, which reveals how the multitude of techniques and approaches are in fact all related to one another. Basic notions from probability theory are introduced. Executable code examples are included to enhance the book’s practical use for scientific modellers, and all code is available online as well.Introduction to Bayesian Thinking
Introduction to Bayesian Science
Assigning a Prior Distribution
Assigning a Likelihood Function
Deriving the Posterior Distribution
Sampling from Any Distribution by MCMC
Sampling from the Posterior Distribution by MCMC
Twelve Ways to Fit a Straight Line
MCMC and Complex Models
Bayesian Calibration and MCMC: Frequently Asked Questions
After the Calibration: Interpretation, Reporting, Visualization
Model Ensembles: BMC and BMA
Discrepancy
Gaussian Processes and Model Emulation
Graphical Modelling (GM)
Bayesian Hierarchical Modelling (BHM)
Probabilistic Risk Analysis and Bayesian Decision Theory
Approximations to Bayes
Linear Modelling: LM, GLM, GAM and Mixed Models
Machine Learning
Time Series and Data Assimilation
Spatial Modelling and Scaling Error
Spatio-Temporal Modelling and Adaptive Sampling
What Next?