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This book describes how Bayesian methods work. Aiming to demystify the approach, it explains how to parameterize and compare models while accounting for uncertainties in data, model parameters and model structures. Bayesian thinking is not difficult and can be used in virtually every kind of research. How exactly should data be used in modelling? The literature offers a bewildering variety of techniques (Bayesian calibration, data assimilation, Kalman filtering, model-data fusion, …). This book provides a short and easy guide to all these approaches and more. Written from a unifying Bayesian perspective, it reveals how these methods are related to one another. Basic notions from probability theory are introduced and executable R codes for modelling, data analysis and visualization are included to enhance the book’s practical use. The codes are also freely available online.
This thoroughly revised second edition has separate chapters on risk analysis and decision theory. It also features an expanded text on machine learning with an introduction to natural language processing and calibration of neural networks using various datasets (including the famous iris and MNIST). Literature references have been updated and exercises with solutions have doubled in number.
Preface
Why This Book?
Who Is This Book For?
What Is in the Book?
Downloadable Computer Code
What Is New in This 2nd Edition?
Outline of Chapters
Acknowledgements
Science and Uncertainty
Bayesian Inference
Assigning a Prior Distribution
Assigning a Likelihood Function
Deriving the Posterior Distribution
Markov Chain Monte Carlo Sampling (MCMC)
Sampling from the Posterior Distribution by MCMC
MCMC and Multivariate Models
Bayesian Calibration and MCMC: Frequently Asked Questions
After the Calibration: Interpretation, Reporting, Visualisation
Model Ensembles: BMC and BMA
Discrepancy
Approximations to Bayes
Thirteen Ways to Fit a Straight Line
Gaussian Processes and Model Emulation
Graphical Modelling
Bayesian Hierarchical Modelling
Probabilistic Risk Analysis
Bayesian Decision Theory
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?
Notation and Abbreviations
Notation
Abbreviations
Mathematics for Modellers
How to Read an Equation
Dimension Checking of Linear Algebra
Probability Theory for Modellers
Notation
Probability Distributions
Product Rule of Probability
Law of Total Probability
Bayes' Theorem
Sequential Bayesian Updating
Gaussian Probability Distributions
R
Basic R Commands
R-packages
Bayesian Software
Solutions to Exercises
References
Index