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Preface

Introduction

1. Learning from data: Inference
2. Exercise: Jupyter Notebooks and Python
3. Exercise: Python lists and iterations
4. Exercise: Linear algebra operations with NumPy
5. Demonstration: Reading Data and fitting
6. Statistics concepts and notation

Modeling: The optimization approach

7. Linear models
8. Gradient-descent optimization
9. Demonstration: Linear Regression and Model Validation
10. Exercise: Linear Regression

Stochastic processes and Markov Chains

11. Stochastic processes
12. Markov chains
13. Markov chain Monte Carlo sampling
14. Demonstration: Metropolis-Hasting MCMC sampling of a Poisson distribution

Bayesian methods for scientific modeling

15. Bayes’ theorem
16. Demonstration: Bayesian Coin Tossing
17. Exercise: Checking the sum and product rules, and their consequences
18. Data, models, and predictions
19. Advantages of the Bayesian approach
20. Bayesian Linear Regression

Advanced Bayesian methods

21. Assigning probabilities (I): Indifferences and translation groups
22. Assigning probabilities (II): The principle of maximum entropy
23. Demonstration: Assigning probabilities
24. Assigning probabilities (III): Conjugate priors
25. Model Selection

Computational Bayes

26. Advanced Markov chain Monte Carlo sampling
27. Bayes goes fast: Emulators
28. Bayes goes linear: History matching

Machine learning: A Bayesian perspective

29. Gaussian processes
30. Demonstration: Gaussian processes
31. Logistic Regression
32. Demonstration: Neural network classifier
33. Exercise: Logistic Regression and neural networks
34. Convolutional Neural Networks
35. Demonstration: Image recognition with Convolutional Neural Networks
36. Bayesian neural networks
37. Demonstration: Variational Inference and Bayesian Neural Networks
38. Exercise: Bayesian neural networks

Backmatter

39. Bibliography

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By Christian Forssén

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