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Learning from data for physicists

Overview

1. Invitation to inductive inference
2. Introduction

Part I: Bayesian methods for scientific modeling

3. Overview of Part I
4. Inference and PDFs
5. More on PDFs
6. Updating via Bayes' rule
7. Error propagation
8. Bayes in practice
9. Exercises for Part I

Part II: Advanced Bayesian methods

10. Overview of Part II
11. Assigning probabilities
12. Dealing with outliers
13. Bayes goes linear — History matching
- 13.1. Bayes linear methods
- 13.2. Iterative history matching
14. Model selection
15. Discrepancy Models with GPs
16. Model averaging and mixing

Part III: MCMC sampling

17. Overview of Part III
18. Intuition for MCMC
19. Details of MCMC
20. MCMC in practice
21. Advanced sampling algorithms
22. State-of-the-art sampling implementations

Part IV: Machine learning: A Bayesian perspective

23. Overview of Part IV
24. Overview of Gaussian processes
25. Logistic Regression
- 25.5. Machine Learning: First Examples
- 25.6. Exercise: Logistic Regression and Neural Networks
26. Bayesian Optimization
27. Machine learning: Overview
28. ANNs in the large-width limit (ANNFT)
- 28.11. Demo: Distributions of Randomly-Initialized ANNs
29. Bayesian neural nets
- 29.4. Demo: Variational Inference and Bayesian Neural Networks
- 29.5. Exercise: Bayesian neural networks
30. *Convolutional neural nets

Part V: Other topics

31. Overview of Part V
32. Emulators
33. PCA, SVD, and all that
- 33.5. Demonstration: SVD
34. QBism: Bayesian quantum mechanics

Backmatter

35. Bibliography
36. Guide to Jupyter Book markdown

Appendix A: Statistics

37. Overview of Appendix A

Appendix B: Scientific modeling

38. Overview of scientific modeling material
39. Overview of modeling
40. Linear models
41. Mathematical optimization

Appendix C: Getting started

42. Overview of Getting started material
43. Setting up for interactive use of this Jupyter book
- 43.1. Using git for cloning the book repository
- 43.2. Setting up your Python enviroment
44. Jupyter notebooks and Python
45. Guides on Jupyter notebooks and Python

TALENT mini-projects

Overview of mini-projects
MP I: Parameter estimation for a toy model of an EFT
MP IIa: Model selection basics
MP IIb: How many lines?
- Mini-project IIb: How many lines are there?
MP IIIa: Bayesian optimization
MP IIIb: Bayesian Neural Networks

Repository
Open issue

.md

Ensemble sampling

\[\newcommand\pos{\boldsymbol{x}} \newcommand\mom{\boldsymbol{p}} \newcommand\mass{\mathcal{M}}\]

21.1. Ensemble sampling#

Section to be added.

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21. Advanced sampling algorithms

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21.2. Parallel tempering

By Christian Forssén, Dick Furnstahl, and Daniel Phillips

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