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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 and problems 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
17. Problems for Part II

Part III: MCMC sampling

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

Part IV: Machine learning basics

24. Overview of Part IV
25. Machine learning overview
26. Logistic Regression
- 26.5. Machine Learning: First Examples
- 26.6. Exercise: Logistic Regression and Neural Networks
27. Artificial neural networks (ANNs)
28. *Convolutional neural nets
29. Problems for Part IV

Part V: Probabilistic machine learning

30. Overview of Part V
31. Bayesian neural nets
- 31.4. Demo: Variational Inference and Bayesian Neural Networks
32. Gaussian processes
33. ANNs in the large-width limit (ANNFT)
34. Bayesian Optimization
35. Dimensionality reduction and emulators
36. Problems for Part V
- 36.1. Bayesian neural networks

Backmatter

37. Bibliography
38. Guide to Jupyter Book markdown

Appendix A: Statistics

39. Notation and overview of statistics material
40. The probability measure
41. Working with probability distributions

Appendix B: Scientific modeling

42. Overview of scientific modeling material
43. Overview of modeling
44. Linear models
45. Mathematical optimization

Appendix C: Getting started

46. Overview of Getting started material
47. Setting up for interactive use of this Jupyter book
- 47.1. Using git for cloning the book repository
- 47.2. Setting up your Python enviroment
48. Jupyter notebooks and Python
49. 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 IIIa: Bayesian optimization
MP IIIb: Bayesian Neural Networks

Repository
Open issue

.md

Ensemble sampling

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

22.1. Ensemble sampling#

Section to be added.

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22. Advanced sampling algorithms

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22.2. Parallel tempering

By Christian Forssén, Dick Furnstahl, and Daniel Phillips

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