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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. Bayesian posteriors
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. Discrepancy Models
12. Assigning probabilities
13. 📥 Dealing with outliers
14. Bayes goes linear: History matching
15. Multi-model inference with Bayes
- 15.1. Model Selection
- 15.2. Model averaging and mixing

Part III: MCMC sampling

16. Overview of Part III
17. Intuition for MCMC
18. Details of MCMC
19. MCMC in practice
20. Advanced sampling

Part IV: Machine learning: A Bayesian perspective

21. Overview of Part IV
22. Overview of Gaussian processes
23. Logistic Regression
- 23.5. Machine Learning: First Examples
- 23.6. Exercise: Logistic Regression and neural networks
24. Machine learning: Overview
25. ANNs in the large-width limit (ANNFT)
- 25.3. 📥 Distributions of Randomly-Initialized ANNs
26. Bayesian neural nets
- 26.4. Demonstration: Variational Inference and Bayesian Neural Networks
- 26.5. Exercise: Bayesian neural networks
27. *Convolutional neural nets
- 27.6. Demonstration: Image recognition with Convolutional Neural Networks

Part V: Other topics

28. Overview of Part V
29. Emulators
- 29.1. Bayes goes fast: Emulators
- 29.2. RBM emulators
30. 📥 Student t distribution from Gaussians
31. PCA, SVD, and all that
- 31.5. 📥 demo-SVD notebook
32. QBism: Bayesian quantum mechanics

Backmatter

33. Bibliography
34. Guide to Jupyter Book markdown

Appendix A: Reference

35. Statistics concepts and notation
36. Gradient-descent optimization

Appendix B: Scientific modeling

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

Appendix C: Getting started

41. Overview of Getting started material
42. 📥 Exercise: Jupyter notebooks and Python
43. More about Python and Jupyter notebooks
44. Setting up for using this Jupyter Book
- 44.1. Using Anaconda
- 44.2. Using GitHub

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?
- Overview of Mini-project IIb: How many lines?
📥 MP IIIa: Bayesian optimization
📥 MP IIIb: Bayesian Neural Networks

Repository
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Advanced sampling

20. Advanced sampling#

In this section we look at Hamiltonian Monte Carlo (HMC) in theory and in practice, plus a selection of other samplers.

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19.4. Best practices for MCMC sampling

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20.1. Introduction to Hamilton Monte Carlo

By Christian Forssén, Dick Furnstahl, and Daniel Phillips

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