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Learning from data

  • About this Jupyter Book

Course overview

  • Objectives

Topics

  • 1. Basics of Bayesian statistics
    • 1.1. Lecture 1
    • 1.2. Exploring PDFs
    • 1.3. Checking the sum and product rules, and their consequences
    • 1.4. Lecture 2
    • 1.5. Interactive Bayesian updating: coin flipping example
    • 1.6. Standard medical example by applying Bayesian rules of probability
    • 1.7. Radioactive lighthouse problem
    • 1.8. Lecture 3
  • 2. Bayesian parameter estimation
    • 2.1. Lecture 4: Parameter estimation
    • 2.2. Parameter estimation example: Gaussian noise and averages
    • 2.3. Assignment: 2D radioactive lighthouse location using MCMC
    • 2.4. Lecture 5
    • 2.5. Parameter estimation example: fitting a straight line
    • 2.6. Linear Regression and Model Validation demonstration
    • 2.7. Lecture 6
    • 2.8. Amplitude of a signal in the presence of background
    • 2.9. Assignment: Follow-ups to Parameter Estimation notebooks
    • 2.10. Linear Regression exercise
    • 2.11. Linear algebra games including SVD for PCA
    • 2.12. Follow-up: fluctuation trends with # of points and data errors
  • 3. MCMC sampling I
    • 3.1. Lecture 7
    • 3.2. Metropolis-Hasting MCMC sampling of a Poisson distribution
    • 3.3. Lecture 8
    • 3.4. Exercise: Random walk
  • 4. Why Bayes is better
    • 4.1. Lecture 9
    • 4.2. A Bayesian Billiard game
    • 4.3. Lecture 10
    • 4.4. Parameter estimation example: fitting a straight line II
    • 4.5. Lecture 11
    • 4.6. Error propagation: Example 3.6.2 in Sivia
    • 4.7. Visualization of the Central Limit Theorem
    • 4.8. Building intuition about correlations (and a bit of Python linear algebra)
    • 4.9. Lecture 12
    • 4.10. Overview: MCMC Diagnostics
    • 4.12. Lecture 13
    • 4.13. Dealing with outliers
  • 5. Model selection
    • 5.1. Lecture 14
    • 5.2. Lecture 15
    • 5.3. Evidence calculation for EFT expansions
    • 5.4. Lecture 16
    • 5.5. Example: Parallel tempering for multimodal distributions
    • 5.6. Example: Parallel tempering for multimodal distributions vs. zeus
  • 6. MCMC sampling II
    • 6.1. Lecture 17
    • 6.2. Quick check of the distribution of normal variables squared
    • 6.3. Liouville Theorem Visualization
    • 6.4. Solving orbital equations with different algorithms
    • 6.5. Lecture 18
    • 6.6. PyMC3 Introduction
    • 6.7. Getting started with PyMC3
    • 6.8. Comparing samplers for a simple problem
    • 6.9. zeus: Sampling from multimodal distributions
  • 7. Gaussian processes
    • 7.1. Lecture 19
    • 7.2. Gaussian processes demonstration
    • 7.3. Learning from data: Gaussian processes
    • 7.4. Exercise: Gaussian Process models with GPy
    • 7.5. Lecture 20
  • 8. Assigning probabilities
    • 8.1. Lecture 21
    • 8.2. Ignorance pdfs: Indifference and translation groups
    • 8.3. MaxEnt for deriving some probability distributions
    • 8.4. Maximum Entropy for reconstructing a function from its moments
    • 8.5. Making figures for Ignorance PDF notebook
  • 9. Machine learning: Bayesian methods
    • 9.1. Lecture 22
    • 9.2. Bayesian Optimization
    • 9.3. Lecture 23
    • 9.4. What Are Neural Networks?
    • 9.5. Neural networks
    • 9.6. Neural network classifier demonstration
    • 9.7. Bayesian neural networks
    • 9.8. Lecture 24
    • 9.9. Variational Inference: Bayesian Neural Networks
    • 9.10. What is a convolutional neural network?
  • 10. PCA, SVD, and all that
    • 10.1. Lecture 25
    • 10.2. Linear algebra games including SVD for PCA

Mini-projects

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

Reference material

  • Bibliography
  • Related topics
  • Using Anaconda
  • Using GitHub
  • Python and Jupyter notebooks
    • Python and Jupyter notebooks: part 01
    • Python and Jupyter notebooks: part 02
  • Examples: Jupyter jb-book

Notebook keys

  • Checking the sum and product rules, and their consequences Key
  • Standard medical example by applying Bayesian rules of probability Key
  • Radioactive lighthouse problem Key
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Contents
  • QBism references

Related topics¶

Here we gather references to various topics somehow connected to the themes of these notes.

QBism references¶

From the Wikipedia article on QBism: “In physics and the philosophy of physics, quantum Bayesianism is a collection of related approaches to the interpretation of quantum mechanics, of which the most prominent is QBism (pronounced “cubism”). QBism is an interpretation that takes an agent’s actions and experiences as the central concerns of the theory.”

Here are some references:

  • David Mermin columns from Physics Today (2012) and response by Robert Griffiths:

    • “Quantum mechanics: Fixing the shifty split”

    • Robert Griffiths response and other responses

    • Mermim replies

  • Scientific American short article from 2013: “Can Quantum Bayesianism Fix the Paradoxes of Quantum Mechanics?”

  • Several works by Christopher Fuchs or interviews with him:

    • From Quanta magazine A Private View of Quantum Reality

    • From Discover magazine: “Quantum Physics is No More Mysterious Than Crossing the Street: A Conversation with Chris Fuchs”

    • “Interview with a Quantum Bayesian”

    • “QBism, the Perimeter of Quantum Bayesianism”

    • Fuchs and Schack on Quantum-Bayesian coherence

  • Critical view of QBism by Guido Bacciagaluppi from 2013.

Bibliography Using Anaconda

By Dick Furnstahl
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