Return to home

Lectures of the first week

Monday, June 10

Introduction, Bayes theorem (Daniel Phillips)

• Lecture [pdf]
• Simple sum and product rule [ipynb] (key ipynb)
• Exploring pdfs [ipynb]
• Bayesian updating: Coinflipping [ipynb]
• Medical examples [ipynb] (key ipynb)

Bayesian parameter estimation (Dick Furnstahl)

• Overview of parameter estimation, frequentist vs. bayesian
• Examples: parameters of Gaussian noise, fitting a straight line
• Scanned lecture notes
• Intro notebook revisited [ipynb]
• Parameter estimation: fitting a straight line [ipynb]

Jupyter notebooks and python basics

This directory contains notebooks introducing the basics of python programming and jupyter notebooks

• Jupyter and Python intro 01 [ipynb]
• Jupyter and Python intro 02 [ipynb]

Introduction to git (John Bower, Christian Drischler)

Initial configuration

git config --global user.name "Oski Bear"
git config --global user.email obear@example.com

Use here your name as well as your email.

Discussed commands relevant for this course

• git status
• git branch
• git merge
• git log
• git checkout [-b]
• git pull
• git clone
• git commit
• git reset [--hard]
• …

Tuesday, June 11

Bayesian updating, Bayesian convergence (Daniel Phillips)

• Lecture [pdf]

Bayesian Parameter Estimation (Dick Furnstahl)

• Central limit theorem
• Correlations and the likelihood / posterior
• Amplitude of a signal in the presence of background
• Scanned lecture notes
• Exploring pdfs [ipynb]
• Signal and background [ipynb]

Wednesday, June 12

MCMC sampling (Dick Furnstahl)

• Why Markov Chain Monte Carlo (MCMC)?
• Metropolis-Hastings algorithm
• Visualization of MCMC
• Poisson distribution example
• Scanned lecture notes
• Visualization of MCMC sampling (Richard McElreath)
• Metropolis Poisson example [ipynb]

Why Bayes is Better (1) (Christian Forssén)

• Prior information
• Marginalization
• Scanned lecture notes [pdf]
• Why Bayes is Better I [ipynb]
• Fitting a straight line II [ipynb]
• A Bayesian billiard game [ipynb]

Thursday, June 13

Bayesian Parameter Estimation (Dick Furnstahl)

• Recap of signal + background
• Error probagation for multivariate Gaussians
• Maximum likelihood in linear algebra form
• Scanned lecture notes
• Signal and background recap [ipynb]
• Data analysis recipes: Fitting a model to data — article from Hogg, Bovy, and Lang about real-world fitting (many interesting annotations!).

MCMC sampling (Christian Forssén)

• Assessing convergence of MCMC simulations
• Multimodal distributions and parallel tempering
• Scanned lecture notes
• MCMC diagnostics [ipynb]
• MCMC PT [ipynb]

Friday, June 14

Introduction to EFT and why Bayesian methods are particularly relevant there (Dick Furnstahl)

• ISNET-6 website — Uncertainty Quantification at the Extremes (Darmstadt, 8-12 October, 2019).
• Talk on Bayesian Statistics for Effective Field Theories [pdf]

Why Bayes is Better (2) (Christian Forssén)

• Error propagation
• Dealing with outliers
• Scanned lecture notes [pdf]
• Why Bayes is Better II [ipynb]