Lectures of the second week
Monday, June 17
Assigning probabilities (Daniel Phillips)
- Choosing priors, Maximum Entropy
- Keynote of first lecture [.pdf]
- Maximizing the Entropy of Australians [ipynb]
Model selection (Christian Forssén)
- Model evidence
- Bayes factor
- Bayesian hypothesis testing
- Lecture notes in pdf or html
- Bayesian model selection [ipynb]
- Bayes in the sky: Bayesian inference and model selection in cosmology by Robert Trotta.
- Why every statistician should know about cross-validation blog post by Rob J Hyndman.
Tuesday, June 18
Assigning probabilities (2) (Daniel Phillips)
- Summary of prior choice discussion, Maximum Entropy for reconstructing functions
- Keynote of second lecture [.pdf]
Model selection (Dick Furnstahl)
- Recap of 2019-06-17 exercises: Prior sensitivity of model evidence
- Evidence when there is a naturalness prior
- Computational issues for evidence and alternatives
- Scanned lecture notes [pdf]
- Bayes in the sky: Bayesian inference and model selection in cosmology by Robert Trotta.
- Bayesian model selection revisited [ipynb]
- Evidence for EFT coefficients [ipynb]
- EFT slides II [pdf]
Wednesday, June 19
Gaussian processes (Christian Forssén)
- Gaussian processes as infinite-dimensional Gaussian distributions
- From parametric models to Gaussian processes
- Covariance functions
- Scanned lecture notes [pdf]
- Gaussian processes - Part I ipynb
Gaussian process models for regression (Christian Forssén)
- Gaussian process emulators
- Scanned lecture notes [pdf]
- A Bayesian Approach for Parameter Estimation and Prediction using a Computationally Intensive Model by D. Higdon et al.
Thursday, June 20
Gaussian processes (Christian Forssén)
- Gaussian process models for regression
- Gaussian process emulators
- Scanned lecture notes [pdf]
- A Bayesian Approach for Parameter Estimation and Prediction using a Computationally Intensive Model by D. Higdon et al.
MCMC sampling (Dick Furnstahl)
- Visualization of Hamiltonian Monte Carlo (HMC) and the No-U-Turn Sampler (NUTS)
- Physics of HMC
- PyMC3 overview
- Scanned lecture notes
- HMC visualization I (Richard McElreath)
- HMC visualization II (Alex Rogozhnikov)
- Bettencourt, A conceptual introduction to Hamiltonian Monte Carlo
- Neal, MCMC using Hamiltonian dynamics
- PyMC3: Introduction [ipynb]
- PyMC3 Docs: Getting started [ipynb]
- PyMC3 Docs: Quick start [ipynb]
- PyMC3 linear regression example (from Duke course)[ipynb]
- PyMC3: Rob Hicks Bayesian 8 [ipynb] Shows a comparison between Gibbs sampling, PyMC3, and emcee plus an example of using corner with PyMC3 output.
- Liouville theorem visualization [ipynb]
- Orbital equations solved with different algorithms, including 2nd-order leapfrog [ipynb]
Friday, June 21
Applications of Bayesian Methods in Nuclear Physics (Dick Furnstahl)
Why Bayes is Better (3) (Daniel Phillips)
- Systematic errors: offset, normalization uncertainty, other experimental systematics, theory systematic from an EFT
- Lecture on systematic errors [pdf]