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Lecture plan

Lecture 1. Basics of Bayesian statistics and parameter estimation

- Probability theory
- Inference
- Bayesian parameter estimation

Lecture 2. Assigning probabilities with limited knowledge

- Informative priors
- Maximum entropy
- Error models for your EFT

Exercise session 1. Getting familiar with Bayes;

Day 1 Nuclear Physics Example: How ab initio nuclear theory 
offers an inferential advantage
- Problem set
- Project: Bayesian linear regression

Lecture 3. Markov chains and MCMC sampling

- Stochastic processes, Markov chains
- Stationary and limiting distributions
- The Metropolis algorithm
- Autocorrelation

Lecture 4. Advanced MCMC sampling

- Hamiltonian Monte Carlo
- Sampling/Importance resampling
- Example: Inference of the low-energy constants in delta-full chiral
  effective field theory including a correlated truncation error

Exercise session 2. Tools and tricks for MCMC sampling;

Day 2 Nuclear Physics Example: Fast and rigorous constraints on 
three-nucleon forces from few-body observables
- Problem set
- Project: Fast and rigorous constraints on chiral effective field
  theory forces from few-body observables

Lecture 5. Bayes goes fast: Reduced-order modeling, emulators

- Non-intrusive vs intrusive reduced-order models
- GP emulators
- EVC and other variational formulations

Lecture 6. Bayes goes linear: History matching

- History matching
- Example: Ab initio predictions link the neutron skin of 208Pb 
  to nuclear forces