MCMC sampling
Lecture 1:
Dick Furnstahl, 2019-06-12
- 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]
Lecture 2:
Christian Forssén, 2019-06-13
- Assessing convergence of MCMC simulations
- Multimodal distributions and parallel tempering
- Scanned lecture notes
- MCMC diagnostics [ipynb]
- MCMC PT [ipynb]
Lecture 3:
Dick Furnstahl, 2019-06-20
- 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]
Further reading on adaptive Monte Carlo integration: Vegas algorithm
- A new algorithm for adaptive multidimensional integration by G. Peter Lepage
- Lepage’s improved/multi-processor Vegas written in Python with documention
- Vegas Revisited: Adaptive Monte Carlo Integration Beyond Factorization by Thorsten Ohl
- Cuba –a library for multidimensional numerical integration by Thomas Hahn
- When Random Numbers Are Too Random: Low Discrepancy Sequences