Markov chain Monte Carlo
(1.2 hours to learn)
Summary
Markov Chain Monte Carlo (MCMC) is a set of techniques for approximately sampling from a probability distribution p by running a Markov chain which has p as its stationary distribution. Gibbs sampling and Metropolis-Hastings are the most common examples.
Context
This concept has the prerequisites:
- Monte Carlo estimation (MCMC is a kind of sampling method.)
- conditional distributions (MCMC is often used to sample from conditional distributions.)
- Markov chains
Core resources (read/watch one of the following)
-Free-
→ Coursera: Probabilistic Graphical Models (2013)
An online course on probabilistic graphical models.
Other notes:
- Click on "Preview" to see the videos.
→ Machine learning summer school: Markov chain Monte Carlo (2009)
→ Information Theory, Inference, and Learning Algorithms
A graudate-level textbook on machine learning and information theory.
-Paid-
→ Pattern Recognition and Machine Learning
A textbook for a graduate machine learning course, with a focus on Bayesian methods.
Location:
Section 11.2, pages 537-542
Additional dependencies:
- multivariate Gaussian distribution
→ Probabilistic Graphical Models: Principles and Techniques
A very comprehensive textbook for a graduate-level course on probabilistic AI.
Location:
Section 12.3-12.3.3, pages 505-515
See also
- Some commonly used MCMC algorithms include:
- Gibbs sampling , where one variable is resampled given the others
- Metropolis-Hastings , a very general technique
- While MCMC is normally used as an approximate inference technique, it can also be used to get exact samples .
- We can analyze the mixing rate of MCMC samplers using spectral graph theory.