An Introduction to Markov Chain Monte Carlo

Instructor:

Prof. Carlos C. Rodriguez

Office Hours:

Tues., Wed. and Thurs. after lectures or by appointment on Weds..

Text:

Radford M. Neal, 1993. Probabilistic Inference Using Markov Chain Monte Carlo Methods. Available online at https://omega0.xyz/omega8008/neal.pdf and https://omega0.xyz/omega8008/neal-review.ps

Software:

If you don't get the fonts for the equations click here

• Lecture I:
  Introduction, the basics of Monte Carlo Integration, and the elements of statistical physics (part 1).
  [.html] [.pdf] [.ps] [.tex]
  Links: [History of Statistical Mechanics]
• Lecture II:
  Statistical Physics (part 2), the original Metropolis Algorithm, Simulated Annealing.
  [.html] [.pdf] [.ps] [.tex]
• Lecture III:
  Bringing Metropolis to Statistics, Hastings generalization, Component-wise Metropolis, Gibbs Sampler.
  [.html] [.pdf] [.ps] [.tex]
  Links: [Gaussian sampler with Unif(x-1,x+1) proposal]
• Lecture IV:
  Being Exact: The essential Rejection Method and the Acceptance Complement Method
  [.html] [.pdf] [.ps] [.tex]
  Links: [Ke's Javascript with histogram] [See the source and use his histogram()]
• Lecture V:
  Examples of Applications of MCMC: Statistical Inference and Combinatorial Optimization. Reconstruction of a binary Image. Nonparametric Denstity Estimation.
  [.html] [.pdf] [.ps] [.tex]
• Lecture VI:
  MCMC Application: Neural Networks as a way to specify nonparametric regression and classification models.
  [.html] [.pdf] [.ps] [.tex]
  Links: [10 Lectures] by Kevin Gurney [gurney10.tar.gz] [Brian Ripley's 8 year old but still cool paper]
• Lecture VII:
  The Hybrid Monte Carlo Method: Hamiltonian Dynamics, Liouville's Theorem, Leap-frog Discretization. The Non-Reversible Directed Metropolis.
  [.html] [.pdf] [.ps] [.tex]
  
• Lecture VIII:
  Using the exponential and mixture connections in the space of distributions for sampling. Appications: Thermodynamic integration, The half Monty-Carlos Method for sampling from one distribution by generating from another.
  [.html] [.pdf] [.ps] [.tex]
  
• In the Oven... IX,...,to be continued...?:
  Overview of the theory of Markov Chains: Basic definitions, Invariant Distributions, Ergodicity, Reversibility, Continuous Time Chains, Coupling, examples. Convergence Theorems, examples. Propp and Wilson Algorithm and Perfectly Random Sampling. The full Monty-Carlos.