An Introduction to Markov Chain Monte Carlo
- Prof. Carlos C. Rodriguez
- Office Hours:
- Tues., Wed. and Thurs. after lectures or by appointment on Weds..
- Radford M. Neal, 1993. Probabilistic Inference Using Markov Chain Monte Carlo Methods.
Available online at http://omega.albany.edu:8008/neal.pdf and
Neal's MCMC package is now installed and accessible from any Unix machine
with access to the /home part of the tree directory. To
access the programs from your account just add the directory:
to your search path.
There is an
with examples, available online. Use this User Friendly Window for 1D Metropolis.
A Virtual Monte Carlo Summer at State College, PA
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).
of Statistical Mechanics]
- Lecture II:
Statistical Physics (part 2), the original Metropolis Algorithm,
- Lecture III:
Bringing Metropolis to Statistics, Hastings generalization,
Component-wise Metropolis, Gibbs Sampler.
Links: [Gaussian sampler
with Unif(x-1,x+1) proposal]
- Lecture IV:
Being Exact: The essential Rejection Method
and the Acceptance Complement Method
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
- Lecture VI:
MCMC Application: Neural Networks as a way to specify nonparametric
regression and classification models.
Links: [10 Lectures] by Kevin
[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
- 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.
- 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.
Based on attendance and on a computer project assigned individually during
the first week of class and due before the end of the course.
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On 7 Jun 1999, 16:53.