**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

to your search path. There is an extensive documentation with examples, available online. Use this User Friendly Window for 1D Metropolis.

- 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.

Based on attendance and on a computer project assigned individually during the first week of class and due before the end of the course.

JAVASCRIPT and HTML resources:

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On 7 Jun 1999, 16:53.