## Markov Chain Monte Carlo and Optimization

`MWF 11:00-11:50 am, Spring 2011,     PAB 2748.`
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`www.stat.ucla.edu/~yuille/Courses/UCLA/Stat_231/Stat_231.html.`
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### Course Description

This course describes MCMC sampling techniques with emphasis on optimization and statistical estimation. Topics covered include Gibbs samplers, Metropolis-Hastings, importance sampling, and simulated annealing. In addition, the course covers alternative optimization techniques including Newton-Raphson, dynamic programming, belief propagation, and variational methods.
Note: course will be very similar to Spring 2010, there will be small changes to the lecture notes.

### Textbook

• Jun S. Liu. "Monte Carlo Strategies in Scientific Computing", Springer 2001. [Required]
• C.R. Robert and G. Casella. Monte Carlo Statistical Methods. Optional Reading.

### Instructors

• Prof. Alan Yuille, yuille@stat.ucla.edu, 310-267-5383, office Math Sciences 8967. Office Hours: Wed 4:00-5:00 pm and by request.

Grading Plan: 4 units, letter grades. 4 homework assignments. 1 final exam.
Homework 1:
Homework 2:
Homework 3:
Homework 4:

Tentative Schedule.

 Lecture Date Topics Reading Materials Handouts Roberts & Casella 1 3-28 `Introduction to Sampling and Monte Carlo:` ` Issues, Applications, and Examples.` Ch 1 2011lecture1.pdf Ch 2 2 3-30 `Basic Monte Carlo:` `Inversion Method, Gaussians, Mixtures` Ch 2.1 2011lecture2.pdf Ch 2.2 3 4-1 `Basic Monte Carlo:` `Rejection Methods.` Ch 2.2 2011lecture3.pdf Ch 2.3, 2.4 4 4-4 `Basic Monte Carlo:` `Rao-Blackwellization and Exact Methods.` Ch 2 2011lecture4.pdf Ch  4.2 5 4-6 `Basic Monte Carlo:` `Importance Sampling` Ch 2.5 2011lecture5.pdf Ch 3.1-3.3 6 4-8 `Basic Monte Carlo:` `Importance Sampling, ` Ch 2.5 2011lecture6.pdf Ch 3.1-3.3 7 4-11 `Basic Monte Carlo` `Weighted Sampling.` Ch 2.6 2011lecture7.pdf Ch 3.1-3.3 8 4-13 `Exact Monte Carlo` `Dynamic Programming` Ch 2.4 9 4-15 `Exact Monte Carlo (cont)` `Dynamic Programming` Ch 2.4 2011lecture9.pdf 10 4-18 `Structured Probability Distributions` `Examples. ` GYtics.pdf 2011lecture10.pdf 11 4-20 `Kalman Filters: ` `Filtering and Tracking Examples.` Ch 3.2 2011lecture11.pdf 12 4-22 ```Particle (Boostrap) Filters: (Cont)Filtering and Tracking Examples. ``` Ch 3.2-3.3, 4.5 2011lecture12.pdf 13 4-25 `Particle (Boostrap) Filters: (Cont)Filtering and Tracking Examples` Ch 3.2-3.3, 4.5 2011lecture13.pdf 14 4-27 `Particle (Boostrap) Filters: (Cont)Filtering and Tracking Examples` Ch 3.2-3.3, 4.5 2011lecture14.pdf 15 4-29 `Sequential Importance SamplingSaw Examples` Ch 3.2-3.3, 4.5 2011lecture15.pdf 16 5-2 `Markov Chain Monte Carlo: ` `Introduction` Ch 5.0, 5.1 2011lecture16.pdf 17 5-4 Markov Chain Monte Carlo:  Example: Ising Model ` ` Ch 5.2, 5.3 2011lecture17.pdf 18 5-6 `Markov Chain Monte Carlo: ` `Metropolis-Hastings ` Ch 5.3 2011lecture18.pdf 19 5-9 `Gibbs Sampler` `Data Augmentation` Ch 6.1,6.2 2011lecture19.pdf 20 5-11 `Gibbs Sampler` `Data Augmentation (Cont)` Ch 6.3 Previous Lecture 21 5-13 `Reversible Jumps and Multiple Try MH` ` Hybrid Monte Carlo` Ch 5.5,5.6 2011lecture20.pdf 22 5-16 `Convergence of MCMC` Ch 12 2011lecture21.pdf 23 5-18 `            Hybrid Monte Carlo ` Ch 9.1,9.2,9.3 2011lecture22.pdf 24 5-20 `Genetic Algorithms` GA Handout 2011lecture23.pdf ga_tutorial.pdf 25 5-23 `Population Methods and Simulated Annealing` Ch 11.1-11.3 Previous Lecture 26 5-25 ` ` `Swenson-Wang  ` Ch 7 2011lecture24.pdf 27 5-27 `Deterministic Methods` 2010lecture25.pdf 5-30 `Memorial Day Holiday  ` 28 6-1 `Deterministic Methods ` ` ` Reading List Previous Lecture 29 6-3 `Overview:` 2010lecture26.pdf