## Markov Chain Monte Carlo and Optimization

`MWF 11:00-11:50 am, Spring 2010,     Maths/Sciences 5128.`
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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.

### 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 3-29 `Introduction to Sampling and Monte Carlo:` ` Issues, Applications, and Examples.` Ch 1 2010lecture1.pdf Ch 2 2 3-31 `Basic Monte Carlo:` `Inversion Method, Gaussians, Mixtures` Ch 2.1 2010lecture2.pdf Ch 2.2 3 4-2 `Basic Monte Carlo:` `Rejection Methods.` Ch 2.2 2010lecture3.pdf Ch 2.3, 2.4 4 4-5 `Basic Monte Carlo:` `Rao-Blackwellization and Exact Methods.` Ch 2 Ch  4.2 5 4-7 `Basic Monte Carlo:` `Importance Sampling` Ch 2.5 2010lecture5.pdf Ch 3.1-3.3 6 4-9 `Basic Monte Carlo:` `Importance Sampling, ` Ch 2.5 2010lecture6.pdf Ch 3.1-3.3 7 4-12 `Basic Monte Carlo` `Weighted Sampling.` Ch 2.6 2010lecture7.pdf Ch 3.1-3.3 8 4-14 `Exact Monte Carlo` `Dynamic Programming` Ch 2.4 9 4-16 `Exact Monte Carlo (cont)` `Dynamic Programming` Ch 2.4 Same as previous lecture 10 4-19 `Structured Probability Distributions` `Examples. ` GYtics.pdf 2010lecture9.pdf 11 4-21 `Kalman Filters: ` `Filtering and Tracking Examples.` Ch 3.2 2010lecture10.pdf 12 4-23 ```Particle (Boostrap) Filters: (Cont)Filtering and Tracking Examples. ``` Ch 3.2-3.3, 4.5 2010lecture11.pdf 13 4-26 `Particle (Boostrap) Filters: (Cont)Filtering and Tracking Examples` Ch 3.2-3.3, 4.5 2010lecture12.pdf 14 4-28 `Particle (Boostrap) Filters: (Cont)Filtering and Tracking Examples` Ch 3.2-3.3, 4.5 2010lecture13.pdf 15 4-30 `Sequential Importance SamplingSaw Examples` Ch 3.2-3.3, 4.5 2010lecture14.pdf 16 5-3 `Markov Chain Monte Carlo: ` `Introduction` Ch 5.0, 5.1 2010lecture15.pdf 17 5-5 Markov Chain Monte Carlo:  Example: Ising Model ` ` Ch 5.2, 5.3 `Same as previous lecture ` 18 5-7 `Markov Chain Monte Carlo: ` `Metropolis-Hastings and Gibbs Sampler.` Ch 5.3 2010lecture16.pdf 19 5-10 `Metropolis-Hastings Examples` Guest Lecture: Prof. Q. Zhou 20 5-12 `Physical Methods:` ` Hybrid Monte Carlo` Ch 9.1-9.4 2010lecture17.pdf 21 5-14 `Data Augmentation` Ch 6.4 Same as lecture 16.pdf 22 5-17 `Data Augmentation and EM` Appendix A4. 2010lecture18.pdf 23 5-19 `Reversible Jumps and Multiple Try MH:` `             ` Ch 5.5, 5.6 2010lecture19.pdf 24 5-21 `Swendsen-Wang` Ch 7.1,7.2,7.4 See lecture 18. 25 5-24 `Genetic Algorithms: ` GA Handout 2010lecture20.pdf 26 5-26 ` ` `Genetic Algorithms (Cont)::  ` Previous lecture Previous Lecture 27 5-28 `Convergence and Review` 5-31 `Memorial Day Holiday  ` 2010lecture21.pdf 28 6-2 `Deterministic Methods ` ` ` Reading List 29 6-4 `Assorted Topics:`