STAT 598C

STAT 598C

Lectures: TTH 12:00PM - 1:15PM, BROWN 3102

Syllabus
Computer language/software: R ( Short Reference Card)
Lecture Notes:
1. Introduction (Tue 08/23). R source code: Creating data frames EM
2. Random number generation (Thu 08/25). References: An overview Acceptance-Rejection Ratio-of-uniforms A normal random number generator. R source code: rnorm.rou
3. Multivariate normal and Wishart distributions (Tue 08/30). R source code: chol.Stat598C
4. The sweep operator and its applications (Thu 09/01). [Goodnight, 1979] [swp.R]
5. Unconstrained optimization (Tue 09/06). [Fletcher, 1994] [bisection.R, newton.R]
6. Quasi-Newton methods (Thu 09/08, Tue 09/13). [Liu and Vander Wiel, 2005]
  09/15 R Script
7. EM (outline and homework assignment) (Tue 09/20 - Thu 09/29).
  - Theory: [Dempster, Laird, and Rubin, 1977; Wu, 1983]
  - Applications: [Vardi, Shepp, and Kaufman, 1985; Vardi, 1996; Lawrence and Reilly, 1990 (Proteins: Structure, Function, and Genetics, 7, 41-51); Liu and Sun, 2000; Liu, 2000; Pinheiro, Liu, and Wu, 2001, JCGS; term projects? ]
  - Supplements and extensions [ Meng and Rubin, 1991, 1993; Liu and Rubin, 1994; Meng and van Dyk, 1997; Liu, Rubin, and Wu, 1998; Liu, 1998; term projects?]
  - R scripts: [emMultinomial.R]
8. Numerical Integration (Tue 10/04). [NRC-Gassian Quadrature] [Alzheimer.R, Alzheimer.dat]
  10/06 R Script
9. Simulation and Monte Carlo Integration (Thu 10/13) [Kong, J. Liu, and Wong, 1994] [network.R]
10. Markov chain Monte Carlo (MCMC) methods (Tue 10/18 - )
  - The Data Augmentation Algorithm (Tue 10/18) [Tanner and Wong, 1987]
  - The Gibbs Sampler (Thu 10/20) [Gelfand and Smith, 1990, Tierney, 1994, Lawrence, et al., 1993]
    An Numerical Example (Tue, 10/25) [Robit Regression] [finney.dat, robit.R]
  - The Metropolis-Hastings Algorithm (Thu, 10/27) [Logistic Regression (Holmes and Held, 2006; Holmes and Held, 200?)]
  - Reversible Jump MCMC (Tue, 11/01 and Thu, 11/03) [Green, 1995] [rj.R]
  - Efficient Iterative Simulation Methods (Selected Topics) (Tue, 11/08 and Thu, 11/10)
    - Stochastic versions of the PX-EM algorithm (Part I, Part II)
    - Stochastic Approximation in Monte Carlo Computation
    - [References: Swendsen and Wang, 1987; Liu, 2003; Wang and Landau, 2001; Liang, 2005; see also the references given in the text book]
  - (Tue, 11/15) Applications of MCMC in advanced multiple biopolymer sequence alignment (Dr. Jun. Xie)
  - Miscellaneous Topics (term projects?)
    - Convergence Diagnostics
    - Exact Simulation/Perfect Sampling
11. Data Stream Processing (selected topics)
  - Particle Filter (Tue, 11/22)
  - Monitoring Streams of Network Counts (Tue, 11/29)

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