Syllabus

1. Locating Modes -- Selected Optimization Techniques
Standard derivative and non-derivative based methods; the EM algorithm and simulated annealing.

2. Likelihood Approximations
Normal approximations; the delta method; Laplace approximations.

3. Numerical Integration 1: Quadrature
Quadrature techniques applied to marginalizing densities and estimating (their) moments.

4. Numerical Integration 2: Simulation-Based Methods
Non-iterative simulation-based techniques in numerical integration applied to marginalizing densities and estimating (their) moments. Monte Carlo integration; importance sampling.

5. Numerical Integration 3: Markov Chain Monte Carlo
Markov Chain Monte Carlo methods for inference. Metropolis-Hastings methods including Gibbs sampling; convergence and applications.

---Digressions---

A. Simulation and Monte Carlo Methods
Pseudo-random numbers, simulation techniques and Monte Carlo methods.

B. Assorted Numerical Methods
Computer representation and manipulation of numeric data and ramifications for statistical algorithms; matrix and linear computations.

C. Computing Tools & Issues
Interface b/w Splus and C; libraries; make files; web resources; etc.

Schedule

Date	Topic
Wedn, Jan 10:	Course overview & description.
Mon, Jan 15:	Dr. Martin Luther King, Jr. Holiday.
Wedn, Jan 17:	Univariate optimization.
Mon, Jan 22:	Multivariate optimization.
Wedn, Jan 24:	Modes via iterative reweighted least squares; digression on linear computations.
Mon, Jan 29:	The EM algorithm & exonential families.
Wedn, Jan 31:	The EM algorithm, cont'd.; SE estimates.
Mon, Feb 5:	Modifications & extensions of the EM algorithm.
Wedn, Feb 7:	Normal approximations; the Delta Method.
Mon, Feb 12:	Laplace approximations.
Wedn, Feb 14:	Numerical quadrature.
Mon, Feb 19:	Example: latent class model; digression on Splus--Fortran/C interface.
Wedn, Feb 21:	Digression on Fortan/C with numerical libraries.
Mon, Feb 26:	Stochastic integration; importance sampling.
Wedn, Feb 28:	Importance sampling; example using Splus.
Mon, Mar 5:	Importance sampling; example using Lapack, Randlib and Blas.
Wedn, Mar 7:	MCMC overview; large sample proposals; example.
Mon, Mar 12:	Spring break.
Wedn, Mar 14:	Spring break.
Mon, Mar 19:	MCMC overview & example continued.
Wedn, Mar 21:	Sampling schemes for full conditionals: acceptance sampling.
Mon, Mar 26:	Sampling schemes for full conditionals: ratio of uniforms.
Wedn, Mar 28:	Adaptive rejection sampling & BUGS
Mon, Apr 2:	MCMC diagnostics; Raftery & Lewis, Gelman and Rubin.
Wedn, Apr 4:	MCMC diagnostics; digression on web resources and BOA/CODA.
Mon, Apr 9:	Latent/auxiliary variables.
Wedn, Apr 11:	Output analysis: Rao-Blackwellization, importance sampling reweighting.
Mon, Apr 16:	Reversible jump & model selection/averaging computations
Wedn, April 18:	Model selection/averaging computations, cont'd.

Return to 376 home page.