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 R (and Splus) and C; libraries; make files; web resources; etc.

Schedule

Date	Topic
Wedn, Jan 9:	Course overview & description.
Mon, Jan 14:	Univariate optimization.
Wed, Jan 16:	Multivariate optimization.
Mon, Jan 21:	Dr. Martin Luther King, Jr. Holiday.
Wedn, Jan 23:	Modes via iterative reweighted least squares; digression on linear computations.
Mon, Jan 28:	The EM algorithm & exonential families.
Wedn, Jan 30:	The EM algorithm, cont'd.; SE estimates.
Mon, Feb 4:	Modifications & extensions of the EM algorithm.
Wedn, Feb 6:	Normal approximations; the Delta Method.
Mon, Feb 11:	Laplace approximations.
Wedn, Feb 13:	Numerical quadrature.
Mon, Feb 18:	Example: latent class model; digression on Splus--Fortran/C interface.
Wedn, Feb 20:	Digression on Fortan/C with numerical libraries.
Mon, Feb 25:	Stochastic integration; importance sampling.
Wedn, Feb 27:	Importance sampling; example using Splus.
Mon, Mar 4:	Importance sampling; example using Lapack, Randlib and Blas.
Wedn, Mar 6:	MCMC overview; large sample proposals; example.
Mon, Mar 11:	Spring break.
Wedn, Mar 13:	Spring break.
Mon, Mar 18:	MCMC overview & example continued.
Wedn, Mar 20:	Sampling schemes for full conditionals: acceptance sampling.
Mon, Mar 25:	Sampling schemes for full conditionals: ratio of uniforms.
Wedn, Mar 27:	Adaptive rejection sampling & BUGS
Mon, Apr 1:	MCMC diagnostics; Raftery & Lewis, Gelman and Rubin.
Wedn, Apr 3:	MCMC diagnostics; digression on web resources and BOA/CODA.
Mon, Apr 8:	Latent/auxiliary variables.
Wedn, Apr 10:	Output analysis: Rao-Blackwellization, importance sampling reweighting.
Mon, Apr 15:	Reversible jump & model selection/averaging computations
Wedn, April 17:	Model selection/averaging computations, cont'd.

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