### Course Meeting Times

Lectures: 1 session / week, 2 hours / session

### Prerequisites

Permission of instructor.

### Objectives

- To understand the methods by which we can represent, propagate and infer uncertainty.
- To explore “interdisciplinary” application.
- To build an intellectual community around uncertainty quantification.

### Topics Covered

The specific topics vary between offerings, but are generally drawn from the following:

- Density Estimation: Exponential Family, Mixture Models, Kernels, Markov Chain Monte Carlo
- Model Selection: Jacknife, Bootstrap, Cross-validation and Information Criteria
- Dimensionality Reduction: PCA, ICA, and other nonlinear modes
- Model Reduction: POD / EOF, Krylov, Response Surface Models, Polynomial Chaos
- Inference: Hierarchical Bayes, Graphical Models
- Time-dependent Inference: Linear, Ensemble, Mixture, Kernel, Mutual Information, and Particle Filtering and Smoothing
- Statistical Models: Regression Machines, Gaussian Processes, Markov Models
- Manifold Learning
- Information Theoretic Estimation, Control and Learning

### Expectations

- Attend class.
- Read the assigned papers/readings.
- Every participant “recites” a paper.
- Do a project.
- Use a method studied here in your application.
- Develop a new method for applications studied here.
- Write a review paper in a subject area.

### General References

Bryson, Jr. Arthur E. and Yu-Chi Ho. *Applied Optimal Control: Optimization, Estimation and Control*. Taylor & Francis, 1975. ISBN: 9780891162285.

Gelb, Arthur. *Applied Optimal Estimation*. MIT Press, 1974. ISBN: 9780262570480.

Gelman, A., J. Carlin, et al. *Bayesian Data Analysis*. Chapman and Hall, 2003. ISBN: 9781584883883.

Martinez, W. L., and A. R. Martinez. *Computational Statistics Handbook with MATLAB*. 2nd ed. Chapman and Hall/CRC, 2007. ISBN: 978158488566. [Preview with Google Books]

Papoulis, A. *Probability, Random Variables & Stochastic Processes*. McGraw-Hill, 2002. ISBN: 9780071226615.

Silverman, B. W. *Density Estimation for Statistics and Data Analysis*. Chapman and Hall/CRC, 1986. ISBN: 9780412246203.

### Grading

The course grade is based upon paper explanation, project, and class participation.