12.S990 | Fall 2012 | Undergraduate, Graduate

Quantifying Uncertainty


Course Meeting Times

Lectures: 1 session / week, 2 hours / session


Permission of instructor.


  • 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


  • 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.

Buy at MIT Press 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.

Double Pendulum.


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