First day handout

The course will cover Markov chain Monte Carlo methods and their use
in inverse problems.  We
will consider theoretical foundations of the methods as well
as their applications to porous media flows. Multiscale aspects
of the flow will be explored.
This is an advanced interdisciplinary course and the instructor's
permission is required.
Course outline: Brief introduction to Monte Carlo methods, Markov chains
(ergodicity, invariant measures) and Bayesian statistics. Markov Fields.
Markov chain Monte Carlo methodology.
Metropolis-Hasting algorithm and Gibbs sampler. Various Metropolis-Hasting
algorithms. Convergence properties. Application of Markov chain Monte
Carlo methods to porous media flows. Brief introduction to porous
media flow equations and simulation techniques used for porous media
flows. The formulation of inverse problems and some existing
inverse methods.
Markov chain Monte Carlo methods vs. traditional
inversion techniques. Multiscale aspects of the problem and  the linking
of the scales via Markov chain Monte Carlo methods. Multiscale methods
and their use in inverse problems.


TEXTBOOK:  No textbook is required. I will distribute handouts.

PROCEDURE FOR CALCULATING GRADES.   Grades will be computed based on homework and project scores. There will be no  exams.
Homework and projects will be posted on the web.

INCOMPLETES: I will consider giving you an incomplete if you have successfully completed all but a small portion of the work of the
course and some severe, unexpected event prevents you from completing the course. This means that you must have taken at least 1 exam and quiz
and must be doing work at the C level or better. You will have to sign a contract detailing what you have to do to complete the course.
I cannot give you an incomplete simply because you are behind in your work; in the latter case you should try to drop the course.

S/U GRADE: If you are registered S/U we will submit a grade of S if your letter grade is C or above, and otherwise a grade of U.

Scholastic Dishonesty: Students may work together and discuss the homework problems with each other. Copying work done by others is an act of scholastic dishonesty and will be prosecuted to the full extent allowed by University policy. For more information on university policies regarding scholastic dishonesty, see University Student  Rules and the Aggie Honor Code: "An Aggie does not lie, cheat, or steal or tolerate those who do." For more information see the Honor Council Rules and Procedures on the web at

Students with Disabilities: The Americans with Disabilities Act (ADA) is a federal anti-discrimination statute that provides comprehensive civil rights protection for persons with disabilities. Among other things, this legislation requires that all students with disabilities be guaranteed a learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an accommodation, please contact Services for Students with Disabilities, Koldus 126, 845-1637.

POLICIES AND OTHER INFORMATION:  /teaching/operationspg.html