PHY2603H F specialized: Inverse Theory
|Course Title||PHY2603H F specialized|
|Year of Study||1st year|
|Time and Location||
Time and Room: TBA
Organization Meeting: Monday, Sept 9th, 2-3pm in MP505
Evolving from year to year, but addressing the problems of fitting physical models (both discreet and continuous) to data, and roughly comprising:
* What is inverse theory in physics and geophysics? When do data-consistent models even exist?
* Multivariate regression modelling of discrete models, Bayesian approaches, maximum likelihood estimation, with errors and
* hypothesis testing, both classical and resampling(e.g. bootstrap).
* Continuous models where spatial resolution is a meaningful concept (Backus-Gilbert theory).
* The Singular Value Decomposition approach to modelling.
* Answerable and unanswerable questions in modelling:
* Singular Value Decompositions, exotic norms such as L-1, L-infinity.
* Methods for non-linear modelling: e.g. Markov Chain Monte Carlo
(MCMC), simulated annealing, genetic algorithms.
|Prerequisite:||Recommended: PHY308/408S & this course uses MATLAB as its programming language, and expects some knowledge on complex analysis.|
No official text. Online notes will be made available as we cover the material. Other useful (but strongly overlapping) references might be:
1. Any book on multivariate regression methods in statistics;
2. Bill Menke's book on Inverse Theory;
3. Bob Parker's book on Inverse Theory;
4. Tarantola's book on Inverse Theory;
5. John Scale's web text on Inverse Theory;
6. Most importantly (for purposes of defining the syllabus), whatever I tell you in class.