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PHY2603H F specializedInverse Theory

Course Title PHY2603H F specialized
Session fall
Year of Study 1st year
Time and Location Time: MW 11
Location: MP505

Qinya  Liu
MP504A
416-978-5434

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Official Description

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.
Textbook 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.