# PHY2603H F specialized: Inverse Theory

Course Title | PHY2603H F specialized |
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Session | fall |

Year of Study | 1st year |

Time and Location |
Time: MW 11 Location: MP505 |

Qinya
Liu |

#### 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. |
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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. |