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PHY2603H1: Inverse Theory

This course addresses problems of fitting physical models (both discreet and continuous) to data, and covers topics such as

* 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.