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.