• Introduction Forward and Inverse problem, What is an inverse
problem?, Interpretation of inaccurate, insufficient and inconsistent data,
Examples – Geophysics, Reservoir Engineering, Medicine etc

• Statistics – Review Definition of Probability – fequentist vs Bayesian,
Probability density functions, Bayes Theorem, Markov chain, Importance
sampling, stationary distribution

• Classical Inverse Theory Existence, stability, uniqueness, Underdetermined, Over-determined and mixed determined problems, Least
squares and maximum likelihood, Data and Model Norm, Langrange
multipliers, Statistical description, Likelihood, Prior and posterior; Cd and
Cm, MAP estimation, Linear, Quasi-linear, and non-linear problems

• Local Optimization Line search – golden section search, Steepest
descent, Newton’s method, Conjugate gradients, Gauss-Newton and
Quasi-Newton Methods, Simplex

• Regularization Motivation and examples, Tikhonov regularization,
Estimation of regularization weights: L curve, GCV, Bayesian,
Discrepancy principle

• Global Optimization and uncertainty estimation MCMC,
Metropolis/Gibbs’ sampler ,Simulated Annealing, Genetic Algorithms.

• Miscellaneous topics: Computation of sensitivities: finite differences,
analytic methods, adjoint state approach, Migration as least squares