Content:
Gaussian measures on infinite-dimensional spaces.
Chaining arguments.
Non-Gaussian measures.
Introduction to Bayesian inversion.
Priors as random functions.
Posterior distribution.
Well-Posedness and approximation of the posterior.
Posterior-preserving stochastic dynamics (SPDEs and MCMC).

Books:
Preliminary reading comprises:
Martin’s lectures on SPDEs, which may be found at:
http://arxiv.org/abs/0907.4178. (See, in particular, Chap­ters 3 and 4);
Andrew’s lectures on Inverse Problems, which may be found at:
http://arxiv.org/abs/1302.6989.