Kody Law (King Abdullah University): Dimension-independent likelihood-informed MCMC samplers

Many Bayesian inference problems require exploring
the posterior distribution of high-dimensional parameters,
which in principle can be described as functions.
Formulating algorithms which are defined on function space
yields dimension-independent algorithms.
By exploiting the intrinsic low dimensionality of the
likelihood function, we introduce a newly developed suite
of proposals for the Metropolis Hastings MCMC algorithm
that can adapt to the complex structure of the posterior
distribution, yet are defined on function space. I will
present numerical examples indicating the efficiency of
these dimension-independent likelihood-informed samplers.
I will also present some applications of function-space
samplers to problems relevant to numerical weather prediction and subsurface reconstruction.