| Abstract: |
| This talk will concern new algorithms for solving Bayesian inverse problems; in particular multilevel sequential Monte Carlo (SMC) samplers. Even when the underlying forward PDE model is linear for a fixed value of the parameter, the map from parameter to observation is often nonlinear. One cannot sample from the posterior distribution directly, but can only evaluate it, up to a normalizing constant. Therfore one must resort to computationally-intensive inference algorithms in order to construct estimators. Another difficulty which arises is that the PDE typically cannot be solved and needs to be approximated at finite resolution. The multilevel Monte Carlo method provides a way of optimally balancing discretization and sampling error on a hierarchy of approximation levels, such that cost is optimized. Recently this has been applied to computationally intensive inference. The resulting multilevel SMC samplers will be presented. |
|