COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Signal Processing and Communications Lab Seminars > Geometric MCMC for infinite-dimensional inverse problems

## Geometric MCMC for infinite-dimensional inverse problemsAdd to your list(s) Download to your calendar using vCal - Dr Alexandros Beskos, UCL
- Thursday 26 April 2018, 15:00-16:00
- LT6, Baker Building, CUED.
If you have a question about this talk, please contact Dr Ramji Venkataramanan. Bayesian inverse problems often involve sampling posterior distributions on infinite-dimensional function spaces. Traditional Markov chain Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing times upon mesh-refinement, when the finite-dimensional approximations become more accurate. Such methods are typically forced to reduce step-sizes as the discretization gets finer, and thus are expensive as a function of dimension. Recently, a new class of MCMC methods with mesh-independent convergence times has emerged. However, few of them take into account the geometry of the posterior informed by the data. At the same time, recently developed geometric MCMC algorithms have been found to be powerful in exploring complicated distributions that deviate significantly from elliptic Gaussian laws, but are in general computationally intractable for models defined in infinite dimensions. In this work, we combine geometric methods on a finite-dimensional subspace with mesh-independent infinite-dimensional approaches. Our objective is to speed up MCMC mixing times, without significantly increasing the computational cost per step (for instance, in comparison with the vanilla preconditioned CrankâNicolson (pCN) method). This is achieved by using ideas from geometric MCMC to probe the complex structure of an intrinsic finite-dimensional subspace where most data information concentrates, while retaining robust mixing times as the dimension grows by using pCN-like methods in the complementary subspace. The resulting algorithms are demonstrated in the context of three challenging inverse problems arising in subsurface flow, heat conduction and incompressible flow control. The algorithms exhibit up to two orders of magnitude improvement in sampling efficiency when compared with the pCN method. This talk is part of the Signal Processing and Communications Lab Seminars series. ## This talk is included in these lists:- All Talks (aka the CURE list)
- Cambridge Big Data
- Cambridge University Engineering Department Talks
- Centre for Smart Infrastructure & Construction
- Featured lists
- Information Engineering Division seminar list
- LT6, Baker Building, CUED
- School of Technology
- Signal Processing and Communications Lab Seminars
- ndk22's list
- rp587
Note that ex-directory lists are not shown. |
## Other listsCUUEG talks The obesity epidemic: Discussing the global health crisis "Investigating Interactions" Symposium## Other talksNovel kinases controlling T cell development, trafficking and immune responses My Life in Science Seminar NatHistFest: the 99th Conversazione and exhibition on the wonders of the natural world. Bradford Hill Seminar with Professor Andrew Morris - Title TBC Colour and Vision HE@Cam Seminar: Tray Brown - Building a Discrete Event Simulation to Determine the Cost-Effectiveness of Treatments for Systemic Lupus Erythematosus |