BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Geometric MCMC for infinite-dimensional Bayesian Inverse Problems 
 - Alexandros Beskos\, University College London 
DTSTART:20190125T160000Z
DTEND:20190125T170000Z
UID:TALK115909@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:Bayesian inverse problems often involve sampling posterior dis
 tributions on infinite-dimensional function spaces. Traditional Markov cha
 in Monte Carlo (MCMC) algorithms are characterized by deteriorating mixing
  times upon mesh-refinement\, when the finite-dimensional approximations b
 ecome more accurate. Such methods are typically forced to reduce step-size
 s 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 th
 e geometry of the posterior informed by the data. At the same time\, recen
 tly developed geometric MCMC algorithms have been found to be powerful in 
 exploring complicated distributions that deviate significantly from ellipt
 ic Gaussian laws\, but are in general computationally intractable for mode
 ls defined in infinite dimensions. In this work\, we combine geometric met
 hods on a finite-dimensional subspace with mesh-independent infinite-dimen
 sional approaches. Our objective is to speed up MCMC mixing times\, withou
 t significantly increasing the computational cost per step (for instance\,
  in comparison with the vanilla preconditioned Crank–Nicolson (pCN) meth
 od). This is achieved by using ideas from geometric MCMC to probe the comp
 lex structure of an intrinsic finite-dimensional subspace where most data 
 information concentrates\, while retaining robust mixing times as the dime
 nsion grows by using pCN-like methods in the complementary subspace. The r
 esulting algorithms are demonstrated in the context of three challenging i
 nverse problems arising in subsurface flow\, heat conduction and incompres
 sible flow control. The algorithms exhibit up to two orders of magnitude i
 mprovement in sampling efficiency when compared with the pCN method.
LOCATION:MR12
END:VEVENT
END:VCALENDAR