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SUMMARY:Optimisation methods for Bayesian inference: Application to high d
 imensional inverse problems - Audrey Repetti\, Heriot-Watt University
DTSTART:20180601T130000Z
DTEND:20180601T140000Z
UID:TALK95446@talks.cam.ac.uk
CONTACT:Rachel Furner
DESCRIPTION:An important number of scientific and technological applicatio
 ns (ranging from healthcare to astronomy) consist in solving high dimensio
 nal inverse problems\, where an unknown object is estimated from the provi
 ded measurements.  A common method to solve these problems is to rely on a
  Bayesian maximum a posteriori (MAP) approach. A main limitation of this a
 pproach is that it does not provide any information regarding the uncertai
 nty in the solution delivered. This analysis is particularly important in 
 imaging problems that are ill-posed or ill-conditioned\, for subsequent de
 cision making processes (e.g. decision concerning a tumor appearing on a b
 rain image from MRI). \nIn this presentation I will present a methodology 
 to probe the data and perform uncertainty quantification. In the proposed 
 method\, we quantify the uncertainty associated with particular structures
  appearing in the MAP estimate\, obtained from a log-concave Bayesian mode
 l.  A hypothesis test is defined\, where the null hypothesis represents th
 e non-existence of the structure of interest in the true image. To determi
 ne if this null hypothesis is rejected\, we use the data and prior knowled
 ge. Computing such test in the context of imaging problem is often intract
 able for state-of-the-art Markov chain Monte Carlo algorithms\, due to the
  high dimensionality involved. In this work\, we formulate the Bayesian hy
 pothesis test as a convex minimization problem\, which is subsequently sol
 ved using a proximal primal-dual algorithm. The proposed method is applied
  to astronomical and medical imaging.\n\nJoint work with Marcelo Pereyra a
 nd Yves Wiaux
LOCATION:MR11\, Centre for Mathematical Sciences
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