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SUMMARY:Bayesian inference in infinite dimensions - Aad van der Vaart (Del
 ft)
DTSTART:20230504T160000Z
DTEND:20230504T170000Z
UID:TALK184304@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:The Bayesian statistical method consists of updating a prior p
 robability distribution\nover the unknown parameters of a stochastic syste
 m into a posterior probability distribution \nafter seeing the system's ou
 tput. It is perhaps the oldest statistical paradigm\, going\nback to the 1
 8th century\, in abstract terms as straightforward and elegant as can be\,
  and \nwith the promise of not only giving a best guess of the system para
 meters\, but also a\nquantification of remaining uncertainty. Only in the 
 last two decades has the method\nbeen applied to infinite-dimensional para
 meters\, most recently to inverse problems\ndefined e.g. by PDEs or in mac
 hine learning. We discuss some of the mathematical\nissues\, with a main f
 ocus on the question whether the method works and when\, and\nhow we can d
 efine "works". We review some classical success stories and recent \nfindi
 ngs and open questions\, borrowing from our own work and that of others.\n
 \nThe talk will be followed by a wine reception in the Central Core CMS\n
LOCATION:MR2\, CMS
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