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UID:news1785@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20250417T144636
DTSTART;TZID=Europe/Zurich:20250425T110000
SUMMARY:Seminar in Numerical Analysis: Björn Sprungk (TU Freiberg) 
DESCRIPTION:In this talk we consider the Bayesian approach to inverse probl
 ems which allows for uncertainty quantification for the data-driven recons
 truction of the ground truth. After a brief dicussion of the well-posednes
 s and local Lipschitz stability of Bayesian inverse problems\, we focus on
  Markov chain Monte Carlo methods for sampling and integration with respec
 t to the posterior probability distribution. Here we present our contribut
 ions to Metropolis-Hastings algorithms in function spaces\, discuss conve
 rgence in terms of geometric ergodicity and present numerical experiments 
 which show a dimension-indepedent performance which is\, moreover\, robust
  to the level of observational noise in the data. In the last part of the 
 talk we present recent results of combining Metropolis-Hastings with inter
 acting particle sampling methods based on Euler-Maruyama discretizations o
 f stochastic differential equations of McKean-Vlasov type.\\r\\n\\r\\nFor 
 further information about the seminar\, please visit this webpage [t3://pa
 ge?uid=1115].
X-ALT-DESC:<p>In this talk we consider the Bayesian approach to inverse pro
 blems which allows for uncertainty quantification for the data-driven reco
 nstruction of the ground truth. After a brief dicussion of the well-posedn
 ess and local Lipschitz stability of Bayesian inverse problems\, we focus 
 on Markov chain Monte Carlo methods for sampling and integration with resp
 ect to the posterior probability distribution. Here we present our contrib
 utions to Metropolis-Hastings algorithms in function spaces\, discuss&nbsp
 \;convergence in terms of geometric ergodicity and present numerical exper
 iments which show a dimension-indepedent performance which is\, moreover\,
  robust to the level of observational noise in the data. In the last part 
 of the talk we present recent results of combining Metropolis-Hastings wit
 h interacting particle sampling methods based on Euler-Maruyama discretiza
 tions of stochastic differential equations of McKean-Vlasov type.</p>\n\n<
 p>For further information about the seminar\, please visit this <a href="t
 3://page?uid=1115" title="Opens internal link in current window">webpage</
 a>.</p>
DTEND;TZID=Europe/Zurich:20250425T123000
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