BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Bayesian inference of a non-local proliferation model - Zuzanna Sz
 ymańska (University of Warsaw)
DTSTART:20230911T151500Z
DTEND:20230911T160000Z
UID:TALK203350@talks.cam.ac.uk
DESCRIPTION:Joint work with Jakub Skrzeczkowski\, Błażej Miasojedow and 
 Piotr Gwiazda.\nWe present a new proliferation model of cells living withi
 n a colony\, that is a non-local equation with a discontinuous interaction
  kernel. We discuss the range of applicability of the model\, select suita
 ble data and apply the Bayesian method to perform parameter estimation. We
  discuss proof of the problem's well-posedness and investigate the converg
 ence of the EBT algorithm applied to solve the equation. The main difficul
 ty lies in the kernel's low regularity\, which is not Lipschitz continuous
 \, thus preventing the application of standard arguments. Therefore\, we u
 se the radial symmetry of the problem instead and transform it using spher
 ical coordinates. The resulting equation has a Lipschitz kernel with only 
 one singularity at zero. We introduce a new weighted flat norm and prove t
 hat the particle method converges in this norm. We prove the problem's wel
 l-posedness and investigate the convergence of the EBT algorithm applied t
 o solve the equation. Finally\, we prove the stability of posterior distri
 butions in the total variation norm which exploits the theory of spaces of
  measures equipped with the weighted flat norm.\nReferences[1] Szymańska\
 , Z.\, Skrzeczkowski\, J.\, Miasojedow\, B.\, Gwiazda\, P. "Bayesian&nbsp\
 ;inference&nbsp\;of a non-local proliferation model"\, R. Soc. Open Sci. 8
 (11)\, 211279\, 2021\;[2] Gwiazda\, P.\, Miasojedow\, B.\, Skrzeczkowski\,
  J.\, Szymańska\, Z.\, "Convergence of the EBT method for a non-local mod
 el of cell proliferation with discontinuous interaction kernel"\, IMA J. N
 umer. Anal. 43(1)\, 590-626\, 2023\;
LOCATION:Seminar Room 1\, Newton Institute
END:VEVENT
END:VCALENDAR