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SUMMARY:Stochastic Epidemic Models with Partial Information: Optimal Contr
ol Problems
DTSTART;VALUE=DATE-TIME:20220805T080000Z
DTEND;VALUE=DATE-TIME:20220805T082000Z
DTSTAMP;VALUE=DATE-TIME:20231210T045843Z
UID:indico-contribution-206-1230@conference2.aau.at
DESCRIPTION:This presentation is based on and continues the companion talk
of Florent Ouabo Kamkumo. We consider stochastic optimal control problems
arising in the mathematical modeling of decision-making processes in the
cost-optimal management and containment of epidemics. We focus on the impa
ct of uncertainties such as dark figures which have been addressed in the
companion talk and can be treated as optimal control problems under partia
l information. Working with the diffusion approximations for the populatio
n dynamics and the associated Kalman filter estimates of non-observable st
ate variables leads to \n control problems for controlled diffusion proce
sses.\n This is joint work with Ralf Wunderlich\n\nhttps://conference2.aa
u.at/event/131/contributions/1230/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1230/
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SUMMARY:Stochastic Epidemic Models with Partial Information : Dark Figure
and Parameters Estimation
DTSTART;VALUE=DATE-TIME:20220805T073000Z
DTEND;VALUE=DATE-TIME:20220805T075000Z
DTSTAMP;VALUE=DATE-TIME:20231210T045843Z
UID:indico-contribution-206-1232@conference2.aau.at
DESCRIPTION:Mathematical models of epidemics such as the current COVID-19
pandemics often use compartmental models dividing the population into seve
ral compartments. Based on a microscopic setting describing the temporal e
volution of the subpopulation sizes in the compartments by stochastic coun
ting processes one can derive macroscopic models for large populations des
cribing the average behavior by associated ODEs such as the celebrated SIR
model. Further\, diffusion approximations allow to address fluctuations f
rom the average and to describe the state dynamics also for smaller popula
tions by stochastic differential equations (SDE).\nUsually not all of the
state variables are directly observable and we are facing the so-called
“dark figure” problem addressing for example the unknown number of asy
mptomatic and non-detected infections. Such not directly observable states
are problematic if it comes to the computation of characteristics of the
epidemic such as the effective reproduction rate and the prevalence of the
infection within the population. Further\, the management and containment
of epidemics relying on solutions of (stochastic) optimal control problem
s and the associated feedback controls need observations of the current st
ate as input.\nThe estimation of unobservable states based on records of t
he observable states leads to a non-standard filtering problem for observa
ble stochastic models. We adopt the extended Kalman filter approach coping
with non-linearities in the state dynamics and the state-dependent diffus
ion coefficients in the SDEs. This allows to develop approximative solutio
ns to that filtering problem.\nThe proposed model depends on a variety of
parameters that can be time-dependent and have been calibrated to real-wor
ld data for COVID-19. There\, we apply maximum-likelihood and Kalman filte
r methods. We illustrate our theoretical finding by numerical results.\n\n
https://conference2.aau.at/event/131/contributions/1232/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1232/
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SUMMARY:Adaptive MCMC for doubly intractable distributions
DTSTART;VALUE=DATE-TIME:20220805T070000Z
DTEND;VALUE=DATE-TIME:20220805T072000Z
DTSTAMP;VALUE=DATE-TIME:20231210T045843Z
UID:indico-contribution-206-1229@conference2.aau.at
DESCRIPTION:Bayesian inference in the context of biophysical problems may
lead to posterior densities with two unknown quantities\, the normalizing
constant and \nan intractable multiplicative factor in the likelihood func
tion. \nNot being able to evaluate the likelihood function leads to comput
ational issues in classical (adaptive) MCMC algorithms and in the past yea
rs various methods have been suggested to overcome this problem. \nWe disc
uss an adaptive MCMC scheme that relies on approximating the likelihood fu
nction and\, \nmoreover\, we present a strong law of large numbers for mou
nded measurable functions.\n\nhttps://conference2.aau.at/event/131/contrib
utions/1229/
LOCATION: Universität Klagenfurt HS 4
URL:https://conference2.aau.at/event/131/contributions/1229/
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