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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Bayesian optimal design for ordinary differential
equation models with application in biological sci
ence - David Woods (University of Southampton)
DTSTART;TZID=Europe/London:20180328T110000
DTEND;TZID=Europe/London:20180328T130000
UID:TALK107539AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/107539
DESCRIPTION:Bayesian optimal design is considered for experime
nts where the response distribution depends on the
solution to a system of non-linear ordinary diffe
rential equations. The motivation is an experiment
to estimate parameters in the equations governing
the transport of amino acids through cell membran
es in human placentas. Decision-theoretic Bayesian
design of experiments for such nonlinear models i
s conceptually very attractive\, allowing the form
al incorporation of prior knowledge to overcome th
e parameter dependence of frequentist design and b
eing less reliant on asymptotic approximations. Ho
wever\, the necessary approximation and maximizati
on of the\, typically analytically intractable\, e
xpected utility results in a computationally chall
enging problem. These issues are further exacerbat
ed if the solution to the differential equations i
s not available in closed-form. This paper propose
s a new combination of a probabilistic solution to
the equations embedded within a Monte Carlo appro
ximation to the expected utility with cyclic desce
nt of a smooth approximation to find the optimal d
esign. A novel precomputation algorithm reduces th
e computational burden\, making the search for an
optimal design feasible for bigger problems. The m
ethods are demonstrated by finding new designs for
a number of common models derived from differenti
al equations\, and by providing optimal designs fo
r the placenta experiment.

Joint work with
Antony Overstall and Ben Parker (University of So
uthampton)
LOCATION:Seminar Room 2\, Newton Institute
CONTACT:INI IT
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