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SUMMARY:Bayesian optimal design for ordinary differential equation models 
 with application in biological science - David Woods (University of Southa
 mpton)
DTSTART:20180328T100000Z
DTEND:20180328T120000Z
UID:TALK107539@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:Bayesian optimal design is considered for experiments where th
 e response distribution depends on the solution to a system of non-linear 
 ordinary differential equations. The motivation is an experiment to estima
 te parameters in the equations governing the transport of amino acids thro
 ugh cell membranes in human placentas. Decision-theoretic Bayesian design 
 of experiments for such nonlinear models is conceptually very attractive\,
  allowing the formal incorporation of prior knowledge to overcome the para
 meter dependence of frequentist design and being less reliant on asymptoti
 c approximations. However\, the necessary approximation and maximization o
 f the\, typically analytically intractable\, expected utility results in a
  computationally challenging problem. These issues are further exacerbated
  if the solution to the differential equations is not available in closed-
 form. This paper proposes a new combination of a probabilistic solution to
  the equations embedded within a Monte Carlo approximation to the expected
  utility with cyclic descent of a smooth approximation to find the optimal
  design. A novel precomputation algorithm reduces the computational burden
 \, making the search for an optimal design feasible for bigger problems. T
 he methods are demonstrated by finding new designs for a number of common 
 models derived from differential equations\, and by providing optimal desi
 gns for the placenta experiment. <br><br>Joint work with Antony Overstall 
 and Ben Parker (University of Southampton)
LOCATION:Seminar Room 2\, Newton Institute
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